• 충청수학회지
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• 제23권4호
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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.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2004년도 ICCAS
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• pp.2017-2022
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• 2004

Data association is a process that matches a recent observation with known data set, which is used for the localization of mobile robots. Edges in topological maps have rich information which can be used for the data association. However, no systematic approach on using the edge data for data association has been reported. This paper proposes a systematic way of utilizing the edge data for data association. First, we explain a Local Generalized Voronoi Angle(LGA) to represent the edge data in 1-dimension. Second, we suggest a key factor extraction procedure from the LGA to reduce the number by $2^7-2^8$ times, for computational efficiency using the wavelet transformation. Finally we propose a way of data association using the key factors of the LGA. Simulations show that the proposed data association algorithm yields higher probability for similar edges in computationally efficient manner.

• 한국CDE학회논문집
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• 제1권2호
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• pp.97-106
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• 1996

Existing CAD systems do not provide advanced functions for automatic checking design and drafting errors in mechanical drawings. If the knowledge of checking in mechanical ddrsfting can be implemented into computers, CAD systems could automatically check for design and drafting errors. This paper describes a method for systematic checking of dimension errors. such as deficiency and/or redundancy of dimension input-errors in dimension figures and symbols, etc. The logic for finding dimensional errors is written by using a proccedural language. A geometric model and a topological-graph model are used in this method. Checking for deficiency and redundancy of dimensions is based upon graph Theory.

• 한국경제지리학회지
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• 제10권4호
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• pp.427-443
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• 2007

본 연구의 목적은 현재 서울시를 포함한 수도권 지역에서 가장 높은 수송분담율을 차지하고 있는 지하철망 상 통행흐름의 시 공간적 구조를 밝히고, 그러한 통행흐름과 토지이용의 관계성을 밝히는 것이다. 특히 본 연구에서는 지난 2004년 7월 이후 수도권 대중교통이용자의 대부분이 이용하고 있는 교통카드 통행거래자료 중 매년 주중 하루치의 통행 트랜잭션 데이터베이스에 대하여 데이터마이닝 기법을 적용하여 지난 4년간 수도권 지하철망 상 통행흐름의 위상학적 구조를 비교분석하였다. 또한 하루 중 시간대별 통행흐름의 공간적 특징을 분석하기 위하여 하루를 아침 출근시간대, 낮 시간대, 저녁 퇴근 시간대로 나누어 수도권 지하철망 상의 각 지하철역의 시간대별 출발통행량과 도착통행량을 산출하고, GIS를 이용하여 그 공간적 패턴을 비교한 결과 시간대별로 확연한 차이가 나타남을 확인하였다. 그리고 지하철 통행흐름의 위상학적 구조와 토지이용과의 관계성을 밝히기 위하여 각 지하철역의 시간대별 출발 도착 통행량과 그 지하철역 주변지역의 토지이용상태를 반영하는 지리적 변수들 간의 상관관계분석과 다중회귀분석을 실시하였으며, 분석 결과 시간대별 출발 통행량 및 도착 통행량 관계를 설명하는 선형 대수식을 도출하였다. 함수식의 적합성 판명을 위하여 공선성진단과 이분산성분석을 실시하였다.

• 대한화학회지
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• 제57권2호
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• pp.176-203
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• 2013

In this work is induced a new topology of solutions of chemical equations by virtue of point-set topology in an abstract stoichiometrical space. Subgenerators of this topology are the coefficients of chemical reaction. Complex chemical reactions, as those of direct reduction of hematite with a carbon, often exhibit distinct properties which can be interpreted as higher level mathematical structures. Here we used a mathematical model that exploits the stoichiometric structure, which can be seen as a topology too, to derive an algebraic picture of chemical equations. This abstract expression suggests exploring the chemical meaning of topological concept. Topological models at different levels of realism can be used to generate a large number of reaction modifications, with a particular aim to determine their general properties. The more abstract the theory is, the stronger the cognitive power is.

• 호남수학학술지
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• 제27권3호
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• pp.477-485
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• 2005

Let ($M^n$, g) be a compact oriented Riemannian manifold. It has been conjectured that every solution of the equation $z_g=D_gdf-{\Delta}_gfg-fr_g$ is an Einstein metric. In this article, we deal with the 3 dimensional case of the equation. In dimension 3, if the conjecture fails, there should be a stable minimal hypersurface in ($M^3$, g). We study some necessary conditions to guarantee that a stable minimal hypersurface exists in $M^3$.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제10권2호
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• pp.103-118
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• 2003

We estimate the stable rank of twisted crossed products of $C^{*}-algebras$ by topological Abelian groups. As an application we estimate the stable rank of twisted crossed products of $C^{*}-algebras$ by solvable Lie groups. In particular, we obtain the stable rank estimate of twisted group $C^{*}-algebras$ of solvable Lie groups by the (reduced) dimension and (generalized) rank of groups.

• 대한수학회지
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• 제58권6호
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• pp.1421-1431
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• 2021

In this paper we study the preservation of various notions of expansivity in discrete dynamical systems and the induced map for n-fold symmetric products and hyperspaces. Then we give a characterization of a compact metric space admitting hyper N-expansive homeomorphisms via the topological dimension. More precisely, we show that C⁰-generically, any homeomorphism on a compact manifold is not hyper N-expansive for any N ∈ ℕ. Also we give some examples to illustrate our results.

• 한국수학교육학회지시리즈A:수학교육
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• 제6권2호
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• pp.1-9
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• 1968

In mathematics, a definition must have authentic reasons to be defined so. On defining geometric figures, there must be adequencies in sequel and consistency in the concepts of figures, though the dimensions of them are different. So we can avoid complicated thoughts from the study of geometric property. From the texts of SMSG, UICSM and others, we can find easily that the same concepts are not kept up on defining some figures such as ray and segment on a line, angle and polygon on a plane, and polyhedral angle and polyhedron on a 3-dimensionl space. And the measure of angle is not well-defined on basis of measure theory. Moreover, the concepts for interior, exterior, and frontier of each figure used in these texts are different from those of general topology and algebraic topology. To avoid such absurdness, I myself made new terms and their definitions, such as 'gan' instead of angle, 'polygonal region' instead of polygon, and 'polyhedral solid' instead of polyhedron, where each new figure contains its interior. The scope of this work is hmited to the fundamental idea, and it merely has dealt with on the concepts of measure, dimension, and topological property. In this case, the measure of a figure is a set function of it, so the concepts of measure is coincided with that of measure theory, and we can deduce the topological property for it from abstract stage. It also presents appropriate concepts required in much clearer fashion than traditional method.

• 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.