• Proceedings of the Korean Information Science Society Conference
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• 1998.10c
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• pp.78-80
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• 1998

본 논문은 일차원의 시계열 데이터를 입력을 하여 위상공간 재구성 과정을 거쳐 다차원 위상공간상에서 프랙탈 차원을 계산하는 효율적인 방법을 제안한다. 프랙탈 차원의 추정에 소요되는 계산량을 줄이기 위해 로그 연산을 비트 연산으로 대체하고, 거리계산의 순서를 바꿈으로써 위상공간의 차원에 무관한 상수 시간의 계산복잡도를 가지는 알고리즘을 구현하였다. 또한 최소절단자승 추정기법을 적용하여 로그-로그 그래프 상에서의 기울기 추정을 함으로써 프랙탈 차원의 추정치에 대한 정확도를 높였다. 참값이 알려진 시계열 데이터에 대한 차원 추정 실험을 통하여 제안된 방법의 정확성을 보였다.

• Proceedings of the KSME Conference
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• 2005.11a
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• pp.158.1-158.1
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• 2005

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.43 no.8
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• pp.692-698
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• 2015

This paper represents a trajectory design and analysis technique which uses invariant manifolds of the circular restricted three body problem. Instead of the classical patched conic method based on 2-body problem, the equation of motion and dynamical behavior of spacecraft in the circular restricted 3-body problem are introduced, and the characteristics of Lyapunov orbits near libration points and their invariant manifolds are covered in this paper. The trajectories from/to Lyapunov orbits are numerically generated with invariant manifolds in the Earth-moon system. The trajectories in the Sun-Jupiter system are also analyzed with various initial conditions in the boundary surface. These methods can be effectively applied to interplanetary trajectory designs.

• Journal of Digital Contents Society
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• v.16 no.6
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• pp.909-916
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• 2015

This paper presents a method to display the 3D vector fields by analyzing phase space. This method is based on the connections between ordinary differential equations and the topology of vector fields. The phase space analysis should be geometric interpolation of an autonomous system of equation in the form of the phase space. Every solution of it system of equations corresponds not to a curve in a space, but the motion of a point along the curve. This analysis is the basis of this paper. This new method is required to decompose the hexahedral cell into five or six tetrahedral cells for 3D vector fields. The critical points can be easily found by solving a simple linear system for each tetrahedron. The tangent curves can be integrated by finding the intersection points of an integral curve traced out by the general solution of each tetrahedron and plane containing a face of the tetrahedron.

• Spatial Information Research
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• v.15 no.1
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• pp.35-52
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• 2007

Three-dimensional GIS, which provides spatial information through expression techniques of virtual reality close to the real world and the web, is one of the fields that attract a new attention. In particular, Open GIS Consortium(OGC) announced a topological relationship specification of spatial object which supports interoperability while interest in interoperability of spatial data is increasing. However, this specification is limited to two-dimensional spatial object. So this research established a topological relationship of three-dimensional spatial object in order to improve urban landscape and provide a foundation to use GIS. Based on this, this study proposes ways to visualize landscape information which is appropriate for new town's circumstances. It can be concluded that this research has a bigger meaning since it established a base of sharing information about realistic urban landscape that can be accessed regardless of place and time.

• The KIPS Transactions:PartD
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• v.12D no.6 s.102
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• pp.837-848
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• 2005

A multi-scale database is a set of spatial database, covering same geographic area with different scales and it can be derived from pre-existing databases. In the derivation processes of a new multi-scale spatial database, the geometries and topological relations on the source database can be transformed and the transformation can be the cause of the lack of integrity Therefore, it is necessary to assess the transformation whether it is consistent or not after the derivation process of a new multi-scale database. Thus, we propose assessment methods for the topological consistency between a source database and a derived multi-scale database in this paper. In particular, we focus on the case that 2-dimensional objects are collapsed to 1-dimensional ones in the derivation process of a multi-scale database. We also describe implementation of the assessment methods and show the results of the implementation with experimental data.

• Communications of the Korean Mathematical Society
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• v.15 no.2
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• pp.197-231
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• 2000

평형문제들에서의 기본적인 정리들이 일반화 볼록공간에서 어떻게 확장되는가를 보인다. KKM 이론의 중요한 정리들 대부분이 위상벡터공간에서의 선형성을 가정하지 않아도 위상적인 성질만으로 성립한다. 이같은 정리들의 예로는 KKM정리, von Neumann의 최소최대정리와 교차정리, Nash의 평형정리, 여러 가지 부동점정리, 극대원정리, Ky Fan의 최소최대부등식, 변분부등식들, 최량근사정리, 일반화 의사평형문제들의 해의 존재정리들이 있다.

• Proceedings of the Korean Institute Of Construction Engineering and Management
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• 2007.11a
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• pp.876-879
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• 2007

Large scale composition facility gives in commerce and space structure effect. therefore, this study will estimating locational value of the commercial facilities by separating space analyze to the topological property, predict a pattern and distribution of passenger's routes through the space syntax on the basis of analysis about the topological property which quantitatively using a estimating tool. Moreover, this study should suggest some of present issues at the aspects of inside city plan and design fitting the internalization of street for propelling efficient the locational strategy.

• Proceedings of the Korea Information Processing Society Conference
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• 2004.05a
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• pp.177-180
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• 2004

비디오 데이터베이스에서 움직임 정보를 가지고 있는 이동객체에 대한 모델링은 크게 두 가지 측면 즉, 공간적 혹은 시간적 관계성에 의해 다루어진다. 공간적 관계에서 위상 관계는 근접 그래프에 의한 모델링이 대부분이며, 이를 이용한 내용 기반 비디오 검색에서 자연어 형태의 질의어는 정형화된 위상 관계 표현으로 변환하는 과정을 거친다. 그러나 이 과정에서 위상 관계 표현이 인간이 사용하는 언어의 의미를 정확히 반영하는지는 알 수 없다. 이에 본 논문에서는 위상 관계 표현과 인간이 사용하는 움직임 동사간 의미의 차이를 줄이기 위해 위상 관계 표현과 실제 움직임 동사간의 매칭에 대해 연구했다.

• The Mathematical Education
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• v.14 no.1
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• pp.19-21
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• 1975

약 위상과 강위상이 주어진 선형공간 E에서 수열의 약수렴과 강수렴에 관한 성질을 보조정리로하여 두 Banach공간 E와 F사이에 정의된 연속작용소 공간 L(E.F)에서 작용소열 { $T_{n}$ }이 T에 강수렴하기 위한 필요충분조건은 F가 Hilbert 공간일때는 { $T_{n}$ }이 T에 약수렴함과 동시에 실수열 (equation omitted)$T_{\chi}$ $n^{\chi}$(equation omitted)가 실수 (equation omitted)T$\chi$(equation omitted)에 수렴할 때이다.