• 대한수학회논문집
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• 제9권3호
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• pp.565-570
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• 1994

In this article we prove a version of the Perron-Frobenius Theorem in linear algebra using the Brouwer's Fixed Point Theorem in topology. We will mostly concentrate on he qualitative aspect of the Perron-Frobenius Theorem rather than quantitative formulas, which would be enough for theoretical investigations in ergodic theory. By the nature of the method of the proof, we do not expect to obtain a numerical estimate. But we may regard it worthwhile to see why a certain type of result should be true from a topological and geometrical viewpoint. However, a geometric argument alone would give us a sharp numerical bounds on the size of the eigenvalue as shown in Section 2. Eigenvectors of a matrix A will be fixed points of a certain mapping defined in terms of A. We shall modify an existing proof of Frobenius Theorem and that will do the trick for Perron-Frobenius Theorem.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제9권4호
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• pp.281-284
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• 2009

In [8], we introduced the concept of fuzzy r-minimal structure which is an extension of smooth fuzzy topological spaces and fuzzy topological spaces in Chang's sense. And we also introduced and studied the fuzzy r-M continuity. In this paper, we introduce the concepts of fuzzy r-minimal compactness on fuzzy r-minimal compactness and nearly fuzzy r-minimal compactness, almost fuzzy r-minimal spaces and investigate the relationships between fuzzy r-M continuous mappings and such types of fuzzy r-minimal compactness.

• 한국지능시스템학회논문지
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• 제2권1호
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• pp.3-16
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• 1992

In this paper, we establish the conceptes of compactifications of a L-fuzzy topological space and a order relation in these compactifications. This order is a preorder. The existemce problem and the uniqueness problem of the largest compactifications are closely related to the mapping extension problem. We give out the largest compactifications and show the non-uniqueness of the largest compactifications in the preorder for a kind of spaces. Moreover, under some natural assumptions of separation axioms, we prove that the preorder is just a partial order, thus it ensures the uniqueness of the largest compactification. In addition. the related discussion involves the special properties of fuzzy product space, the latter seems to be independent interesting.

• 한국전기전자재료학회논문지
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• 제31권1호
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• pp.11-18
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• 2018

Two-dimensional (2D) materials such as transition metal dichalcogenides have attracted tremendous scientific interests owing to their potential of solving the zero band-gap issue of graphene. In this work, the research areas and technology evolutionary dynamics of the 2D materials were identified using the scientometric method focusing on keyword mapping and clustering. The time-series analysis showed that the technological progress of 2D material is in the early growth period. The overlay mapping analysis were carried out to investigate the technology evolution of 2D materials with time. The strategic diagram of co-word analysis classifying the topological positions of keyword was derived to support the analysis results. It is conjectured that extensive research will be conducted widely on the application of 2D materials not only in electronic and optoelectronic devices, but also in various other fields such as biomedical applications, and that their development will be more rapid based on accumulated results of extant graphene research.

• 한국정보과학회논문지:데이타베이스
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• 제29권5호
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• pp.358-366
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• 2002

특징정보를 기반으로 한 유사 이미지 검색은 이미지 데이타베이스에 있어서 중요한 과제의 하나이다. 이미지 데이타의 특징정보는 각 이미지를 식별하는데 유용한 정보이다. 본 논문에서는 자기 조직화 맵 기반의 고속 k-NN 탐색 알고리즘을 제안한다. 자기 조직화 맵은 고차원 특징벡터를 2차원 공간에 맵핑하여 위상특징 맵을 생성한다. 위상특징 맵은 입력 데이타의 특징공간과 상호관계(유사성)를 가지고 있으며, 인접노드에 서로 유사한 특징벡터가 클러스터링된다. 그러므로 위상특징 맵상의 각 노드에는 노드 벡터와 각 노드벡터에 가장 가까운 유사 이미지가 분류된다. 이러한 자기 조직화 맵에 의한 유사 이미지 분류결과에 대하여 k-NV 탐색을 구현하기 위하여, (1) 위상특징 맵에 대한 접근방법, (2) 고속탐색을 위한 pruning strategy의 적용을 실현하였다. 본 연구에서는 실험을 통하여 실제 이미지로부터 추출한 색상 특징을 사용하여 제안한 알고리즘의 성능을 평가함으로써 유사 이미지 검색에 유효한 견과를 얻을 수 있었다.

• 대한수학회보
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• 제45권2호
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• pp.207-220
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• 2008

We introduce and study the notions of supra fuzzy convergence of fuzzy filters, $s{\gamma}$-fuzzy open (closed) sets, $s{\gamma}(/TEX>$s{\gamma}^*)$-fuzzy continuous and $s{\gamma}$-fuzzy open mapping. Also. we investigate some of fundamental properties of these notions.

• 한국지능시스템학회논문지
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• 제21권4호
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• pp.525-529
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• 2011

IVF almost ${\alpha}$-연속성의 개념을 소개하고 그 함수의 특성을 조사한다. 그리고 다른 IVF 연속함수와의 관계를 밝힌다.

• East Asian mathematical journal
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• 제26권1호
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• pp.49-58
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• 2010

In this paper, we consider and study a new class of generalized vector quasi-variational type inequalities and obtain some existence theorems for both under compact and noncompact assumptions in topological vector spaces without using monotonicity. For the noncompact case, we use the concept of escaping sequences.

• 대한수학회논문집
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• 제16권2호
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• pp.277-285
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• 2001

The purpose of this paper is to give a proof of a generalized convex-valued selection theorem which is given by weakening a Banach space to a completely metrizable locally convex topological vector space, i.e., a Frechet space. We also develop the properties of upper semi-continuous singlevalued mapping to those of upper semi-continuous multivalued mappings. These properties wil be applied in our further consideraations of selection theorems.

• 한국수학교육학회지시리즈A:수학교육
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• 제22권1호
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• pp.31-33
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• 1983

이 논문에서는 Norman Levin의 논문에서 나타난 semi-open의 개념을 사용하여 정의된 semi-continuous의 여러가지 성질을 조사하였고, semi-continuity를 위상공간의 first-axiom공간 pseudo-metric공간과 n-th product공간까지 조사하였으며, semi-continuous함수의 합성과 함수열의 극한과 Proximity공간의 mapping에 대하여 조사하였다. 그리고 정리의 역이 성립하지 않는 경우 반례를 들어 보였다.