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and Applied Analysis 3 on each of the components of the distribution. We will use the following results: 1̂ (ω 1 , ω 2 ) = (2π) 2 δ (ω 1 , ω 2 ) , (14) ̂ (i−|α|Dαδ) (ω 1 , ω 2 ) = ω α1 1 ω α2 2 , (15) where α = (α 1 , α 2 ), |α| = α 1 + α 2 , D = (∂/∂x 1 ) α1 (∂/∂x 2 ) α2 , and δ is the usual Dirac delta function. In the following we introduce the LCT for(More)
Collaborative representation-based classification (CRC) and sparse RC (SRC) have recently achieved great success in face recognition (FR). Previous CRC and SRC are originally designed in the real setting for grayscale image-based FR. They separately represent the color channels of a query color image and ignore the structural correlation information among(More)
Rotation moment invariants have been of great interest in image processing and pattern recognition. This paper presents a novel kind of rotation moment invariants based on the Slepian functions, which were originally introduced in the method of separation of variables for Helmholtz equations. They were first proposed for time series by Slepian and his(More)
The classical uncertainty principle of harmonic analysis states that a nontrivial function and its Fourier transform cannot both be sharply localized. It plays an important role in signal processing and physics. This paper generalizes the uncertainty principle for measurable sets from complex domain to hypercomplex domain using quaternion algebras,(More)
In this paper, the global exponential stability for recurrent neural networks (QVNNs) with asynchronous time delays is investigated in quaternion field. Due to the non-commutativity of quaternion multiplication resulting from Hamilton rules: ij=-ji=k, jk=-kj=i, ki=-ik=j, ijk=i2=j2=k2=-1, the QVNN is decomposed into four real-valued systems, which are(More)