• Journal of the Institute of Electronics Engineers of Korea SP
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• v.37 no.1
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• pp.37-48
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• 2000

In this paper, we propose a new connected operator Using morphological grayscale reconstruction for region-based coding First, an effective method of reference-image creation lis proposed, which is based on the Size as well as the contrast. This improves the performance of simplification, because It preserves perceptually important components and removes unnecessary components The conventional connected operators are good for removing small regions, but have a serious drawback for low-contrast regions that are larger than the structuring element. That is, when the conventional connected operators are applied to tills region, the simplification becomes less effective or several meaningful regions are merged to one region to avoid this, the conventional geodesic dilation is modified to propose an adaptive operator to reduce the effect of inappropriate propagation, pixels reconstructed to the original values are excluded m the dilation operation Experimental results have shown that the proposed algorithm achieves better performance In terms of the reconstruction of flat zones. The Picture quality has also been improved by about 7dB, compared to the conventional methods.

• Communications of the Korean Mathematical Society
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• v.34 no.4
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• pp.1135-1143
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• 2019

The matrix representation of the Toeplitz operator on the Hardy space with respect to a generalized orthonormal basis for the space of square integrable functions associated to a bounded simply connected region in the complex plane is completely computed in terms of only the Szegő kernel and the Garabedian kernels.

• Bulletin of the Korean Mathematical Society
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• v.54 no.4
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• pp.1421-1441
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• 2017

We compute explicitly the matrix represented by the Toeplitz operator on the Hardy space over a smoothly finitely connected bounded domain in the plane with respect to special orthonormal bases consisting of the classical kernel functions for the space of square integrable functions and for the Hardy space. The Fourier coefficients of the symbol of the Toeplitz operator are obtained from zeroth row vectors and zeroth column vectors of the matrix. And we also find some condition for the product of two Toeplitz operators to be a Toeplitz operator in terms of matrices.

• Journal of the Korean Mathematical Society
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• v.57 no.4
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• pp.973-986
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• 2020

In this paper, we compute the Hankel matrix representation of the Hankel operator on the Hardy space of a general bounded domain with respect to special orthonormal bases for the Hardy space and its orthogonal complement. Moreover we obtain the compact form of the Hankel matrix for the unit disc case with respect to these bases. One can see that the Hankel matrix generated by this computation turns out to be a generalization of the case of the unit disc from the single simply connected domain to multiply connected domains with much diversities of bases.

• Journal of applied mathematics & informatics
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• v.40 no.5_6
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• pp.979-982
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• 2022

This paper covers some important operator inequalities connected with traces of matrices, from the classical inequalities we obtained new inequalities connected with traces of matrices which are better than the others.

• Bulletin of the Korean Mathematical Society
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• v.41 no.2
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• pp.337-345
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• 2004

In allelic model X = ($\chi_1\chi$_2ㆍㆍㆍ, \chi_d$), M_f(t) = f(p(t)) - ${{\int^t}_0}\;Lf(p(t))ds$ is a P-martingale for diffusion operator L under the certain conditions. In this note, we can show existence and uniqueness of solution for stochastic differential equation and martingale problem associated with mean vector. Also, we examine that if the operator related to this martingale problem is connected with Markov processes under certain circumstance, then this operator must satisfy the maximum principle.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 1999.11b
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• pp.3-8
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• 1999

In this paper, we propose a new connected operator using morphological grayscale reconstruction for region-based coding. First, an effective method of reference-image creation is proposed, which is based on the size as well as the contrast. The conventional connected operators are good for removing small regions, but have a serious drawback for low-contrast regions that are larger than the structuring element. That is, when the conventional connected operators are applied to these regions. the simplification becomes less effective or several meaningful regions are merged to one region. To avoid this, the conventional geodesic dilation is modified to propose an adaptive operator. To reduce the effect of inappropriate propagation, pixels reconstructed to the original values are excluded in the dilation operation. Experimental results have shown that the proposed algorithm achieves better performance in terms of the reconstruction of flat zones. The picture quality has also been improved by about 7dB, compared to the conventional methods.

• Bulletin of the Korean Mathematical Society
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• v.55 no.6
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• pp.1891-1908
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• 2018

In this paper, we investigate the existence of an S-shaped connected component in the set of positive solutions of the Dirichlet problem of the one-dimension Minkowski-curvature equation $$\{\(\frac{u^{\prime}}{\sqrt{1-u^{{\prime}2}}}\)^{\prime}+{\lambda}a(x)f(u)=0,\;x{\in}(0,1),\\u(0)=u(1)=0$$, where ${\lambda}$ is a positive parameter, $f{\in}C[0,{\infty})$, $a{\in}C[0,1]$. The proofs of main results are based upon the bifurcation techniques.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.42 no.6
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• pp.33-42
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• 2005

In this paper, we propose an efficient segmentation algerian using morphological grayscale reconstruction for region-based coding. Each segmentation stage consists of simplification, marker extraction and decision. The simplification removes unnecessary components to make an easier segmentation. The marker extraction finds the flat zones which are the seed points from the simplified image. The decision is to locate the contours of regions detected by the marker extraction. For the simplification, we use a new connected operator based on the size and contrast. In the marker extraction stage, the regions reconstructed to original values we excluded from the candidate marker. For the other regions, the regions which are larger than structuring elements or have higher contrast than a threshold value are selected as markers. For the initial segmentation, the conventional hierarchical watershed algorithm and the extracted markers are used. Finally in the region merging stage, we propose an efficient region merging algorithm which preserves a high quality in terms of the number of regions. At the same time, the pairs which have higher contrast than a threshold are excluded from the region merging stage. Experimental results show that the proposed marker extraction method produces a small number of markers, while maintaining high quality and that the proposed region merging algorithm achieves a good performance in terms of the image quality and the number of regions.

• Kyungpook Mathematical Journal
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• v.56 no.1
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• pp.185-220
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• 2016

We study the Gauss and Poisson semigroups connected with the Riemann-Liouville operator defined on the half plane. Next, we establish a principle of maximum for the singular partial differential operator $${\Delta}_{\alpha}={\frac{{\partial}^2}{{\partial}r^2}+{\frac{2{\alpha}+1}{r}{\frac{\partial}{{\partial}r}}+{\frac{{\partial}^2}{{\partial}x^2}}+{\frac{{\partial}^2}{{\partial}t^2}}};\;(r,x,t){\in}]0,+{\infty}[{\times}{\mathbb{R}}{\times}]0,+{\infty}[$$. Later, we define the Littlewood-Paley g-function and using the principle of maximum, we prove that for every $p{\in}]1,+{\infty}[$, there exists a positive constant $C_p$ such that for every $f{\in}L^p(d{\nu}_{\alpha})$, $${\frac{1}{C_p}}{\parallel}f{\parallel}_{p,{\nu}_{\alpha}}{\leqslant}{\parallel}g(f){\parallel}_{p,{\nu}_{\alpha}}{\leqslant}C_p{\parallel}f{\parallel}_{p,{\nu}_{\alpha}}$$.