Results 1 to 10 of about 12,646 (309)
Enabling quaternion derivatives: the generalized HR calculus [PDF]
Royal Society Open Science, 2015 Quaternion derivatives exist only for a very restricted class of analytic (regular) functions; however, in many applications, functions of interest are real-valued and hence not analytic, a typical case being the standard real mean square error objective
Dongpo Xu +2 more
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Principal Component Analysis Based Quaternion-Valued Medians for Non-Invasive Blood Glucose Estimation [PDF]
SensorsFor four-channel photoplethysmograms (PPGs), this paper employs quaternion-valued medians as features for performing non-invasive blood glucose estimation.
Jingheng Feng, Bingo Wing-Kuen Ling
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The quaternion-type cyclic-Fibonacci sequences in groups [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 In this paper, we define the six different quaternion-type cyclic-Fibonacci sequences and present some properties, such as, the Cassini formula and generating function. Then, we study quaternion-type cyclic-Fibonacci sequences modulo m.
Nazmiye Yilmaz +2 more
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Some Essential Relations for the Quaternion Quadratic-Phase Fourier Transform
Mathematics, 2023 Motivated by the fact that the quaternion Fourier transform is a powerful tool in quaternion signal analysis, here, we study the quaternion quadratic-phase Fourier transform, which is a generalized version of the quaternion Fourier transform.
Mawardi Bahri +1 more
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Characteristic of Quaternion Algebra Over Fields
Cauchy: Jurnal Matematika Murni dan Aplikasi, 2023 Quaternion is an extension of the complex number system. Quaternion are discovered by formulating 4 points in 4-dimensional vector space using the cross product between two standard vectors. Quaternion algebra over a field is a 4-dimensional vector space
Muhammad Faldiyan +2 more
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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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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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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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Quaternion Electromagnetism and the Relation with Two-Spinor Formalism
Universe, 2019 By using complex quaternion, which is the system of quaternion representation extended to complex numbers, we show that the laws of electromagnetism can be expressed much more simply and concisely.
In Ki Hong, Choong Sun Kim
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Machines, 2022 This study derives a learning algorithm for a quaternion neural network using the steepest descent method extended to quaternion numbers. This applies the generalised Hamiltonian–Real calculus to obtain derivatives of a real–valued cost function ...
Kazuhiko Takahashi +2 more
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