• Journal of the Korean Mathematical Society
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• v.53 no.2
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• pp.305-313
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• 2016

In this paper, we give several sufficient conditions ensuring that any positive radial solution (u, v) of the following ${\gamma}$-Laplacian systems in the whole space ${\mathbb{R}}^n$ has the components symmetry property $u{\equiv}v$ $$\{\array{-div({\mid}{\nabla}u{\mid}^{{\gamma}-2}{\nabla}u)=f(u,v)\text{ in }{\mathbb{R}}^n,\\-div({\mid}{\nabla}v{\mid}^{{\gamma}-2}{\nabla}v)=g(u,v)\text{ in }{\mathbb{R}}^n.}$$ Here n > ${\gamma}$, ${\gamma}$ > 1. Thus, the systems will be reduced to a single ${\gamma}$-Laplacian equation: $$-div({\mid}{\nabla}u{\mid}^{{\gamma}-2}{\nabla}u)=f(u)\text{ in }{\mathbb{R}}^n$$. Our proofs are based on suitable comparation principle arguments, combined with properties of radial solutions.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.13 no.1
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• pp.12-18
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• 1988

It is found that the estimation pdf of the real intraframe DPCM prediction error by $x^3$ goodness-of-fit test for the images is nearer gamma distribution that laplacian. Also the new pdf estimation method by NMAE is proposed and applied to the pdf adaptive DPCM system.

• Journal of IKEEE
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• v.26 no.2
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• pp.292-298
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• 2022

There is a limit to improving the image quality through global processing of images taken under backlighting because too bright and dark parts are mixed in one scene. This paper introduces a method to improve the quality of a photo by making two virtual images that improve the dark and bright areas of a backlit photo, and fusing them with the original image into a Laplacian pyramid. The proposed method reduces the computational burden by using histogram stretching and gamma transformation that can be simplified with LUT when creating the two virtual images. In addition, in order to obtain a color-enhanced image, contrast conversion was performed only on the luminance using the HSV coordinate system. The proposed technique showed its effectiveness by calculating several NIQA indicators using standard image data sets.