Results 21 to 30 of about 13,019 (252)
A quaternionic Nullstellensatz [PDF]
Journal of Pure and Applied Algebra, 2021 We prove a Nullstellensatz for the ring of polynomial functions in n non-commuting variables over Hamilton's ring of real quaternions. We also characterize the generalized polynomial identities in n variables which hold over the quaternions, and more generally, over any division algebra.
Alon, Gil, Paran, Elad
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RSVD for Three Quaternion Tensors with Applications in Color Video Watermark Processing
Axioms, 2023 In this paper, we study the restricted singular-value decomposition (RSVD) for three quaternion tensors under the Einstein product, and give higher-order RSVD over the quaternion algebra, which can achieve simultaneous singular value decomposition of ...
Wen-Juan Chen, Shao-Wen Yu
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Quaternions: A Mathematica Package for Quaternionic Analysis [PDF]
, 2011 This paper describes new issues of theMathematica standard package Quaternions for implementing Hamilton's Quaternion Algebra. This work attempts to endow the original package with the ability to perform operations on symbolic expressions involving quaternion-valued functions.
M. Irene Falcão, Fernando Miranda
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An investigation into the accuracy of calculating upper body joint angles using MARG sensors [PDF]
, 2014 We investigate magnetic, angular rate, and gravity (MARG) sensor modules for deriving shoulder, elbow and lumbar joint angles of the human body. We use three tri-axial MARG sensors, placed proximal to the wrist and elbow and centrally on the chest, and ...
Cranny, A +9 more
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Quaternion Filtering Based on Quaternion Involutions and its Application in Signal Processing
IEEE Access, 2019 The quaternion gradient plays an important role in quaternion signal processing, and has undergone several modifications. Recently, three methods for obtaining the quaternion gradient have been proposed based on generalized HR calculus, the quaternion ...
Gang Wang, Rui Xue
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, 2023 Based on the framework of differential inclusion, we design a quaternion-valued neural network (QVNN) to solve a class of nonsmooth nonconvex optimization problems with equality, bounded and inequality constraints in quaternion domain.
Liu, J, Liao, X, Dong, JS
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On Pell Quaternions and Pell-Lucas Quaternions
Advances in Applied Clifford Algebras, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Cimen, Cennet Bolat, Ipek, Ahmet
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Sensors, 2017 Initial alignment of the strapdown inertial navigation system (SINS) is intended to determine the initial attitude matrix in a short time with certain accuracy.
Tao Zhang +4 more
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On balancing quaternions and Lucas-balancing quaternions
Discussiones Mathematicae - General Algebra and Applications, 2021 In this paper we define and study balancing quaternions and Lucas-balancing quaternions. We give the generating functions, matrix generators and Binet formulas for these numbers. Moreover, the well-known properties e.g. Catalan, d’ Ocagne identities have been obtained for these quaternions.
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International Journal of Pure and Apllied Mathematics, 2014 Physics is in its development a major challenge to relate fields, this paper presents a proposal to relate classical fields of physics, ie the electric field, magnetic field and gravitational equations by time-dependent. The proposal begins with the work that determines the Cauchy-Riemann conditions for quaternions [1], and the determination of Laplace’
Marão, José Antonio Pires +1 more
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