• Title, Summary, Keyword: History of Topology

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Implementation of persistent identification of topological entities based on macro-parametrics approach

  • Farjana, Shahjadi Hisan;Han, Soonhung;Mun, Duhwan
    • Journal of Computational Design and Engineering
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    • v.3 no.2
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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.

Leonhard Euler, the founder of topology (위상수학의 시조 Euler)

  • Kim, Sang-Wook;Lee, Seung-On
    • Journal for History of Mathematics
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    • v.19 no.1
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    • pp.17-32
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    • 2006
  • Topology began to be studied relatively later than the other branches of mathematics, such as geometry, algebra and analysis. Leonhard Euler is generally considered to be the founder of topology. In this paper we first investigate the beginning of topology and its development and then study Euler's life and his achievements in mathematics.

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CATEGORICAL TOPOLOGY의 역사

  • 홍성사;홍영희
    • Journal for History of Mathematics
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    • v.10 no.2
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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.

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History of modern mathematics (현대 수학의 역사)

  • Park, Choon-Sung
    • Journal for History of Mathematics
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    • v.19 no.1
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    • pp.55-64
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    • 2006
  • The thesis is about the development of mathematics starting from the old Greece and the old Babylonia. The modem mathematics has been developed, based on the set theory in the axiomatic method since the 19th century. The primary impetus of this thesis will be to summary the development of topology.

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Seismic analysis of steel structure with brace configuration using topology optimization

  • Qiao, Shengfang;Han, Xiaolei;Zhou, Kemin;Ji, Jing
    • Steel and Composite Structures
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    • v.21 no.3
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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.

RDVM Topology Optimization for Optimal Damping Treatment (점탄성물질 위치 최적화를 위한 설계변수감소 위상최적설계 기법)

  • Sun Yong, Kim
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.27 no.1
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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.

순서와 위상구조의 관계

  • 홍성사;홍영희
    • Journal for History of Mathematics
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    • v.10 no.1
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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.

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History of Mathematics in Korea and the Birth of 'Kyungpook School': The formation of mathematics research tradition in Kyungpook National University (한국 수학사와 '경북학파'의 탄생: 경북대학교 수학 연구 전통의 형성과 발전)

  • Moon, Manyong;Sun, You-jeong;Kang, Hyeong-gu
    • Journal for History of Mathematics
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    • v.33 no.3
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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.