Results 41 to 50 of about 666,240 (259)
Roots of unity in definite quaternion orders
, 2014 A commutative order in a quaternion algebra is called selective if it is embeds into some, but not all, the maximal orders in the algebra. It is known that a given quadratic order over a number field can be selective in at most one indefinite quaternion ...
Arenas-Carmona, Luis
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Quaternion algebra for Stokes-Mueller formalism.
Journal of The Optical Society of America A-optics Image Science and Vision, 2019 In this paper, we show that the Stokes-Mueller formalism can be reformulated in terms of quaternions and that the quaternion algebra is a suitable alternative presentation of the formalism of Mueller-Jones states that we have recently described [J.
E. Kuntman +3 more
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, 2021 This open access textbook presents a comprehensive treatment of the arithmetic theory of quaternion algebras and orders, a subject with applications in diverse areas of mathematics. Written to be accessible and approachable to the graduate student reader, this text collects and synthesizes results from across the literature.
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Weighted Convolution for Quaternion Linear Canonical Cosine Transform and Its Application
AxiomsConvolution plays a pivotal role in the domains of signal processing and optics. This paper primarily focuses on studying the weighted convolution for quaternion linear canonical cosine transform (QLCcT) and its application in multiplicative filter ...
Rongbo Wang, Qiang Feng
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IEEE Access, 2021 For scenarios of coherent underwater sources at low signal-to-noise ratio (SNR), a novel quaternion-based DOA algorithm without eigendecomposition is proposed using a linear vector-hydrophone array.
Yi Lou +3 more
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Visualizing Quaternion Multiplication
IEEE Access, 2017 Quaternion rotation is a powerful tool for rotating vectors in 3-D; as a result, it has been used in various engineering fields, such as navigations, robotics, and computer graphics. However, understanding it geometrically remains challenging, because it
Jongchan Baek +3 more
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Modified Hand–Eye Calibration Using Dual Quaternions
Applied Sciences, 2022 This paper presents a modified model for hand–eye calibration based on dual quaternion algebra. By using dual quaternions to represent the rotations and translations of a rigid body simultaneously in the task space, the formulation is elegant for the ...
Guozhi Li +3 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-L vy type theorem and a factorization theorem. We give applications to Toeplitz and Wiener-Hopf operators.
Alpay, Daniel +3 more
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The 2-refined neutrosophic quaternions numbers [PDF]
Neutrosophic Sets and SystemsThis paper explores the concept of 2-refined neutrosophic quaternion numbers by first introducing their formal definition along with the notion of equality between two such numbers.
Iqbal Ahmed Musa +2 more
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Fractal and Fractional, 2023 Very recently, a different generalization of real-valued neural networks (RVNNs) to multidimensional domains beside the complex-valued neural networks (CVNNs), quaternion-valued neural networks (QVNNs), and Clifford-valued neural networks (ClVNNs) has ...
Călin-Adrian Popa
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