• Nonlinear Functional Analysis and Applications
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• 제28권4호
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• pp.929-942
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• 2023

In this paper, we discuss topological ergodic shadowing property and topological pseudo-orbital specification property of iterated function systems(IFS) on uniform spaces. We show that an IFS on a sequentially compact uniform space with topological ergodic shadowing property has topological shadowing property. We define the notion of topological pseudo-orbital specification property and investigate its relation to topological ergodic shadowing property. We find that a topologically mixing IFS on a compact and sequentially compact uniform space with topological shadowing property has topological pseudo-orbital specification property and thus has topological ergodic shadowing property.

• KIEE International Transactions on Power Engineering
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• 제4A권1호
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• pp.18-25
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• 2004

This paper proposes a totally new method in the chaos characteristics' analysis of power systems, the introduction of topological invariants. Using a return histogram, a bifurcation graph was drawn. As well, the periodic orbits and topological invariants - the local crossing number, relative rotation rates, and linking number during the process of period-doubling bifurcation and chaos were extracted. This study also examined the effect on the topological invariants when the sensitive parameters were varied. In addition, the topological invariants of a three-dimensional embedding of a strange attractor were extracted and the result was compared with those obtained from differential equations. This could be a new approach to state detection and fault diagnosis in dynamical systems.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2003년도 추계학술대회 논문집 전력기술부문
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• pp.297-299
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• 2003

This paper proposes a totally new method in the chaos characteristics analysis of power systems, the introduction of topological invariants. Using a return histogram the bifurcation graph was drawn, the periodic orbits and topological invariants the local crossing number, relative rotation rates, and linking number during the process of period-doubting bifurcation and chaos were extracted. This study also examined the effect on the topological invariants when the sensitive parameters were varied. In addition, the topological invariants of a three-dimensional embedding of the strange attractor was extracted and the result was compared with those obtained from differential equations. This could be a new way for a state detection and fault diagnosis in a dynamical system.

• 한국정보통신설비학회:학술대회논문집
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• 한국정보통신설비학회 2006년도 하계학술대회
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• pp.166-169
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• 2006

High Frequency에서 회로를 해석할 때 기존의 Full-wave Analysis Method와는 다른 Topological Analysis Method에 기반한 BLT equation을 도입하여 새로운 해석을 시도해본다. 이 해석방법은 기존의 방법과는 다르게 회로를 junction과 node로 구분하여 회로 방정식을 만들어 해석을 하는 새로운 방식이다. 이 논문에서는 간단한 회로를 제작하여 BLT equation과 기존의 Simulation Tool을 사용한 해석과 실제 실험결과와 비교하면서 BLT equation을 검증하고, 실제적인 적용 회로를 선정하여 해석을 시도하였다.

• Korean Journal of Mathematics
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• 제29권4호
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• pp.649-664
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• 2021

There have been numerous efforts to provide legal information to the general public easily. Most of the existing legal information services are based on keyword-oriented legal ontology. However, this keyword-oriented ontology construction has a sense of disparity from the relationship between the laws used together in actual cases. To solve this problem, it is necessary to study which laws are actually used together in various judicial precedents. However, this is difficult to implement with the existing methods used in computer science or law. In our study, we analyzed this by using topological data analysis, which has recently attracted attention very promisingly in the field of data analysis. In this paper, we applied the the Mapper algorithm, which is one of the topological data analysis techniques, to visualize the relationships that laws form organically in actual precedents.

• 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.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2003년도 춘계학술대회
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• pp.822-827
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• 2003

Topological maps have drawn more attention recently because they are compact, provide natural interfaces, and are applicable to path planning easily. To build a topological map incrementally, Voronoi diagram was used by many researchers. The Voronoi diagram, however, has difficulty in applying to arbitrarily shaped objects and needs long computation time. In this paper, we present a new method for global topological map from the local topological maps incrementally. The local topological maps are created through a thinning algorithm from a local grid map, which is built based on the sensor information at the current robot position. A thinning method requires simpler computation than the Voronoi diagram. Localization based on the topological map is usually difficult, but additional nodes created by the thinning method can improve localization performance. A series of experiments have been conducted using a two-wheeled mobile robot equipped with a laser scanner. It is shown that the proposed scheme can create satisfactory topological maps.

• Steel and Composite Structures
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• 제21권6호
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• pp.1389-1410
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• 2016

This paper proposes a hybrid of topological derivative-based level set method (LSM) and isogeometric analysis (IGA) for structural topology optimization. In topology optimization a significant drawback of the conventional LSM is that it cannot create new holes in the design domain. In this study, the topological derivative approach is used to create new holes in appropriate places of the design domain, and alleviate the strong dependency of the optimal topology on the initial design. Furthermore, the values of the gradient vector in Hamilton-Jacobi equation in the conventional LSM are replaced with a Delta function. In the topology optimization procedure IGA based on Non-Uniform Rational B-Spline (NURBS) functions is utilized to overcome the drawbacks in the conventional finite element method (FEM) based topology optimization approaches. Several numerical examples are provided to confirm the computational efficiency and robustness of the proposed method in comparison with derivative-based LSM and FEM.

• Bulletin of the Korean Chemical Society
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• 제16권2호
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• pp.169-180
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• 1995

A topological theory is introduced to extend Tsenoglou's theory to polymer blends having temporary and permanent networks composed of multicomponent polymers which have miscible and flexible chains. The topological theory may estimate the values of free elastic energy, the molecular weight between entanglements, and the equilibrium shear moduli, and it may establish more correctly the topological relations among these physical quantities. Through such introduction of the topological theory, there can be topologically analyzed the mixing law for the rubbery plateau modulus of a fluid polymer blend, and there can be considered the topological relationship to the equilibrium modulus of an interpenetrating polymer network containing trapped entanglements and dangling segments. The theoretically predictive values are compared and show good agreement with the experimental data for several miscible polymer blends.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2006년도 정기 학술대회 논문집
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• pp.299-306
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• 2006

Using a level set method and topological derivatives, a topological shape optimization method that is independent of an initial design is developed for linearly elastic structures. In the level set method, the initial domain is kept fixed and its boundary is represented by an implicit moving boundary embedded in the level set function, which facilitates to handle complicated topological shape changes. The 'Hamilton-Jacobi (H-J)' equation and computationally robust numerical technique of 'up-wind scheme' lead the initial implicit boundary to an optimal one according to the normal velocity field while minimizing the objective function of compliance and satisfying the constraint of allowable volume. Based on the asymptotic regularization concept, the topological derivative is considered as the limit of shape derivative as the radius of hole approaches to zero. The required velocity field to update the H -J equation is determined from the descent direction of Lagrangian derived from optimality conditions. It turns out that the initial holes is not required to get the optimal result since the developed method can create holes whenever and wherever necessary using indicators obtained from the topological derivatives. It is demonstrated that the proper choice of control parameters for nucleation is crucial for efficient optimization process.