• 한국수학교육학회지시리즈B:순수및응용수학
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• 제3권1호
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• pp.33-40
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• 1996

A convergence structure defined by Kent [4] is a correspondence between the filters on a given set X and the subsets of X which specifies which filters converge to points of X. This concept is defined to include types of convergence which are more general than that defined by specifying a topology on X. Thus, a convergence structure may be regarded as a generalization of a topology. With a given convergence structure q on a set X, Kent [4] introduced associated convergence structures which are called a topological modification and a pretopological modification. (omitted)

• 대한수학회지
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• 제58권2호
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• pp.265-281
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• 2021

In the kneading theory developed by Milnor and Thurston, it is proved that the kneading matrix and the kneading determinant associated with a continuous piecewise monotone map are invariant under orientation-preserving conjugacy. This paper considers the problem for orientation-reversing conjugacy and proves that the former is not an invariant while the latter is. It also presents applications of the result towards the computational complexity of kneading matrices and the classification of maps up to topological conjugacy.

• 충청수학회지
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• 제34권1호
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• pp.77-84
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• 2021

Let f : [0, 1] → [0, 1] be a multimodal map with positive topological entropy. The dynamics of the renormalization operator for multimodal maps have been investigated by Daniel Smania. It is proved that the measure of maximal entropy for a specific category of Cr interval maps is unique.

• 정보처리학회논문지:소프트웨어 및 데이터공학
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• 제5권11호
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• pp.569-584
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• 2016

본 논문에서는 Hadoop MapReduce 병렬 분산 컴퓨팅 환경을 이용해 개발한 공간 지식 추출기를 제안한다. 이 공간 지식 추출기는 대용량의 공간 데이터 집합으로부터, 임의의 두 공간 객체들 사이에 만족되는 위상 관계와 방향 관계를 나타내는 정성 공간 지식 베이스를 생성해낸다. 본 논문에서 제안하는 MapReduce 기반의 대용량 공간 지식 추출기 MRSPAKE는 HDFS 상의 분산 공간 데이터 파일에 대한 R 트리 색인과 범위 질의들을 이용함으로써, 웹 규모의 정성 공간 지식 베이스를 매우 효율적으로 추출해낸다. 대표적인 공개 데이터 집합인 Open Street Map(OSM)을 이용한 성능 분석 실험을 통해, 본 논문에서 제안하는 웹 규모의 공간 지식 추출기 MRSPAKE의 높은 성능과 확장성을 확인할 수 있었다.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2007년도 춘계학술대회 학술발표 논문집 제17권 제1호
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• pp.179-182
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• 2007

In this paper, we introduce the concepts of fuzzy (r, s)-semi-preopen sets and fuzzy (r, s)-semi-precontinuous maps on intuitionistic fuzzy topological spaces in Sostak's sense. The relations among fuzzy (r, s)-semicontinuous, fuzzy (r, s)-precontinuous, and fuzzy (r, s)-semi-precontinuous maps are discussed. The concepts of fuzzy (r, s)-semi-preinterior, fuzzy (r, s)-semi-preclosure, fuzzy (r, s)-semi-preneighborhood, and fuzzy (r, s)-quasi-semi-preneighborhood are given. Using these concepts, the characterization for the fuzzy (r, s)-semi-precontinuous map is obtained. Also, we introduce the notions of fuzzy (r, s)-semi-preopen and fuzzy (r, s)-semi-preclosed maps on intuitionistic fuzzy topological spaces in Sostak's sense, and then we investigate some of their characteristic properties.

• 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.

• 로봇학회논문지
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• 제4권1호
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• pp.25-33
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• 2009

One of the main problems of topological localization in a real indoor environment is variations in the environment caused by dynamic objects and changes in illumination. Another problem arises from the sense of topological localization itself. Thus, a robot must be able to recognize observations at slightly different positions and angles within a certain topological location as identical in terms of topological localization. In this paper, a possible solution to these problems is addressed in the domain of global topological localization for mobile robots, in which environments are represented by their visual appearance. Our approach is formulated on the basis of a probabilistic model called the Bayes filter. Here, marginalization of dynamics in the environment, marginalization of viewpoint changes in a topological location, and fusion of multiple visual features are employed to measure observations reliably, and action-based view transition model and action-associated topological map are used to predict the next state. We performed experiments to demonstrate the validity of our proposed approach among several standard approaches in the field of topological localization. The results clearly demonstrated the value of our approach.

• 충청수학회지
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• 제4권1호
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• pp.103-113
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• 1991

Some properties of a path space and the fundamental group ${\sigma}(X,x_0,G)$ of a topological transformation group (X, G, ${\pi}$) are described. It is shown that ${\sigma}(X,x_0,H)$ is a normal subgroup of ${\sigma}(X,x_0,G)$ if H is a normal subgroup of G ; Let (X, G, ${\pi}$) be a transformation group with the open action property. If every identification map $p:{\Sigma}(X,x,G)\;{\longrightarrow}\;{\sigma}(X,x,G)$ is open for each $x{\in}X$, then ${\lambda}$ induces a homeomorphism between the fundamental groups ${\sigma}(X,x_0,G)$ and ${\sigma}(X,y_0,G)$ where ${\lambda}$ is a path from $x_0$ to $y_0$ in X ; The space ${\sigma}(X,x_0,G)$ is an H-space if the identification map $p:{\Sigma}(X,x_0,G)\;{\longrightarrow}\;{\sigma}(X,x_0,G)$ is open in a topological transformation group (X, G, ${\pi}$).

• ETRI Journal
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• 제29권5호
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• pp.655-666
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• 2007

There are nodes and edges in a topological map. Node data has been used as a main source of information for the localization of mobile robots. In contrast, edge data is regarded as a minor source of information, and it has been used in an intuitive and heuristic way. However, edge data also can be used as a good source of information and provide a way to use edge data efficiently. For that purpose, we define a data format which describes the shape of an edge. This format is called local generalized Voronoi graph's angle (LGA). However, the LGA is constituted of too many samples; therefore, real time localization cannot be performed. To reduce the number of samples, we propose a compression method which utilizes wavelet transformation. This method abstracts the LGA by key factors using far fewer samples than the LGA. Experiments show that the LGA accurately describes the shape of the edges and that the key factors preserve most information of the LGA while reducing the number of samples.

• 호남수학학술지
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• 제33권1호
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• pp.11-17
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• 2011

We study some properties of quasi-topological spaces. Also we introduce the concept of Q-continuity and investigate several types of quasi-topology on an SGNS.