• Korean Journal of Mathematics
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• v.29 no.2
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• pp.271-291
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• 2021

Hom-Lie-Yamaguti color algebras are defined and their representation and cohomology theory is considered. The (2, 3)-cocycles of a given Hom-Lie-Yamaguti color algebra T are shown to be very useful in a study of its deformations. In particular, it is shown that any (2, 3)-cocycle of T gives rise to a Hom-Lie-Yamaguti color structure on T⊕V , where V is a T-module, and that a one-parameter infinitesimal deformation of T is equivalent to that a (2, 3)-cocycle of T (with coefficients in the adjoint representation) defines a Hom-Lie-Yamaguti color algebra of deformation type.

• Journal of the Optical Society of Korea
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• v.20 no.1
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• pp.42-54
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• 2016

A hybrid color and grayscale images encryption scheme based on the quaternion Hartley transform (QHT), the two-dimensional (2D) logistic map, the double random phase encoding (DRPE) in gyrator transform (GT) domain and the three-step phase-shifting interferometry (PSI) is presented. First, we propose a new color image processing tool termed as the quaternion Hartley transform, and we develop an efficient method to calculate the QHT of a quaternion matrix. In the presented encryption scheme, the original color and grayscale images are represented by quaternion algebra and processed holistically in a vector manner using QHT. To enhance the security level, a 2D logistic map-based scrambling technique is designed to permute the complex amplitude, which is formed by the components of the QHT-transformed original images. Subsequently, the scrambled data is encoded by the GT-based DRPE system. For the convenience of storage and transmission, the resulting encrypted signal is recorded as the real-valued interferograms using three-step PSI. The parameters of the scrambling method, the GT orders and the two random phase masks form the keys for decryption of the secret images. Simulation results demonstrate that the proposed scheme has high security level and certain robustness against data loss, noise disturbance and some attacks such as chosen plaintext attack.

• Korean Journal of Optics and Photonics
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• v.20 no.2
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• pp.110-117
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• 2009

This work introduces the uncertainty evaluation formulation on color measurement of light sources and display devices, such as CIE 1931 (x, y) chromaticity, CIE 1960 (u, v) chromaticity, correlated color temperature, and distribution temperature. All the mentioned quantities are reduced from spectral data in the visible range, for which uncertainties are strongly correlated between different wavelengths. Using matrix algebra we have formulated the uncertainty propagation from the SI- traceable spectral irradiance standard to the individual color related measurement quantities taking the correlation between wavelengths into account. As a result, we have demonstrated uncertainty evaluation examples of 3 types of light sources: CIE illuminant A, LED white light, and LCD white light. This method can be applied to any other quantities based on spectral measurement such as solar irradiance, material color measurement, etc.