• 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.

• Journal of the Korean Institute of Intelligent Systems
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• v.20 no.6
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• pp.848-851
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• 2010

In this paper, we introduce the concept of fuzzy quasi topologies which are generalizations of smooth topologies and Chang's fuzzy topologies, and obtain some basic properties of their structures.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.4
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• pp.387-396
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• 2018

Topology may described a pattern of existence of elements of a given set X. The family ${\tau}(X)$ of all topologies given on a set X form a complete lattice. We will give some topologies on this lattice ${\tau}(X)$ using a fixed topology on X and we will regard ${\tau}(X)$ a topological space. Our purpose of this study is to comparison new topologies on the family ${\tau}(X)$ of all topologies induced old one.

• Proceedings of the KIEE Conference
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• 2003.07b
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• pp.705-707
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• 2003

The design of multi-domain that considers all components of the electromagnetic systems such as air, iron, magnet, and coil is investigated using the topology optimization, interpolation method, and FEM. The design sensitivity equation for the topology optimization is derived using the adjoint variable method and the continuum approach. The proposed method is applied to the topology optimization of C-core actuator.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.20 no.4
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• pp.412-418
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• 2011

Reliability-based Topology optimization(RBTO) is to get an optimal design satisfying uncertainties of design variables. Although RBTO based on homogenization and density distribution method has been done, RBTO based on BESO has not been reported yet. This study presents a reliability-based topology optimization(RBTO) using bi-directional evolutionary structural optimization(BESO). Topology optimization is formulated as volume minimization problem with probabilistic displacement constraint. Young's modulus, external load and thickness are considered as uncertain variables. In order to compute reliability index, four methods, i.e., RIA, PMA, SLSV and ADL(adaptive-loop), are used. Reliability-based topology optimization design process is conducted to obtain optimal topology satisfying allowable displacement and target reliability index with the above four methods, and then each result is compared with respect to numerical stability and computing time. The results of this study show that the RBTO based on BESO using the four methods can effectively be applied for topology optimization. And it was confirmed that DLSV and ADL had better numerical efficiency than SLSV. ADL and SLSV had better time cost than DLSV. Consequently, ADL method showed the best time efficiency and good numerical stability.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.47 no.2
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• pp.1-10
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• 2010

Mapping virtual process topology to physical processor topology is one of the most important design issues in parallel programming. However, the mapping problem is complicated due to the topology irregularity and routing complexity. This paper proposes a new process mapping scheme called adjacency-based mapping (AM) for irregular cluster systems assuming that the two-dimensional mesh process topology is specified as an interprocess communication pattern. The cluster systems have been studied and developed for many years since they provide high interconnection flexibility, scalability, and expandability which are not attainable in traditional regular networks. The proposed AM tries to map neighboring processes in virtual process topology to adjacent processors in physical processor topology. Simulation study shows that the proposed AM results in better mapping quality and shorter interprocess latency compared to the conventional approaches.

• Journal of the Korea Society of Computer and Information
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• v.17 no.5
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• pp.49-57
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• 2012

In P2P streaming management, peer's churning and finding efficient topology architecture optimization algorithm that reduces streaming delay is important. This paper studies a topology optimization algorithm based on the P2P streaming using peer's link information. The proposed algorithm is based on the estimation of peer's upload bandwidth using peer's link information on mesh-network. The existing algorithm that uses the information of connected links is efficient to reduce message overload in the point of resource management. But it has a risk of making unreliable topology not considering upload bandwidth. And when some network error occurs in a server-closer-peer, it may make the topology worse. In this paper we propose an algorithm that makes up for the weak point of the existing algorithm. We compare the existing algorithm with the proposed algorithm using test data and analyze each simulation result.

• Journal of Ocean Engineering and Technology
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• v.34 no.4
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• pp.263-271
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• 2020

In this study, we performed a three-dimensional (3D) topology optimization of a fixed offshore structure to enhance its structural stiffness. The proposed topology optimization is based on the solid isotropic material with penalization (SIMP) method, where a volume constraint is applied to utilize an equivalent amount of material as that used for the rule-based scantling design. To investigate the effects of the main legs of the fixed offshore structure on its structural stiffness, the leg region is selectively considered in the design domain of the topology optimization problem. The obtained optimal designs and the rule-based scantling design of the structure are manufactured by 3D metal printing technology to experimentally validate the topology optimization. The behaviors under compressive loading of the obtained optimal designs are compared with those of the rule-based scantling design using a universal testing machine (UTM). Based on the structural experiments, we concluded that by employing the topology optimization method, the structural stiffness of the structure was enhanced compared to that of the rule-based scantling design for an equal amount of the fabrication material. Furthermore, by effectively combining the topology optimization and rule-based scantling methods, we succeeded in enhancing the structural stiffness and improving the breaking load of the fixed offshore structure.

• Journal of Korean Association for Spatial Structures
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• v.5 no.3 s.17
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• pp.83-89
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• 2005

This paper provides the results of the investigation on the optimum topology of simply supported deep beam structures with multi-point load cases. In this study, the strain energy to be minimized is considered as the objective function and the initial volume of structures is used as the constraint function. The resizing algorithm based on the optimality criteria is adopted to update the hole size existing inside the material. In this study, the sensitivities of topology optimization parameters to the optimum topology of the deep bean structures is investigated and also the effect of filtering process on the optimum topology is thoroughly tested. From numerical tests, the optimum topology of the deep beam is closely related with the optimization parameters used in the iteration and the filtering process play important role in order to find the optimum topology of the deep beam.

• Convergence Security Journal
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• v.21 no.2
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• pp.47-56
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• 2021

Network topology visualization has been studied a lot since the past and developed with many tools. The network topology has strength in understanding the overall structure of a network physically and is useful for understanding data flow between nodes logically. Although there are existing tools, not many can be utilized efficiently while using the general network node data structure and express the topology similar to the actual network structure. In this paper, we propose an efficient method to visualize topology using only connection information of network nodes. The method finds the central node by using the centrality, the influence of nodes in the network, and visualizes the topology by dynamically segmenting all nodes and placing network nodes in 3D space using the weight of the child node. It is a straightforward method, yet it effectively visualizes in the form of an actual network structure.