• 한국공간정보시스템학회 논문지
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• 제3권1호
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• pp.49-62
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• 2001

공간정보 및 속성정보를 저장 및 관리하여 서비스하는 지리정보시스템은 최근 네트워크 및 분산환경의 기술개발과 더불어 급격히 변화하고 있다. 이러한 지리정보시스템은 컴포넌트 기반 기술로 자리매김하고 있으며 OGC(OpenGIS Consortium)에서는 지리정보시스템의 설계 및 구현에 대한 다양한 사양과 토픽을 제시하고 있다. OGC의 사양을 충족하는 개방형 지리정보시스템은 다양한 컴포넌트들로 구성되어 있으며, 이러한 컴포넌트 기반의 시스템에 추가적인 요소로써 공간분석 컴포넌트를 구현하였다. 지리정보시스템에서 공간분석기능은 중요한 요소 중 하나이며 전체 시스템의 성능적, 기능적 평가 기준이 되기도 한다. OGC에서 제시하는 기본 공간데이터 모델인 Geometry 모델은 기본 기하공간객체를 관리하는 모델이며, 다양한 분석 컴포넌트들의 연동을 위하여 확장이 필요하다. 즉 기본 기하공간데이터 모델뿐 아니라, 기본 위상공간데이터 모델을 제공해야 하며 또한 이러한 기본 위상공간모델을 다양한 분석기능에 맞게끔 확장이 필요하다. 본 논문에서는 개방형 GIS컴포넌트의 전체 아키텍쳐와 이와 연동되는 분석 컴포넌트로써 네트?p 분석, TIN 분석 컴포넌트에 대하여 살펴보고 또한 기본 기하 데이터 모델인 OGC Simple Feature Geometry의 확장과 연등방법에 대하여 논의해 볼 것이다.

• 한국주거학회논문집
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• 제22권2호
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• pp.101-109
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• 2011

Until now, several comparative approaches were developed within the studies of Korean, Chinese, and Japanese traditional housings. In those studies, however, each space in the traditional houses was only treated in individual and fragmentary manners, and they lacked the interpretation of the topological attribute of each space within a holistic structure organized by unit spaces, and of the cultural-behavioral meaning of them within a holistic space-use pattern of the housing. The topological attribute and behavioral meaning can be analyzed and interpreted with the quantitative spatial analysis method such as Space Syntax. This study aims to analyze the traditional housings in Korea, China and Japan in the holistic aspect of spatial structure using Space Syntax, and to compare the analysis results with relating the structural attributes to the space-use pattern. In this study, the 'Banga' in Chosun era, the 'Siheyuan' in Ming-Ching era, and the 'Shoinzukuri' in Edo era were selected as the analysis subjects. The integration indices were calculated from the convex maps representing the subjects, and the common and different attributes of the three subjects were defined through comparative analyses.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제25권4호
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• pp.296-311
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• 2021

Topological Data Analysis (TDA), a relatively new field of data analysis, has proved very useful in a variety of applications. The main persistence tool from TDA is persistent homology in which data structure is examined at many scales. Representations of persistent homology include persistence barcodes and persistence diagrams, both of which are not straightforward to reconcile with traditional machine learning algorithms as they are sets of intervals or multisets. The problem of faithfully representing barcodes and persistent diagrams has been pursued along two main avenues: kernel methods and vectorizations. One vectorization is the Betti sequence, or Betti curve, derived from the persistence barcode. While the Betti sequence has been used in classification problems in various applications, to our knowledge, the stability of the sequence has never before been discussed. In this paper we show that the Betti sequence is unstable under the 1-Wasserstein metric with regards to small perturbations in the barcode from which it is calculated. In addition, we propose a novel stabilized version of the Betti sequence based on the Gaussian smoothing seen in the Stable Persistence Bag of Words for persistent homology. We then introduce the normalized cumulative Betti sequence and provide numerical examples that support the main statement of the paper.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제27권4호
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• pp.324-341
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• 2023

Topological data analysis (TDA) is a data analysis technique, recently developed, that investigates the overall shape of a given dataset. The mapper algorithm is a TDA method that considers the connectivity of the given data and converts the data into a mapper graph. Compared to persistent homology, another popular TDA tool, that mainly focuses on the homological structure of the given data, the mapper algorithm is more of a visualization method that represents the given data as a graph in a lower dimension. As it visualizes the overall data connectivity, it could be used as a prediction method that visualizes the new input points on the mapper graph. The existing mapper packages such as Giotto-TDA, Gudhi and Kepler Mapper provide the descriptive mapper algorithm, that is, the final output of those packages is mainly the mapper graph. In this paper, we develop a simple predictive algorithm. That is, the proposed algorithm identifies the node information within the established mapper graph associated with the new emerging data point. By checking the feature of the detected nodes, such as the anomality of the identified nodes, we can determine the feature of the new input data point. As an example, we employ the fraud credit card transaction data and provide an example that shows how the developed algorithm can be used as a node prediction method.

• 정보처리학회논문지A
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• 제14A권5호
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• pp.263-268
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• 2007

본 논문에서는 Folded 하이퍼-스타 FHS(2n,n)의 위상적 성질들을 분석한다. 먼저, FHS(2n,n)이 최대고장허용도를 가짐을 보이고, double rooted 스패닝 트리를 이용한 방송 수행 시간이 2n-1임을 보인다. 그리고 FHS(2n,n)이 Folded 하이퍼큐브에 연장율 1로 임베딩 가능함을 보이고, Folded 하이퍼큐브가 FHS(2n,n)에 연장율 2, 밀집율 1로 임베딩 가능함을 보인다.

• 한국CDE학회논문집
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• 제5권4호
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• pp.293-300
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• 2000

The non-manifold geometric modeling technique is to improve design process and to Integrate design, analysis, and manufacturing by handling mixture of wireframe model, surface model, and solid model in a single data structure. For the non-manifold geometric modeling, Euler operators and other high level modeling methods are necessary. Boolean operation is one of the representative modeling method for the non-manifold geometric modeling. This thesis studies Boolean operations of non-manifold model with the data structure of selective storage. The data structure of selective storage is improved non-manifold data structure in that existing non-manifold data structures using ordered topological representation method always store non-manifold information even if edges and vortices are in the manifold situation. To implement Boolean operations for non-manifold model, intersection algorithm for topological cells of three different dimensions, merging and selection algorithm for three dimensional model, and Open Inventor(tm), a 3D toolkit from SGI, are used.

• 대한전기학회논문지:전기기기및에너지변환시스템부문B
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• 제50권2호
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• pp.79-85
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• 2001

In this paper, a novel Zero-Current-Transition (ZCT) technique, which provides Zero-Current-Switching (ZCS) turn-off of the main switch, the main diode and the auxiliary switch, is presented. The proposed auxiliary circuit consists of minimum elements only one auxiliary switch, resonant inductor and resonant capacitor. Also the reduced di/dt, which is obtained by resonant inductor, helps soft turn-on of the main switch. Besides, to eliminate the additional conduction loss and current stress on main switch, a topological variation was performed. The theoretical analysis and the operation principle of the new ZCT techniques are described in detail with a boost converter as an example. To verify the validity of the proposed ZCT techniques, the simulation and the experiment were performed under 1kW output power and 100kHz switching frequency.

• Bulletin of the Korean Chemical Society
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• 제16권11호
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• pp.1046-1056
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• 1995

A topological theory has been introduced to evaluate the degree of complexation and the viscosity of polymer complexes by extending the theory of Iliopoulos and Audebert for aqueous polymer solutions. The previous theory of Iliopoulos and Audebert has offered only a semiquantitative theoretical model for polymer complex systems, whereas our present work gives a general theoretical model applicable to all the polymer complex systems. Their theories considered only the physical property term caused by the displacement of complexed points between polymer solute chains, while our theory deals with all the physical effects, caused by the displacement of complexed points entangled points in polymer solute chains. There have been predicted the characteristics of physical properties from the expression. It is exposed that the predictive values show good agreement with the experimental data for polymer complexes.

• Bulletin of the Korean Chemical Society
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• 제17권3호
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• pp.245-253
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• 1996

A topological theory has been introduced to explain and evaluate the fractional volumes of system materials, the change of the weight and concentration of monomer molecules, molecular weight distribution, and interaction functions of polymer-polymer and polymer-oligomer, etc. for dispersion polymerization. The previous theory of Lu et al. has offered only an incomplete simulation model for dispersion polymer systems, whereas our present one gives a general theoretical model applicable to all the polymerization systems. The theory of Lu et al. considered only the physical property term caused by interaction between matters of low molecular weight (i.e., diluent, monomer, and oligomer) and polymer particles without dealing with physical properties caused by the structure of polymer networks in polymer particles, while our theory deals with all physical effect possible, caused by the displacement of not only entangled points but also junction points in polymer particles. The theoretically predictive values show good agreement with the experimental data for dispersion polymerization systems.

• Nonlinear Functional Analysis and Applications
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• 제27권4호
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• pp.839-853
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• 2022

We define the notions of ergodic shadowing property, $\underline{d}$-shadowing property and eventual shadowing property in terms of the topology of the phase space. Secondly we define these notions in terms of the compatible uniformity of the phase space. When the phase space is a compact Hausdorff space, we establish the equivalence of the corresponding definitions of the topological approach and the uniformity approach. In case the phase space is a compact metric space, the notions of ergodic shadowing property, $\underline{d}$-shadowing property and eventual shadowing property defined in terms of topology and uniformity are equivalent to their respective standard definitions.