• Journal of the Chungcheong Mathematical Society
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• v.26 no.1
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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.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.22 no.8
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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.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.3
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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 [?].

• Transactions of the Korean Society of Mechanical Engineers B
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• v.23 no.11
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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.

• The Journal of Engineering Geology
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• v.31 no.1
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• pp.1-17
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• 2021

It is important to evaluate the fracture network in a rock volume because fractures control the ground conditions and fluid flow characteristics. Therefore, various attempts have been made to quantify fracture networks to better understand ground and flow conditions. The use of fracture density alone (a quantitative parameter based on geometric analysis) does not fully explain the evolution of fracture networks, or quantify the spatial relationship (e.g. connectivity) of fractures in a rock mass. Therefore, the need for fracture network characterization based on topological analysis has recently emerged. In Korea however, the topological analysis of fracture networks within a rock mass has rarely been studied. As such, the definition of the topological analysis of fracture networks and the graph theory related to the topological analysis are briefly summarized in this study. We also introduce an application method for these analyses to fracture characterization. If the topological method is used for the analysis of fracture networks, it can also be adopted to analyze fluid flow characteristics of groundwater, characterize petroleum reservoirs, and analyze the evolution of a fracture network. In addition, topological analysis can be useful for site selection of major facilities such as nuclear waste disposal sites because it can be used to evaluate the stability of the potential sites.

• Journal of the Korean Mathematical Society
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• v.57 no.5
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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.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.36 no.11
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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.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.11 no.1
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• pp.43-54
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• 2001

In this paper we study the use of polyinstantiation for spatial data, for the purpose of solving cover in topology channel in multilevel secure spatial database systems. Spatial database system with topological structure has a number of spatial analysis function using spatial data and neighbored one\`s each other. But. it has problems that information flow is occurred by topological relationship in spatial database systems. Geographic Information System(CIS) must be needed mandatory access control because there ,are many information flow through positioning information And topological relationship between spatial objects. Moreover, most GIS applications also graphe user interface(GUI). In addressing these problems, we design the MLS/SRDM(Multi Level Security/Spatial Relational Data Model) and propose polyinstantiation for spatial data for solving information flow that occurred by toplogical relationship of spatial data.

• Journal of Environmental Science International
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• v.21 no.4
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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.

• Bulletin of the Korean Mathematical Society
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• v.55 no.3
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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.