• Korean Journal of Mathematics
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• 제12권2호
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• pp.107-115
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• 2004

In this paper, the new subclass denoted by $S_p({\alpha},{\beta},{\xi},{\gamma})$ of $p$-valent holomorphic functions has been introduced and investigate the several properties of the class $S_p({\alpha},{\beta},{\xi},{\gamma})$. In particular we have obtained integral representation for mappings in the class $S_p({\alpha},{\beta},{\xi},{\gamma})$) and determined closed convex hulls and their extreme points of the class $S_p({\alpha},{\beta},{\xi},{\gamma})$.

• 산업경영시스템학회지
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• 제23권61호
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• pp.127-135
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• 2000

This paper provides a new method of initializing neurons used in self-organizing neural networks and sequencing input nodes for applying to Euclidean traveling salesman problem. We use a general property that in any optimal solution for Euclidean traveling salesman problem, vertices located on the convex hull are visited in the order in which they appear on the convex hull boundary. We composite input nodes as number of convex hulls and initialize neurons as shape of the external convex hull. And then adapt input nodes as the convex hull unit and all convex hulls are adapted as same pattern, clockwise or counterclockwise. As a result of our experiments, we obtain l∼3 % improved solutions and these solutions can be used for initial solutions of any global search algorithms.

• International Journal of Naval Architecture and Ocean Engineering
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• 제11권1호
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• pp.202-210
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• 2019

The obstacles modeling is a fundamental and significant issue for path planning and automatic navigation of Unmanned Surface Vehicle (USV). In this study, we propose a novel obstacles modeling method based on high resolution satellite images. It involves two main steps: extraction of obstacle features and construction of convex hulls. To extract the obstacle features, a series of operations such as sea-land segmentation, obstacles details enhancement, and morphological transformations are applied. Furthermore, an efficient algorithm is proposed to mask the obstacles into convex hulls, which mainly includes the cluster analysis of obstacles area and the determination rules of edge points. Experimental results demonstrate that the models achieved by the proposed method and the manual have high similarity. As an application, the model is used to find the optimal path for USV. The study shows that the obstacles modeling method is feasible, and it can be applied to USV path planning.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2003년도 춘계 학술대회 학술발표 논문집
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• pp.14-17
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• 2003

By Mazur's theorem, the convex hull of a relatively compact subset a Banach space is also relatively compact. But this is not true any more in the space of fuzzy numbers endowed with the Hausdorff-Skorohod metric. In this paper, we establish a necessary and sufficient condition for which the convex hull of K is also relatively compact when K is a relatively compact subset of the space F(R$\^$k/) of fuzzy numbers of R$\^$k/ endowed with the Hausdorff-Skorohod metric.

• 한국정보처리학회:학술대회논문집
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• 한국정보처리학회 2012년도 춘계학술발표대회
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• pp.1073-1074
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• 2012

최근 인터넷의 발달과 사용량의 증가로 데이터의 양이 급증함에 따라 대용량 데이터를 효율적으로 검색하는 top k 질의 처리가 중요시 되고 있다. Layer 기반 방법은 가장 잘 알려진 top k 질의처리 방법이며, 객체의 모든 속성의 값들을 이용하여 객체들을 layer들의 리스트로 구성하는 방법이다. 본 논문에서는 그 중에서 convex hull을 사용하여 layer list를 생성하는 기존 연구를 조사하고 문제점을 파악한다.

• Communications for Statistical Applications and Methods
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• 제25권1호
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• pp.79-89
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• 2018

In this paper, we study the maximal property of the volume of the convex hull of d-dimensional independent random vectors. We show that the volume of the random convex hull from a multivariate location-scale family indexed by ${\Sigma}$ is stochastically maximized in simple stochastic order when ${\Sigma}$ is diagonal. The claim can be applied to a broad class of multivariate distributions that include skewed/unskewed multivariate t-distributions. We numerically investigate the proven stochastic relationship between the dependent and independent random convex hulls with the Gaussian random convex hull. The numerical results confirm our theoretical findings and the maximal property of the volume of the independent random convex hull.

• 한국CDE학회논문집
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• 제7권2호
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• pp.131-139
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• 2002

Custom-tailored products always vary their sizes and shapes to satisfy the customers' tastes and requirements but they have to be fabricated as fast as possible when ordered. One way to solve this problem is to prepare several representative products in advance and each custom-tailored product is generated by machining the closest representative product. To realize this approach, it would be necessary to be able to group the products into several groups each of which has a representative product. Once the similar products are identified to be grouped, the representative shape can be generated such that all the products in the group can be made by machining the representative product. The custom-tailored products considered in this work have similar shapes but different sizes. Since these products have free surfaces, that are hard to be compared, their convex hulls are used for the grouping. Among all the products to be grouped, one product is chosen as a base shape. The shape and overall similarity values between the base shape and the remaining shapes are calculated as their convex hulls are rotated virtually. By calculating these similarity values at each rotation, the optimal alignment of the reference shape with respect to the base shape is determined. Overall similarity value at this optimal alignment is used as a measure for grouping. A prototype system based on the proposed methodology has been implemented and used to group the shoe-lasts for custom-tailored shoes.

• 콘크리트학회논문집
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• 제20권5호
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• pp.627-634
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• 2008

이 연구에서는 한정된 데이터베이스를 바탕으로 콘크리트 물성 예측 모델을 만들어 최적 배합을 구할 때, 탐색 범위를 한정된 데이터베이스로 제안함으로써 보다 신뢰성 있는 콘크리트 배합을 제시할 수 있는 기법을 제안하였다. 제안한 기법은 각 구성 재료의 가능한 모든 영역을 포함하는 데이터베이스를 구축하지 않고 최적화 과정에서 탐색 범위를 한정된 데이터베이스로 제안함으로써 콘크리트 물성 예측 모델이 신뢰성을 확보할 수 있게 된다. 이 연구에서 이러한 영역을 유효영역으로 정의 하였다. 제안한 기법은 유전자 알고리즘, 인공신경회로망, 그리고 최소 볼록 집합을 이용하여 구현하였으며, 이 방법의 타당성을 검증하기 위하여 주어진 강도 조건을 만족하면서 최저의 가격으로 제조할 수 있는 배합을 찾는 최적화 문제에 적용하였으며 검증 실험을 수행하였다. 실험 결과 데이터베이스의 영역 특성을 반영하는 제안한 기법을 통하여 보다 정확하고 신뢰성 있는 최적 배합을 찾을 수 있음을 확인하였다.

• Journal of applied mathematics & informatics
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• 제8권2호
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• pp.473-489
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• 2001

The notion of difference for two convex compact sets in Rⁿ, proposed by Rubinov et al, is generalized to R/sub mxn/. A formula of the difference for the two sets, which are convex hulls of a finite number of points, is developed. In the light of this difference, the relation between Clarke generalized Jacobian and quasidifferential, in the sense of Demyanov and Rubinov, for a nonsnooth function, is established. Based on the relation, the method of estimating Clarke generalized Jacobian via quasidifferential for a certain class of function, is presented.

• 한국컴퓨터그래픽스학회논문지
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• 제2권2호
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• pp.61-68
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• 1996

본 논문에서는 대용량의 DNA 염기 배열의 정성 정보를 특징짓기 위한 새로운 가시화 방법을 제안한다. DNA 배열은 배열 자체가 방대한 양의 정보를 포함하고 있기 때문에 분석에 많은 어려움이 있다. 우리는 DNA 염기 배열들사이의 상사성 비교를 위해 DNA 염기 배열을 하나의 이미지 도메인으로 변환한다. 프로그램은 random walk plot으로 DNA 염기 배열을 가시화한 후에 k-convex hull로 단순화 시킨다. Random Walk plot은 염기배열을 평면상에 하나의 커브로 표현한다. k-convex hull은 walk plot으로부터 무의미한 부분을 제거함으로서 walk plot을 단순화한다. 이러한 방법은 유전공학자들에게 쉽게 DNA 배열의 특징을 인식하고 분류할 수 있는 직관을 제공한다. 실제 게놈 데이터로 실험한 결과는 논문에서 제안하는 방법이 긴 DNA 염기배열들 사이의 유사성 분석을 위해 좋은 가시화 도구임을 보여준다.