• Bulletin of the Korean Mathematical Society
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• v.43 no.4
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• pp.861-868
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• 2006

We present a Choquet-Deny-type theorem for downward filtering convex sets of continuous functions and show that the Identity Korovkin cone of a downward filtering convex cone S is exactly the uniform closure of S.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.4
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• pp.345-353
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• 2021

In this paper, first, we present new fixed point theorems for Mönch type multimaps on abstract convex uniform spaces and, also, a fixed point theorem for Mönch type multimaps in Hausdorff KKM L𝚪-spaces. Second, we show that Mönch type multimaps in the better admissible class defined on an L𝚪-space have fixed point properties whenever their ranges are Klee approximable. Finally, we obtain fixed point theorems on 𝔎ℭ-maps whose ranges are 𝚽-sets.

• Journal of Broadcast Engineering
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• v.21 no.6
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• pp.878-888
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• 2016

This paper proposes an efficient method to remove the boundary artifacts of rendered views caused by damaged depth maps in the 3D video system. First, characteristics of boundary artifacts with the compression noise in depth maps are carefully studied. Then, the artifacts suppression method is proposed by the iterative projection onto convex sets (POCS) algorithm with setting the convex set in pixel and frequency domain. The proposed method is applied to both texture and depth maps separately during view rendering. The simulation results show the boundary artifacts are greatly reduced with improving the quality of synthesized views.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2001.05a
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• pp.21-24
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• 2001

In this paper, we investigate some properties of the Skorokhod metric on the space F(R$\^$p/) of upper semicontinuous fuzzy subsets of R$\^$p/ with compact support, which include the continuity of operations, the translation inveriance and convexity.

• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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• pp.175-184
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• 2013

In this paper, the reverse Bonnesen style inequalities for convex domain in the Euclidean plane $\mathbb{R}^2$ are investigated. The Minkowski mixed convex set of two convex sets K and L is studied and some new geometric inequalities are obtained. From these inequalities obtained, some isoperimetric deficit upper limits, that is, the reverse Bonnesen style inequalities for convex domain K are obtained. These isoperimetric deficit upper limits obtained are more fundamental than the known results of Bottema ([5]) and Pleijel ([22]).

• Journal of the Korean Mathematical Society
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• v.26 no.2
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• pp.175-179
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• 1989

• Journal of the Korean Mathematical Society
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• v.14 no.1
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• pp.81-92
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• 1977

• Honam Mathematical Journal
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• v.34 no.3
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• pp.403-408
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• 2012

In this paper, we prove that if K is a convex body in $E^n$ and $E_i$ and $E_o$ are inscribed ellipsoid and circumscribed ellipsoid of K respectively with ${\alpha}E_i=E_o$, then $\[({\alpha})^{\frac{n}{p}+1}\]^n{\omega}^2_n{\geq}V(K)V({\Gamma}^{\ast}_pK){\geq}\[(\frac{1}{\alpha})^{\frac{n}{p}+1}\]^n{\omega}^2_n$. Lutwak and Zhang[6] proved that if K is a convex body, ${\omega}^2_n=V(K)V({\Gamma}_pK)$ if and only if K is an ellipsoid. Our inequality provides very elementary proof for their result and this in turn gives a lower bound of the volume product for the sets of constant width.

• Journal of Institute of Control, Robotics and Systems
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• v.8 no.12
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• pp.991-997
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• 2002

The concept of feasible & invariant region plays an important role to derive closed loop stability and achie adequate performance of constrained receding horizon predictive control. In this paper, we define a complex polyhedral feasible & invariant set for all stabilizable input-constrained linear systems by using a complex transform and propose a one-norm based receding horizon control scheme using these invariant sets. In order to get a larger stabilizable set, a convex hull of invariant sets which are defined for different state feedback gains is used as a target invariant set of the constrained receding horizon control. The proposed constrained receding horizon control scheme is formulated so that it can be solved via linear programming.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2016.06a
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• pp.302-305
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• 2016

This paper proposes a boundary artifacts reduction method for synthesized views in 3D video system using Projection onto Convex Sets (POCS). In 3D video system, boundary artifacts are occurred in synthesized views by distorted depth map. In this paper, we analyze boundary artifacts, and show the experimental results by the proposed algorithm on various situations.