• 호남수학학술지
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• 제32권3호
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• pp.375-387
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• 2010

The paper studies an existence problem of a (generalized) universal covering space over a digital wedge with a compatible adjacency. In algebraic topology it is well-known that a connected, locally path connected, semilocally simply connected space has a universal covering space. Unlike this property, in digital covering theory we need to investigate its digital version which remains open.

• 호남수학학술지
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• 제25권1호
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• pp.153-162
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• 2003

Recently, the generalized digital $(k_{0},\;k_{1})$-continuity and its properties are investigated. Furthermore, the k-type digital fundamental group for digital image has been studies with the generalized k-adjacencies. The main goal of this paper is to find some properties of the k-type digital fundamental group of Boxer and to investigate some properties of minimal simple closed k-curves with relation to their embedding into some spaces in ${\mathbb{Z}}^n(2{\leq}n{\leq}3)$.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제18권2호
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• pp.141-155
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• 2011

We compute zeta functions of 1-solenoids. When our 1-solenoid is nonorientable, we compute Artin-Mazur zeta function and Lefschetz zeta function of the 1-solenoid and its orientable double cover explicitly in terms of adjacency matrices and branch points. And we show that Artin-Mazur zeta function of orientable double cover is a rational function and a quotient of Artin-Mazur zeta function and Lefschetz zeta function of the 1-solenoid.

• 호남수학학술지
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• 제30권4호
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• pp.589-602
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• 2008

As a survey-type article, the paper reviews various digital topological utilities from digital covering theory. Digital covering theory has strongly contributed to the calculation of the digital k-fundamental group of both a digital space(a set with k-adjacency or digital k-graph) and a digital product. Furthermore, it has been used in classifying digital spaces, establishing almost Van Kampen theory which is the digital version of van Kampen theorem in algebrate topology, developing the generalized universal covering property, and so forth. Finally, we remark on the digital k-surface structure of a Cartesian product of two simple closed $k_i$-curves in ${\mathbf{Z}}^n$, $i{\in}{1,2}$.

• 대한수학회지
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• 제46권4호
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• pp.841-857
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• 2009

In this paper, we give and study the notion of computer topological function space between computer topological spaces with $k_i$ adjacency, i $\in$ {0, 1}. Using this notion, we study various properties of topologies of a computer topological function space.

• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.505-512
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• 2005

In this paper, we introduce another statement of a digital $(k_{0}, k_{1})-homeomorphism$ which is suitable for an approach to write an efficient algorithm for discriminating digital images with respect to the digital $(k_{0}, k_{1})-homeomorphism$.

• 응용통계연구
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• 제33권2호
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• pp.115-122
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• 2020

K-평균 클러스터링은 매우 널리 사용되고 있으나 유사도가 구면체 또는 타원체로 정의되어 각 클러스터가 볼록 집합 형태인 자료에는 좋은 결과를 주지만 그렇지 않은 경우에는 매우 형편 없는 결과를 나타낸다. 스펙트럴 클러스터링은 K-평균 클러스터링의 단점을 잘 보완해 줄 뿐아니라 여러 형태의 자료나 고차원 자료 등에 대해서도 좋은 결과를 나타내서 최근 인공 신경망 모형에 많이 이용되고 있다. 하지만, 개선되어야 할 단점도 여전히 많다. 본 논문에서는 스펙트럴 클러스터링에 대해 알기 쉽게 소개하고, 클러스터 갯수의 추정, 척도모수의 추정, 고차원 자료의 차원 축소 등 스펙트럴 클러스터링에 대한 최근의 연구 동향을 소개한다.

• 한국CDE학회논문집
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• 제1권1호
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• pp.1-19
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• 1996

Non-manifold topological representations can provide a single unified representation for mixed dimensional models or cellular models and thus have a great potential to be applied in many application areas. Various boundary representations for non-manifold topology have been proposed in recent years. These representations are mainly interested in describing the sufficient adjacency relationships and too redundant as a result. A model stored in these representations occupies too much storage space and is hard to be manipulated. In this paper, we proposed a compact hierarchical non-manifold boundary representation that is extended from the half-edge data structure for solid models by introducing the partial topological entities to represent some non-manifold conditions around a vertex, edge or face. This representation allows to reduce the redundancy of the existing schemes while full topological adjacencies are still derived without the loss of efficiency. To verify the statement above, the storage size requirement of the representation is compared with other existing representations and present some main procedures for querying and traversing the representation. We have also implemented a set of the generalized Euler operators that satisfy the Euler-Poincare formula for non-manifold geometric models.

• 한국정밀공학회지
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• 제13권7호
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• pp.100-114
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• 1996

In order to create a solid model more efficiently for a plastic or sheet metal product with a thin and constant thickness, various methods have been proposed up to now. One of the most typical approaches is to create a sheet model initially and then transform it into a solid model automatically for a given thickness. The sheet model as well as the transitive model in sheet modeling procedure is a non-manifold model. However, the previous methods adopted the boundary representations for a solid model as their topological framework. Thus, it is difficult to represent the exact adjacency relationship between topological entities and to implement the topological operations for sheet modeling and the transformation procedure of a sheet into a solid. In this paper, we proposed a sheet modeling system based on a non-manifold topological representation which can represent solids, sheets, wireframes, and their mixture. A set of generalized Euler operators for non-manifold topology as well as the sheet modeling capabilities including adding, bending, and punching functions are provided for easy modeling of sheet objects, and they are perfomed interactively with a two dimensional curve editor. Once a sheet model is completed, it can be transformed into a solid automatically. The transformation procedure is composed of the offset functions and the Boolean operations of sheet models, and it is even more comprehensive and easier to be implemented than the precious methods.