• Journal of Electrical Engineering and information Science
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• v.3 no.3
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• pp.281-285
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• 1998

Consider the two-dimensional sorted-set convex hull problem: Given N points in a plane sorted by the x coordinates, compute the convex hull of the points. We propose an O(logNlog logN)-time algorithm that solves the sorted-set convex hull problem on an N\ulcorner\ulcorner${\times}$N\ulcorner\ulcorner reconfigurable mesh. The best known algorithm for the problem on an N\ulcorner\ulcorner${\times}$N\ulcorner\ulcorner reconfigurable mesh takes O(log\ulcornerN) time. Although there is a constant-time algorithm on an N${\times}$N reconfigurable mesh for general two-dimensional convex hull problem, the general convex hull problem requires Θ(N\ulcorner\ulcorner) time on an N\ulcorner\ulcorner${\times}$N\ulcorner\ulcorner reconfigurable mesh due to bandwidth constraints.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2002.12a
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• pp.267-270
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• 2002

본 논문에서는 Support Vector Machines (SVM) 을 이용하여, 빠르고 정확한 두 convex한 클러스터 간의 거리 측정 방법을 제시한다 제시된 방법에서는, SVM에 의해서 생성되는 최적 다차원 평면이 두 클러스터간의 최소 거리를 계산하는데 사용된다. 또한, 본 논문에서는 이러한 두 클러스터 간의 최적의 거리를 사용하여, Fuzzy Convex Clustering (FCC) 방법 (1) 에 의해서 생성되는 Convex 클러스터들을 묶어주는 효과적인 클러스터 결합 알고리즘을 제시하였다. 그러므로, 데이터의 부적절한 표현을 유발하지 않고도 클러스터들의 개수를 좀 더 줄일 수 있었다. 제시한 방법의 타당성을 위하여 여러 실험 결과를 제시하였다

• Journal of the Korean Mathematical Society
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• v.36 no.4
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• pp.823-823
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• 1999

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.37 no.2
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• pp.1-7
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• 2000

In this paper, an adaptive control law for nonlinear systems represented by input-output models are proposed under the assumption that unknown system parameters are in a known compact and convex set. Contrary to the previous results, the compact and convex set is not restricted to a ball whose center is at the origin or convex hypercube. It is proven that the proposed parameter update rule produces a sequence of parameters which reside in the set and guarantees that the position, velocity, and acceleration error converges to zero as time goes to infinity. This theoretical result was justified through simulations.

• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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• pp.641-651
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• 2014

Because of difficulty of using Schauder's fixed point theorem to the polynomial-like iterative equation, a lots of work are contributed to the existence of solutions for the polynomial-like iterative equation on compact set. In this paper, by applying the Schauder-Tychonoff fixed point theorem we discuss monotone solutions and convex solutions of the polynomial-like iterative equation on an open set (possibly unbounded) in $\mathbb{R}^N$. More concretely, by considering a partial order in $\mathbb{R}^N$ defined by an order cone, we prove the existence of increasing and decreasing solutions of the polynomial-like iterative equation on an open set and further obtain the conditions under which the solutions are convex in the order.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.9
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• pp.1167-1174
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• 1999

In this paper, we present a new technique for the local decomposition of convex structuring elements for morphological image processing. Local decomposition of a structuring element consists of local structuring elements, in which each structuring element consists of a subset of origin pixel and its eight neighbors. Generally, local decomposition of a structuring element reduces the amount of computation required for morphological operations with the structuring element. A unique feature of our approach is the use of linear integer programming technique to determine optimal local decomposition that guarantees the minimal amount of computation. We defined a digital convex polygon, which, in turn, is defined as a convex structuring element, and formulated the necessary and sufficient conditions to decompose a digital convex polygon into a set of basis digital convex polygons. We used a set of linear equations to represent the relationships between the edges and the positions of the original convex polygon, and those of the basis convex polygons. Further. a cost function was used represent the total processing time required for computation of dilation/erosion with the structuring elements in a decomposition. Then integer linear programming was used to seek an optimal local decomposition, that satisfies the linear equations and simultaneously minimize the cost function.

• Korean Journal of Mathematics
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• v.29 no.3
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• pp.593-602
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• 2021

In this paper, the concept of s-convex function in the third sense is given. Then fundamental characterizations and some basic algebraic properties of s-convex function in the third sense are presented. Also, the relations between the third sense s-convex functions according to the different values of s are examined.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.351-360
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• 2005

This paper finds a new class of generalized convex function which satisfies the following properties: It's level set is $\eta$-convex set; Every feasible Kuhn-Tucker point is a global minimum; If Slater's constraint qualification holds, then every minimum point is Kuhn-Tucker point; Weak duality and strong duality hold between primal problem and it's Mond-Weir dual problem.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.657-661
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• 2010

We study a singular function which we call a generalized cylinder convex(concave) function induced from different generalized dyadic expansion systems on the unit interval. We show that the generalized cylinder convex(concave)function is a singular function and the length of its graph is 2. Using a local dimension set in the unit interval, we give some characterization of the distribution set using its derivative, which leads to that this singular function is nowhere differentiable in the sense of topological magnitude.

• The Pure and Applied Mathematics
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• v.9 no.1
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• pp.1-7
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• 2002

For A bounded subset G of a metric Space (X,d) and $\chi \in X$, let $f_{G}$ be the real-valued function on X defined by $f_{G}$($\chi$)=sup{$d (\chi, g)\in:G$}, and $F(G,\chi)$={$z \in X:sup_{g \in G}d(g,z)=sup_{g \in G}d(g,\chi)+d(\chi,z)$}. In this paper we discuss some properties of the map $f_G$ and of the set $ F(G, \chi)$ in convex metric spaces. A sufficient condition for an element of a convex metric space X to lie in $ F(G, \chi)$ is also given in this pope.