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Quaternion and Split Quaternion Neural Networks for Low-Light Color Image Enhancement
IEEE Access, 2023 In this study, two models of multilayer quaternionic feedforward neural networks are presented. Whereas the first model is based on quaternion algebra, the second model uses split quaternion algebra.
Eduardo Jesus De Davila-Meza +1 more
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Dynamics of Mobile Manipulators using Dual Quaternion Algebra [PDF]
Journal of Mechanisms and Robotics, 2020 This paper presents two approaches to obtain the dynamical equations of mobile manipulators using dual quaternion algebra. The first one is based on a general recursive Newton-Euler formulation and uses twists and wrenches, which are propagated through
F. F. A. Silva +2 more
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Partial Differential Equations in Applied Mathematics, 2023 This paper is devoted to the study of the quaternion Laplace transform, which is a natural generalization of the classical Laplace transform using the quaternion algebra. We find that some of its properties such as derivative, convolution and correlation
Muhammad Afdal Bau +4 more
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Existence of Split Property in Quaternion Algebra Over Composite of Quadratic Fields
Cauchy: Jurnal Matematika Murni dan Aplikasi, 2023 Quaternions are extensions of complex numbers that are four-dimensional objects. Quaternion consists of one real number and three complex numbers, commonly denoted by the standard vectors and .
Muhammad Faldiyan +2 more
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RKHS Representations for Augmented Quaternion Random Signals: Application to Detection Problems
Mathematics, 2022 The reproducing kernel Hilbert space (RKHS) methodology has shown to be a suitable tool for the resolution of a wide range of problems in statistical signal processing both in the real and complex domains.
Antonia Oya
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International Journal of Advanced Robotic Systems, 2011 In this paper, we compare three inverse kinematic formulation methods for the serial industrial robot manipulators. All formulation methods are based on screw theory.
Emre Sariyildiz +2 more
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Wiener Algebra for the Quaternions [PDF]
Mediterranean Journal of Mathematics, 2015 We define and study the counterpart of the Wiener algebra in the quaternionic setting, both for the discrete and continuous case. We prove a Wiener-Lévy type theorem and a factorization theorem. We give applications to Toeplitz and Wiener-Hopf operators.
Alpay, Daniel +3 more
openaire +3 more sources
Pose estimation using linearized rotations and quaternion algebra
Acta Astronautica, 2011 Timothy D Barfoot +2 more
exaly +2 more sources
Algebraic Techniques for Canonical Forms and Applications in Split Quaternionic Mechanics
Journal of Mathematics, 2023 The algebra of split quaternions is a recently increasing topic in the study of theory and numerical computation in split quaternionic mechanics. This paper, by means of a real representation of a split quaternion matrix, studies the problem of canonical
Tongsong Jiang +4 more
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Helmert Transformation Problem. From Euler Angles Method to Quaternion Algebra
ISPRS Int. J. Geo Inf., 2020 The three-dimensional coordinate’s transformation from one system to another, and more specifically, the Helmert transformation problem, is one of the most well-known transformations in the field of engineering.
S. Ioannidou, G. Pantazis
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