• 한국수학사학회지
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• 제19권1호
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• pp.17-32
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• 2006

위상수학은 기하학, 대수학, 해석학 등 수학의 다른 분야에 비하여 비교적 늦게 연구되기 시작하였고 Euler는 위상수학의 시조로 알려져 있다. 우리는 먼저 위상수학의 기원과 발달에 대해 살피고 Euler의 삶과 업적에 대해 알아본다.

• 한국수학사학회지
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• 제10권2호
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• pp.11-23
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• 1997

Category theory gives a convenient language for the study of mathematical structures besides its own study. In this paper, we investigate how the abstract structure theory emerged in 1930s affects the study in Topology and eventually becomes a rudiment for the category theory. Moreover, various extensions and universal mapping problems were put in their proper perspective as reflections by the category theory and by its duality principle, coreflections become an interesting subject in Topology, both of which give rise to a new discipline of the categorical topology.

• 한국수학사학회지
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• 제19권1호
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• pp.55-64
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• 2006

본 논문에서는 고대 Greece, 고대 Babylonia 등에서 시작한 수학의 발전 과정과 19세기 이후 집합론을 바탕으로 공리주의적 방법으로 현대수학이 발전하였음을 알아보고 특히 위상수학의 발전과정을 요약해 보았다.

• Journal of Computational Design and Engineering
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• 제3권2호
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• pp.161-177
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• 2016

In history based parametric CAD modeling systems, persistent identification of the topological entities after design modification is mandatory to keep the design intent by recording model creation history and modification history. Persistent identification of geometric and topological entities is necessary in the product design phase as well as in the re-evaluation stage. For the identification, entities should be named first according to the methodology which will be applicable for all the entities unconditionally. After successive feature operations on a part body, topology based persistent identification mechanism generates ambiguity problem that usually stems from topology splitting and topology merging. Solving the ambiguity problem needs a complex method which is a combination of topology and geometry. Topology is used to assign the basic name to the entities. And geometry is used for the ambiguity solving between the entities. In the macro parametrics approach of iCAD lab of KAIST a topology based persistent identification mechanism is applied which will solve the ambiguity problem arising from topology splitting and also in case of topology merging. Here, a method is proposed where no geometry comparison is necessary for topology merging. The present research is focused on the enhancement of the persistent identification schema for the support of ambiguity problem especially of topology splitting problem and topology merging problem. It also focused on basic naming of pattern features.

• 한국수학사학회지
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• 제2권1호
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• pp.79-89
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• 1985

• Steel and Composite Structures
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• 제21권3호
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• pp.501-515
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• 2016

Seismic analysis for steel frame structure with brace configuration using topology optimization based on truss-like material model is studied. The initial design domain for topology optimization is determined according to original steel frame structure and filled with truss-like members. Hence the initial truss-like continuum is established. The densities and orientation of truss-like members at any point are taken as design variables in finite element analysis. The topology optimization problem of least-weight truss-like continuum with stress constraints is solved. The orientations and densities of members in truss-like continuum are optimized and updated by fully-stressed criterion in every iteration. The optimized truss-like continuum is founded after finite element analysis is finished. The optimal bracing system is established based on optimized truss-like continuum without numerical instability. Seismic performance for steel frame structures is derived using dynamic time-history analysis. A numerical example shows the advantage for frame structures with brace configuration using topology optimization in seismic performance.

• 한국수학사학회:학술대회논문집
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• 한국수학사학회 1997년도 가을학술발표회 논문초록집
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• pp.4.2-4.2
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• 1997

• 한국수학사학회지
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• 제10권1호
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• pp.19-32
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• 1997

This paper deals with the relationship between the order structure and topological structure in the historical point of view. We first investigate how the order structure has developed along with the set theory and logic in the second half of the nineteenth century. After the general topology has emerged in the beginning of the twentieth century, two disciplines of the order theory and topology give each other a great deal of effect for their development via various dualities, compactifications by maximal filter spaces and Alexandroff's specialization order, which form eventually a fundamental setting for the development of the category theory or functor theory.

• 한국소음진동공학회논문집
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• 제27권1호
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• pp.72-79
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• 2017

A full treatment of damping material is not an effective method because the damping effect is not significantly increased compared to that obtained by an effective partial damping treatment. Thus, a variety of methodologies has been considered in order to achieve an optimal damping treatment. One of the widely applied approaches is topology optimization. However, the high computational expenses can be an issue in topology optimization. A new efficient convergence criterion, reducible design variable method (RDVM), is applied to reduce computational expense in topology optimization. The idea of RDVM topology optimization is to adaptively reduce the number of design variables based on the history. The iteration repeats until the number of design variables becomes zero. The aim of this research is to adopt RDVM topology optimization into obtaining an optimal damping treatment. In order to demonstrate the effectiveness and efficiency of RDVM topology optimization, optimal damping layouts and computational expenses are compared between conventional and RDVM topology optimization.

• 한국수학사학회지
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• 제33권3호
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• pp.135-154
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• 2020

This paper tries to show the formation of 'Kyungpook School' that is a nickname given to mathematicians of Kyungpook National University (KNU). In the early period, the role of professor Park Jung-gi was the most important drive to set the research tradition. He made Korea's first english journal in mathematics, Kyungpook Mathematical Journal KMJ which became a cornerstone for students to join the international academic community. Professor Ki U-hang published the most amount of papers in Korea in 1970s and became a role model for young scholars. In this background, KNU's Topology and Geometry Research Center at KNU was chosen as the only Science Research Center in mathematics in 1989, and KNU's mathematicians could get a long-period support for capable mathematics researchers' community.