• 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.

• Korean Journal of Mathematics
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• 제11권1호
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• pp.45-49
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• 2003

We introduce the $k_0$-proximity space as a generalization of the Efremovi$\check{c}$-proximity space. We try to show that $k_0$-proximity structure lies between topological structures and uniform structure in the sense that all topological invariants are $k_0$-proximity invariants and all $k_0$-proximity invariants are uniform invariants.

• EDISON SW 활용 경진대회 논문집
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• 제3회(2014년)
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• pp.516-520
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• 2014

Fractional quantum Hall Effect (FQSH) is one of most fundamental issues in condensed matter physics, and the Topological insulator becomes its prominent applications. This article reviews the general frameworks of these development and the physical properties. FQSH states and topological insulators are supposed to be topologically invariant under the minor change of geometrical shape or internal impurities. The phase transitions involved in this phenomena are known not to be explained in terms of symmetry breaking or Landau-Ginsburg theory. The new type of phase transitions related to topological invariants has acquired new name - topological phase transition. The intuitive concepts and the other area having same type of phase transitions are discussed.

• 한국정보과학회논문지:시스템및이론
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• 제26권8호
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• pp.999-1007
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• 1999

이 논문은 재귀원형군 G(2^m , 2^k )를 그래프 이론적 관점에서 고찰하고 정점이 서로소인 사이클과 그래프 invariant에 관한 위상 특성을 제시한다. 재귀원형군은 1 에서 제안된 다중 컴퓨터의 연결망 구조이다. 재귀원형군 {{{{G(2^m , 2^k )가 길이 사이클을 가질 필요 충분 조건을 구하고, 이 조건하에서 G(2^m , 2^k )는 가능한 최대 개수의 정점이 서로소이고 길이가l`인 사이클을 가짐을 보인다. 그리고 정점 및 에지 채색, 최대 클릭, 독립 집합 및 정점 커버에 대한 그래프 invariant를 분석한다.Abstract In this paper, we investigate recursive circulant G(2^m , 2^k ) from the graph theory point of view and present topological properties of G(2^m , 2^k ) concerned with vertex-disjoint cycles and graph invariants. Recursive circulant is an interconnection structure for multicomputer networks proposed in 1 . A necessary and sufficient condition for recursive circulant {{{{G(2^m , 2^k ) to have a cycle of lengthl` is derived. Under the condition, we show that G(2^m , 2^k ) has the maximum possible number of vertex-disjoint cycles of length l`. We analyze graph invariants on vertex and edge coloring, maximum clique, independent set and vertex cover.

• 대한수학회지
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• 제33권4호
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• pp.1101-1114
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• 1996

In Riemannian geometry, it is one of the important things to study the topological or geometric invariants of manifolds since they characterize the topology of manifolds.

• Kyungpook Mathematical Journal
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• 제59권4호
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• pp.797-820
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• 2019

For every tree T, we introduce a topological invariant, called the T-cross-index, for connected graphs. The T-cross-index of a graph is a non-negative integer or infinity according to whether T is a tree basis of the graph or not. It is shown how this cross-index is independent of the other topological invariants of connected graphs, such as the Euler characteristic, the crossing number and the genus.

• Bulletin of the Korean Chemical Society
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• 제25권2호
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• pp.253-259
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• 2004

Some new topological indices based on the distance matrix and Randic connectivity (as graph invariants) are proposed. The calculation of these indices is simple and they have good discriminating ability toward alkanes. Incorporating the number of carbon atoms to one of the calculated indices gives a highly correlating topological index (Sh index) which found to correlate with selected physicochemical properties of wide range of alkanes, specially, their boiling points. Most of the investigated properties are well modeled (with $r^2$> 0.99) by the Sh index. Meanwhile, the resulting regressions were compared with the results based on the well-established Randic and newly reported Xu indices and, in most cases, better results were obtained by the Sh index. Moreover, multiple linear regression analysis of the alkane properties via calculated indices gives highly correlating models with low standard errors.

• 한국인터넷방송통신학회논문지
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• 제16권1호
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• pp.291-299
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• 2016

본 논문에서는 임의의 주기적인 현상이나 특성은 위상구조와 밀접한 관련이 있음을 추론하고 이를 실험적으로 확인한다. 실험대상으로 주기적 특성이 있는 다양한 악기음을 선택하여 이를 유클리드 공간에 임베딩하고 이로부터 호몰로지 군을 계산하여 위상특성을 분석한다. 이를 위하여, 파형신호에서 추출한 패치모음을 패치 그래프로 구성한 다음, 대표적인 다양체 학습 방식인 통근시간 임베딩 기법을 이용하여 기하구조로 변환한다. 스펙트럼이 시간에 따라 가변적인 파형신호를 통근시간 임베딩할 때, 그에 따라 생성되는 기하구조는 변화하지만 그 신호 고유의 내재된 위상구조는 거의 변하지 않는다. 본 논문에서는 임베딩 데이터의 일부를 표본화하여 단순 복합체를 구성한 다음 이로부터 호몰로지를 계산하여 임베딩 기하구조의 위상특성을 분석하고, 이의 활용방안을 논의한다.

• 한국멀티미디어학회논문지
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• 제19권2호
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• pp.146-154
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• 2016

This paper presents methods to analyze the topological structures of the spaces composed of patches extracted from waveform signals, which can be applied to the classification of signals. Commute time embedding is performed to transform the patch sets into the corresponding geometries, which has the properties that the embedding geometries of periodic or quasi-periodic waveforms are represented as closed curves on the low dimensional Euclidean space, while those of aperiodic signals have the shape of open curves. Persistent homology is employed to determine the topological invariants of the simplicial complexes constructed by randomly sampling the commute time embedding of the waveforms, which can be used to discriminate between the groups of waveforms topologically.