• 충청수학회지
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• 제26권1호
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• pp.53-69
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• 2013

Topology may described a pattern of existence of elements of a given set X. The family ${\tau}(X)$ of all topologies given on a set X form a complete lattice. We will give some topologies on this lattice ${\tau}(X)$ using a topology on X and regard ${\tau}(X)$ a topological space. A topology ${\tau}$ on X can be regarded a map from X to ${\tau}(X)$ naturally. Such a map will be called topology field. Similarly we can also define pe-topology field. If X is a topological flow group with acting group T, then naturally we can get a another topological flow ${\tau}(X)$ with same acting group T. If the topological flow X is minimal, we can prove ${\tau}(X)$ is also minimal. The disjoint unions of the topological spaces can describe some topological systems (topological organisms). Here we will give a definition of topological organism. Our purpose of this study is to describe some properties concerning patterns of relationship between topology fields and topological organisms.

• 설비공학논문집
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• 제22권8호
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• pp.573-578
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• 2010

Topological matrix which reflects characteristics of network connectivity has been widely used in efficient solving for complicated flow network. Using topological matrix, one can easily define continuity at each node of flow network and make algorithm to automatically generate continuity equation of matrix form. In order to analyze flow network completely it is required to satisfy energy conservation in closed loops of flow network. Fundamental cycle retrieving algorithm based on graph theory automatically constructs energy conservation equation in closed loops. However, it is often accompanied by NP-complete problem. In addition, it always needs fundamental cycle retrieving procedure for every structural change of flow network. This paper proposes alternative mathematical method to analyze flow network without fundamental cycle retrieving algorithm. Consequently, the new mathematical method is expected to reduce solving time and prevent error occurrence by means of simplifying flow network analysis procedure.

• 충청수학회지
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• 제34권3호
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• pp.259-269
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• 2021

We shall study the following. Let 𝜙 be an expansive flow on a compact TVS-cone metric space (X, d). First, we give some equivalent ways of defining expansiveness. Second, we show that expansiveness is conjugate invariance. Finally, we prove that lim sup ${\frac{1}{t}}$ log v(t) ≤ h(𝜙), where v(t) denotes the number of closed orbits of 𝜙 with a period 𝜏 ∈ [0, t] and h(𝜙) denotes the topological entropy. Remark that in 1972, R. Bowen and P. Walters had proved this three statements for an expansive flow on a compact metric space [?].

• 대한기계학회논문집B
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• 제23권11호
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• pp.1426-1433
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• 1999

Topological and kinematical studies of the singular points found in flows around a surface-mounted cube in a channel are presented. Numerical simulation was carried out using high-resolution grid systems. Singular points(saddles and nodes) were found around the cube, which satisfy the topological rules suggested by Hunt et al. As the Reynolds number increases, the structure of vortices around the cube becomes complex and the number of singular points increases. Nevertheless, the rule governing the numbers of singular points is still valid. This confirms that our simulation is correct from topological and kinematical point of view, and enables one to infer complex flow patterns in our simulation.

• 지질공학
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• 제31권1호
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• pp.1-17
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• 2021

암체 내에 발달하는 단열계는 지반의 특성뿐만 아니라 유체의 유동특성을 제어하기 때문에 이들을 평가하는 것은 매우 중요하다. 따라서 이들을 정량화하기 위한 다양한 시도가 있어왔다. 그러나 기하학적 분석을 통해 획득한 정량적 매개변수인 단열밀도만으로는 단열계의 진화를 설명하기 어렵고, 단열계의 연결패턴 같은 암석 내 단열의 공간적 관계를 정량화하기 어렵다. 따라서 최근 기존에 이뤄지던 기하학적 분석과 함께 위상기하 분석을 통한 단열계의 특성화 필요성이 대두되고 있다. 그러나 암체에의 다양한 적용성에도 불구하고, 아직 국내에서는 단열계의 위상기하 분석이 지질매체에 적용되어 연구된 적은 거의 없다. 따라서 본 연구에서는 최근 단열연구 분야에서 주목받고 있는 단열계 위상기하 분석의 정의와 개념, 위상기하 분석과 관련된 그래프이론, 그리고 이들을 적용하는 방법에 대해 간략히 소개하고자 한다. 이러한 위상기하학적 연구방법이 단열계의 분석에 사용된다면 암체 내 단열을 따라 흐르는 지하수나 석유 저류암의 유동특성과 단열계의 진화를 정량화하는데 유용하게 사용될 수 있다. 또한 방사성폐기물처분장과 같이 유체의 유동특성이 중요한 주요 시설물의 부지선정 등에 유용하게 활용될 수 있을 것이다.

• 대한수학회지
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• 제57권5호
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• pp.1079-1101
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• 2020

This work is concerned with a geometric inverse problem in fluid mechanics. The aim is to reconstruct an unknown obstacle immersed in a Newtonian and incompressible fluid flow from internal data. We assume that the fluid motion is governed by the Stokes-Brinkmann equations in the two dimensional case. We propose a simple and efficient reconstruction method based on the topological sensitivity concept. The geometric inverse problem is reformulated as a topology optimization one minimizing a least-square functional. The existence and stability of the optimization problem solution are discussed. A topological sensitivity analysis is derived with the help of a straightforward approach based on a penalization technique without using the classical truncation method. The theoretical results are exploited for building a non-iterative reconstruction algorithm. The unknown obstacle is reconstructed using a levelset curve of the topological gradient. The accuracy and the robustness of the proposed method are justified by some numerical examples.

• 대한전기학회논문지
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• 제36권11호
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• pp.769-776
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• 1987

This paper deals with the topological observability analysis and the development of an observable island identification algorithm for state estimation in power systems, by using the incidence matrix and bus voltage grouping. An analogy of the DC power flow method to the DC circuit analysis is introduced, and all the relationships between power flows and phase angles are replaced by the corresponding current-voltage relation. As a result, a set of topological measurement equation expressed in the form of the incidince matrix is derived for the topological analysis, and the observability test is carried out by examining the rand of the measuremint matrix. The integer Gauss elimination method is introduced in the determination of matrix rand, so that the proposed observability test yields a precise observability criterion without any nearly-zero pivot problem encountered in the conventional algorithm. Also, an observable island identification algorithm reduced its computational time in comparision with the conventional algorithms. The proposed algorithms have been tested for sample systems, and their practicability has verified.

• 정보보호학회논문지
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• 제11권1호
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• pp.43-54
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• 2001

본 논문에서는 다단계 공간 데이터베이스 시스템에서 비빌 위상 경로(covert topology channel)를 해결할 목적으로 공간 다중인스턴스화(polyinstantiation fur spatial data)에 대해 연구한다. 위상 구조를 갖는 공간 데이터베이스 시스템은 공간 데이터와 서로 인접한 공간 데이터를 이용하여 다양한 공간 분석을 수행하여야 한다. 그러나, 공간 데이터베이스에서 공간 데이터간의 위상 정보를 지원하는 경우 위상관계 의한 정보의 노출(information flow)이 문제가 된다. 즉, 공간 데이터베이스를 갖는 지리정보시스템의 경우 대부분의 응용업무가 그래픽 사용자 인터페이스를 사용하고 있기 때문에 기밀이 요구되어지는 공간 데이터베이스의 경우, 출력되어진 객체들의 위치 정보나 인접한 객체와의 위상관계를 통해서 많은 정보가 노출되어질 위험이 있으므로 엄격한 사용자의 접근제어가 요구되어진다. 본 논문에서는 이러 한 문제점을 해결하기 위해 MLS/SRDM(Multi Level Security/Spatial Relational Data Model)켤 설계하고 공간 데이터의 위 상관계로 인해 생기는 정보 유출을 방지하기 위해 공간 다중인스턴스화를 제안한다

• 한국환경과학회지
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• 제21권4호
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• pp.471-478
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• 2012

In this study, the flow characteristic analysis at the curved-channel of the actual channel section is compared and reviewed using the 2D RMA-2 model and the 3D FLOW-3D model. the curve section with curve rate 1.044 in the research section is analyzed applying the frequency of he project flood of 100 years. According to the result, the issue for the application of the FLOW-3D Model's three-dimensional numeric analysis result to the actual river is found to be reviewed with caution. Also, application of the 3D model to the wide basin's flood characteristic is determined to be somewhat risky. But, the applicability to the hydraulic property analysis of a partial channel section and the impact analysis and forecast of hydraulic structure is presumed to be high. In addition, if the parameters to reflect the vegetation of basin and the actual channel, more accurate topological measurement data and the topological data with high closeness to the current status are provided, the result with higher reliability is considered to be drawn.

• 대한수학회보
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• 제55권3호
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• pp.851-863
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• 2018

We derive lower bounds of the scalar curvature on complete non-compact gradient Yamabe solitons under some integral curvature conditions. Based on this, we prove that potential functions of Yamabe solitons have at most quadratic growth for distance function. We also obtain a finite topological type property on complete shrinking gradient Yamabe solitons under suitable scalar curvature assumptions.