• East Asian mathematical journal
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• v.26 no.2
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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.

• The Transactions of the Korea Information Processing Society
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• v.7 no.6
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• pp.1778-1784
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• 2000

We consider the weighted shortest path updating problem, that is, the problem to reconstruct the weighted shortest paths in response to topology change of the network. This appear proposes a distributed algorithms that reconstructs the weighted shortest paths after several processors and links are added and deleted. its message complexity and ideal-time complexity are O(p$^2$+q+n') and O(p$^2$+q+n') respectively, where n' is the number of processors in the network after the topology change, q is the number of added links, and p is the total number of processors in he biconnected components (of the network before the topology change) including the deleted links or added links.

• Journal of the Institute of Electronics and Information Engineers
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• v.50 no.12
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• pp.98-106
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• 2013

The duty-cycle synchronization among mobile sensor nodes with energy-harvesting is very important. The nodes should keep their duty-cycle same to others as much as possible because they have to cooperate each other and to consume energy efficiently. The distribution of node position in network affects not only node connectivity but also the active time of synchronized nodes, and it relates to network life-time finally. In this paper, we introduce a network topology change algorithm (TCA) for energy-harvesting mobile sensor networks based on self-synchronized duty-cycling. The algorithm tries to change a network topology into a balanced topology where the mobile sensor nodes are unified according to the density of the number of nodes. For TCA, both fluid flow algorithm and flock dispersion algorithm are proposed and they are evaluated through the simulation in agent based modeling language. TCA is applied to the energy-harvesting mobile sensor networks to improve the synchronization of duty-cycle and to reduce the variation of energy consumption among nodes.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.58 no.10
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• pp.1936-1941
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• 2009

This paper deals with a new methodology for topology optimization in which the topology of the design domain may change during the shape optimization process. To achieve this, the concept of the topological gradient is introduced to compute the sensitivity of an objective function when a small hole is drilled in the domain. Based on shape and topological sensitivity values, the shape and topology of the design domain may be simultaneously changed during design iterations if necessary. To verify the advantages and also to facilitate understanding of the method itself, two electrostatic design problems have been tested by using 2D finite element analysis: the first is the inverse problem of a simple dielectric model and the second is the rotor design of a MEMS actuator.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1996.04a
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• pp.182-189
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• 1996

The focus of this study is on the problem of the design of structure of undetermined topology. This problem has been regarded as being the most challenging of structural optimization problems, because of the difficulty of allowing topology to change. Conventional approaches break down when element sizes approach to zero, due to stiffness matrix singularity. In this study, a novel nonlinear Programming formulation of the topology Problem is developed and examined. Its main feature is the ability to account for topology variation through zero element sizes. Stiffness matrix singularity is avoided by embedding the equilibrium equations as equality constraints in the optimization problem. Although the formulation is general, two dimensional plane elasticity examples are presented. The design problem is to find minimum weight of a plane structure of fixed geometry but variable topology, subject to constraints on stress and displacement. Variables are thicknesses of finite elements, and are permitted to assume zero sizes. The examples demonstrate that the formulation is effective for finding at least a locally minimal weight.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.05a
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• pp.1168-1173
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• 2001

Compressors are the main source of noise of refrigerators and air-conditioning unit. Recent studies on the sound propagation of rotary compressors showed that the accumulator is a significant source of noise generation. This paper describes a design change of a rotary compressor for noise reduction using topology optimization. Topology optimization has been developed and used to find the most effective structural configuration in the early stage of design procedures. FE model of the rotary compressor composed of all the components is built for the topology optimization. Topology optimization results show that the empirical design for the present structure fail to constrain some resonance modes and a new component is required.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.4
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• pp.370-377
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• 2004

The density approach and the homogenization design method are representative methods in topology optimization problems. In the topology optimization in magnetic fields, those methods are applied based on the results of the applications In elastic fields. In this study, the density method is modified considering the concept of the homogenization design method. Also, the results of the topology optimization in magnetic fields by the modified density method as well as the homogenization method are compared especially focusing the change of the penalization parameter in the density approach. The effect of the definition of the design domain such as global/local design domain is also discussed.

• Proceedings of the KSME Conference
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• 2001.06c
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• pp.392-397
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• 2001

Topology optimization is applied to determine the layout of a structure whose eigenfrequency coincides with a specified frequency. The topology optimization problem is formulated to minimize the difference between the structural frequency and a given frequency using the homogenization method and the modified optimality criteria method. It turns out that the value of a weighting factor in the updating scheme plays an important role to achieve both a suitable speed and a stable convergence of an algorithm. Unlike a constant weighting factor in previous works, it is suggested that a weight factor is varied during the iteration to control the amount of the frequency change. To substantiate the proposed approach two-dimensional structural design problems are presented and the resulted topology layouts for the specified eigenfrequency are compared to layouts for maximizing the corresponding eigenfrequency.

• Journal of Information Technology Applications and Management
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• v.11 no.2
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• pp.205-214
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• 2004

Internet evolves into the huge network with new nodes inserted or deleted depending on specific situations. A new model of network topology is needed in order to analyze time-varying Internet more realistically and effectively. In this study the non-monotony models are proposed which can describe topological changes of Internet such as node insertion and deletion, and can be used for predicting its future topology. Simulation is performed to analyze the topology generated by our model. Simulation results show that our proposed model conform the power law of realistic Internet better than conventional ones. The non-monotony model can be utilized for designing Internet protocols and networks with better security.

• The Transactions of the Korea Information Processing Society
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• v.7 no.5
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• pp.1370-1376
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• 2000

Consider the problem to updata breadth-First Spanning Tree in response to topology change of the network. The paper proposes an efficient distributed algorithm that solves such a problem after several processors and links are added and deleted. Its message complexity and its ideal-time complexity are O(p√q+q+a+n') respectively, where n' is the number fo processors in the network after the topology change, a is the number of added links, p is the total number of links in the biconnected component (of the network before the topology change) including the detected links or added links, and q is the total number of processors in the biconnected component (of the network before the topology change) including the deleted links or added links, and q is the total number of processors in the biconnected component including the deleted links or added links.