• East Asian mathematical journal
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• 제26권2호
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• pp.219-232
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• 2010

The main purpose of this work is to suggest a new approach to teaching general topology to undergraduate students. First, we change the order of contents. Usually, we introduce definitions, examples, theorems, and problems in this order. But, showing familiar examples of some concept of topology prior to the definition of one is the best method so far as I know from teaching experience of topology, which students feel very hard because of its abstractness. For more efficiency, mathematics-clubs each consisting of three or four students in topology course are established. This makes students very positive in topology class.

• Journal of applied mathematics & informatics
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• 제15권1_2호
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• pp.323-331
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• 2004

A new topology in terms of order on fuzzy sets, revealing better the relationship between smooth topology and Chang's fuzzy topology, is presented in the paper. Some basic properties are discussed.

• 대한수학회논문집
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• 제12권1호
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• pp.127-133
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• 1997

In order to study the limits of sequences appearing in, for example, stochastic process, A. V. Skorokhod has defined new function space topologies. We compare these topologies with the topology of compact convergence, the topology of pointwise convergence and others.

• Journal of the Korean Data and Information Science Society
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• 제15권4호
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• pp.1019-1031
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• 2004

This paper describes a new modeling method for the prediction of transmembrane protein topology. The structural regions of the transmembrane protein have been modeled by means of a multiple state hidden Markov model that has provided for the detailed modeling of the heterogeneous amino acid distributions of each structural region. Grammatical constraints have been incorporated to the prediction method in order to capture the biological order of membrane protein topology. The proposed method correctly predicted 76% of all membrane spanning regions and 92% sidedness of the integration when all membrane spanning regions were found correctly.

• 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.

• 한국전산구조공학회논문집
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• 제20권1호
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• pp.19-28
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• 2007

이산화 된 구조물의 위상최적화 과정은 균일하게 분포된 재료 밀도의 위상으로 표현되는 초기 설계영역을 시발점으로 한다. 최적화 과정 동안 구조물의 위상은 고정된 설계영역 내에 주어진 최적화 문제를 만족시키는 방향으로 변화하면서, 최종적으로 최적 위상의 재료 밀도 분포를 생산한다. Eschenauer et al.에 의해 제안되었던 설계영역 안에 구멍을 도입하는 개념은 원래 경계면의 최적화 문제에 대해 설계변수의 유한적인 변화를 촉진시켜 최적화의 수렴성 개선을 도모하기 위함이었으나, 위상최적화의 관점에서는 초기 위상의 정의에 따라 다양한 최적 위상이 생산되는 것을 의미한다. 본 연구에서는 초기 설계영역 안에 국소적인 솔리드 상을 도입해 초기 위상에 변화를 주었을 때, 한정된 재료 하에 구조물에 배치 가능한 다양한 최적 위상을 산출할 수 있음을 검증하였다. 수치 예제로서 초기 설계영역 내에 다양한 치수를 가지는 국부적인 원형 솔리드의 고정된 개수를 투입하여 간단한 MBB-보의 위상최적 설계를 수행하였다.

• Kyungpook Mathematical Journal
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• 제64권1호
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• pp.161-169
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• 2024

A semi-well ordered set is a partially ordered set in which every non-empty subset of it contains a least element or a greatest element. It is defined as an extension of the concept of well ordered sets. An attempt is made to identify the properties of a semi-well ordered set equipped with the order topology.

• 정보처리학회논문지A
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• 제8A권2호
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• pp.157-166
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• 2001

A simulation package has been developed as an event-driven system that can handle the hardware configuration of STC104 and algorithm proposed in the sister paper of ‘Study on High Speed Routers(II).’After various STC104 topology of meshes, torus, and hypercubes are constructed using up to 512 switches, the performance of each topology has been analyzed under different message generation rate in terms of throughputs, latency, and packet blocking time. Modified multicast algorithms for STC104 have been proposed for STC104 after U-mesh and U-torus in order to overcome the multicasting difficulty because of the point-to-point communication method found in STC104. The performance of the multicast algorithms have been analyzed over meshes and torus configuration. Throughput gets higher in the order of mesh, torus, and hypercube. Throughput difference among topology were distinctive in the zone of high message generation rate. Latency and blocking time increased in the order of hypercube, torus, and mesh. U-mesh and U-torus of software multicast showed similar throughput, however, U-mesh peformed slightly better result. These algorithms showed eight to ten times better results compared to individual message pass for 90 destination nodes. Multi-link environment also showed better performance than single-link environment because multi-link network used the extra links for communication.

• Structural Engineering and Mechanics
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• 제36권1호
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• pp.79-94
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• 2010

This study shows how uncertainties of data like material properties quantitatively have an influence on structural topology optimization results for dynamic problems, here such as both optimal topology and shape. In general, the data uncertainties may result in uncertainties of structural behaviors like deflection or stress in structural analyses. Therefore optimization solutions naturally depend on the uncertainties in structural behaviors, since structural behaviors estimated by the structural analysis method like FEM need to execute optimization procedures. In order to quantitatively estimate the effect of data uncertainties on topology optimization solutions of dynamic problems, a so-called interval analysis is utilized in this study, and it is a well-known non-stochastic approach for uncertainty estimate. Topology optimization is realized by using a typical SIMP method, and for dynamic problems the optimization seeks to maximize the first-order eigenfrequency subject to a given material limit like a volume. Numerical applications topologically optimizing dynamic wall structures with varied supports are studied to verify the non-stochastic interval analysis is also suitable to estimate topology optimization results with dynamic problems.

• 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.