Extreme Points and Some Quaternion Valued Functions in the Unit Ball of $${\mathbb {R}}^3$$R3
Sign Up to like & getrecommendations! Published in 2018 at "Advances in Applied Clifford Algebras"
DOI: 10.1007/s00006-018-0848-9
Abstract: In this paper, we give a new definition of a class of quaternion function spaces, which will be called $$F(p,\alpha ,s;E)$$F(p,α,s;E)-type spaces. Then, we characterize quaternion $$\alpha $$α-Bloch functions by functions belonging to $$F(p,\alpha ,s;E)$$F(p,α,s;E)… read more here.
Keywords: quaternion; quaternion valued; points quaternion; unit ball ... See more keywords
Quaternion Ridgelet Transform and Curvelet Transform
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DOI: 10.1007/s00006-018-0897-0
Abstract: In this article, we study the quaternion ridgelet transform and curvelet transform associated to the quaternion Fourier transform (QFT). We prove some properties related to such transforms, including reconstruction formulas, reproducing kernels and uncertainty principles. read more here.
Keywords: quaternion; curvelet transform; quaternion ridgelet; transform curvelet ... See more keywords
Eigen-Decomposition of Quaternions
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DOI: 10.1007/s00006-018-0911-6
Abstract: This paper introduces biquaternion eigen-decomposition theory (via Peirce decomposition) with respect to a selected quaternion with a non-zero vector part. The eigen-decomposition allows evaluation of polynomials and power series with real coefficients as functions of… read more here.
Keywords: quaternion; selected quaternion; multiplication; matrix ... See more keywords
Elementary Transformation and its Applications for Split Quaternion Matrices
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DOI: 10.1007/s00006-019-1027-3
Abstract: In this paper, the elementary transformation is discussed for split quaternion matrices and the upper triangulation process is given. Then two new determinants are defined by means of real and complex representation matrices and the… read more here.
Keywords: quaternion; split quaternion; elementary transformation; transformation applications ... See more keywords
Uncertainty Principles for the Two-Sided Quaternion Linear Canonical Transform
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DOI: 10.1007/s00034-020-01376-z
Abstract: The quaternion linear canonical transform (QLCT), as a generalized form of the quaternion Fourier transform, is a powerful analyzing tool in image and signal processing. In this paper, we propose three different forms of uncertainty… read more here.
Keywords: quaternion; two sided; linear canonical; uncertainty ... See more keywords
Motion quaternion-based motion estimation method of MYO using K-means algorithm and Bayesian probability
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DOI: 10.1007/s00500-018-3379-3
Abstract: AbstractThere are diverse types of devices based on natural user interface/experience for humanized computing. One such device, the MYO allows the measurement of arm motions and uses them as an interface based on gestures. There… read more here.
Keywords: quaternion; bayesian probability; motion; motion estimation ... See more keywords
A survey of quaternion neural networks
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DOI: 10.1007/s10462-019-09752-1
Abstract: Quaternion neural networks have recently received an increasing interest due to noticeable improvements over real-valued neural networks on real world tasks such as image, speech and signal processing. The extension of quaternion numbers to neural… read more here.
Keywords: quaternion; quaternion neural; neural networks; survey quaternion ... See more keywords
Stability of Quaternion-Valued Neural Networks with Mixed Delays
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DOI: 10.1007/s11063-018-9849-x
Abstract: In this paper, we investigate the dynamic behaviors of quaternion-valued recurrent neural networks with mixed time delays. On the basis of Brouwer’s fixed point theorem, quaternion-valued variation parameter and quaternion-modulus inequality technique, some sufficient conditions… read more here.
Keywords: quaternion; neural networks; stability quaternion; networks mixed ... See more keywords
Synchronization Control of Quaternion-Valued Neural Networks with Parameter Uncertainties
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DOI: 10.1007/s11063-019-10153-2
Abstract: In this paper, by starting from basic quaternion algebra properties and algorithms, we develop a comprehensive set of properties to ensure the uncertain quaternion-valued neural networks can receive synchronization and quasi-synchronization goals. By endowing the… read more here.
Keywords: quaternion; valued neural; neural networks; control ... See more keywords
Finite-Time Mittag-Leffler Stability of Fractional-Order Quaternion-Valued Memristive Neural Networks with Impulses
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DOI: 10.1007/s11063-019-10154-1
Abstract: The finite-time Mittag-Leffler stability for fractional-order quaternion-valued memristive neural networks (FQMNNs) with impulsive effect is studied here. A new mathematical expression of the quaternion-value memductance (memristance) is proposed according to the feature of the quaternion-valued… read more here.
Keywords: quaternion; finite time; order; mittag leffler ... See more keywords
Synchronization in Quaternion-Valued Neural Networks with Delay and Stochastic Impulses
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DOI: 10.1007/s11063-021-10653-0
Abstract: A class of global exponential synchronization problem for delayed quaternion-valued neural networks with stochastic impulses has been investigated in this paper, where the impulses arouse time and strength both are randomly. Firstly, the delayed quaternion-valued… read more here.
Keywords: quaternion valued; valued neural; neural networks; stochastic impulses ... See more keywords