Results 11 to 20 of about 4,625 (266)

Principal Component Analysis Based Quaternion-Valued Medians for Non-Invasive Blood Glucose Estimation [PDF]

Sensors
For 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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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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Coarse Alignment Technology on Moving base for SINS Based on the Improved Quaternion Filter Algorithm

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, Yongyun Zhu, Feng Zhou, Yaxiong Yan, Jinwu Tong   +4 more
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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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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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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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Feedforward–Feedback Controller Based on a Trained Quaternion Neural Network Using a Generalised $\mathbb{HR}$ Calculus with Application to Trajectory Control of a Three-Link Robot Manipulator

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, Eri Tano, Masafumi Hashimoto   +2 more
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Quaternions [PDF]

Science, 1896
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An Algebraic Relation between Consimilarity and Similarity of Quaternion Matrices and Applications

Journal of Applied Mathematics, 2014
This paper, by means of complex representation of a quaternion matrix, discusses the consimilarity of quaternion matrices, and obtains a relation between consimilarity and similarity of quaternion matrices.
Tongsong Jiang, Xuehan Cheng, Sitao Ling
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Quaternion-Type Catalan Transforms of the ρ-Fibonacci and ρ-Lucas Numbers

Journal of Mathematics, 2023
In this paper, we define a new sequence called the quaternion-type Catalan sequence and give generating function, exponential representation, quaternionic Catalan matrix and its some properties.
Kübra Gül
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