• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.1
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• pp.48-54
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• 2002

A part definition must not only provide shape information of a nominal part but also contain non-shape information such as tolerances, surface roughness and material specifications. Although machining features are useful for suitable shape information fur process reasoning in CAPP, they need to be integrated with tolerance information for effective process planning. We develop a tolerance modeler that efficiently integrates the machining features with the tolerance information fur feature-based CAPP. It is based on the association of machining features, tolerance features, and tolerances. The tolerance features in this study, where tolerances are assigned, are classified into two types; one type is a face that is a topological entity on a solid model and the other type is a functional geometry that is not referenced to topological entities. The (unctional geometry is represented by using machining features. All the data fur representing the tolerance information are stored completely and unambiguously in an independent tolerance data structure. The developed tolerance modeler is implemented as a module of a comprehensive feature-based CAPP system.

• Journal of the Korean Institute of Landscape Architecture
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• v.30 no.2
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• pp.50-62
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• 2002

From modernism to post-modernism, the practice in the design field often reduced the complexity of environment and to remove variety. However, contemporary ideas of space have been changed. The current thought premise is that the environment is mutable and is evolving according to inner and outer forces and elements. Therefore, leading designers recognize that the environment is complex in itself while anticipating a new theory explaining on-going trends. The idea of fold formulated by Gilles Deleuze can provide a theoretical base for new environmental design in constrat to current design practices. The fold is a hybrid by accommodating complex relations within an object. It carries a dynamic world view through continual process and yields a topological space against absolute space like Euclid geometry. The characteristics of the fold can be paraphrased as rhizome, stratification and smooth space. Rhizome forms a non-hierarchial connection like networking in internet space. Stratification is a kind of superimposition of autonomous potential layers within a single object. Smooth space is a free space and event oriented space keeping non-linear form. This study tried to incorporate the idea of fold to environmental design methods and design process in order to make space which can correspond with complex environment and topological form. In the design process adapted to fold theory, rhizome analysis accepts the complexity of environment and stratification strategy embraces the possibility of accidental use. As a result, the designed park carries a monadic image and produces an ambiguous space. Lastly, smooth space makes topological space unlike Euclid geometry and is free space comosed by the user themselves. Transporting the idea of fold into environmental design could be an alterative way for indeterminate and flexible design to accept new identity of place. Therefore, this study accepts the concept of incidental morphogenesis to make space based on the complexity of environment. The designed space based on the idea of fold searches to create free event space determined by user rather than designated by designer.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.21 no.3
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• pp.239-245
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• 2008

A level set based topological shape optimization using extended B-spline basis functions is developed for steady-state heat conduction problems. The only inside of complicated domain identified by the level set functions is taken into account in computation, so we can remove the effects of domain outside parts in heat conduction problem. The solution of Hamilton-Jacobi equation leads to an optimal shape according to the normal velocity field determined from the sensitivity analysis, minimizing a thermal compliance while satisfying a volume constraint. To obtain exact shape sensitivity, the precise normal and curvature of geometry need to be determined using the level set and B-spline basis functions. Using topological derivative concept, the nucleation of holes for topological changes can be made whenever and wherever necessary during the optimization.

• Journal of the Korean Mathematical Society
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• v.53 no.4
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• pp.795-834
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• 2016

The main purpose of this paper is to propose a scheme of a proof of the nonsimpleness of the group $Homeo^{\Omega}$ ($D^2$, ${\partial}D^2$) of area preserving homeomorphisms of the 2-disc $D^2$. We first establish the existence of Alexander isotopy in the category of Hamiltonian homeomorphisms. This reduces the question of extendability of the well-known Calabi homomorphism Cal : $Diff^{\Omega}$ ($D^1$, ${\partial}D^2$)${\rightarrow}{\mathbb{R}}$ to a homomorphism ${\bar{Cal}}$ : Hameo($D^2$, ${\partial}D^2$)${\rightarrow}{\mathbb{R}}$ to that of the vanishing of the basic phase function $f_{\underline{F}}$, a Floer theoretic graph selector constructed in [9], that is associated to the graph of the topological Hamiltonian loop and its normalized Hamiltonian ${\underline{F}}$ on $S^2$ that is obtained via the natural embedding $D^2{\hookrightarrow}S^2$. Here Hameo($D^2$, ${\partial}D^2$) is the group of Hamiltonian homeomorphisms introduced by $M{\ddot{u}}ller$ and the author [18]. We then provide an evidence of this vanishing conjecture by proving the conjecture for the special class of weakly graphical topological Hamiltonian loops on $D^2$ via a study of the associated Hamiton-Jacobi equation.

• Journal of Educational Research in Mathematics
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• v.9 no.1
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• pp.121-132
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• 1999

We have compared Korean and American mathematics curriculums in 5 areas: whole number(concepts and its operations); geometry; pattern and relations; measurements; statistics and probability. We have found significant differences in geometry area. Korean curriculums contain simple planar figures (circles, triangles, rectangles, and squres) and some of the spatial figures until 3rd grades. But in America they learn various planar and spatial fugures(cone, pyramid, triangular prism, etc) since the 1st grade starts. They also start the 1st grade by dealing with topological concepts like open/closed, inside/outside, order, etc. As the grade goes on, students learn other geometrical concepts like congruence, symmetry, 3-dimensional views. We also found that American curriculum focuses on students' activities and courages communication through projects, groupwork, journal writing, etc. It's also superior in respects of motivation, and connections with real life and other subjects. Korean curriculum needs more improvements in these aspects. Furthermore for lower graders reviewing sections need to be enhanced for feedback.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2002.05a
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• pp.272-279
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• 2002

A common task in assembly modeling is the determination of the position and orientation of a set of components by solving the spatial relationships between them. Assembly models could be constructed at various levels of abstraction. They could be classified into component or geometry-level assembly models. The geometry-level assembly design approach using mating constraints such as against and fits is widely used in the commercial modelers, but it may be very tedious in some cases fur designer. In this paper, we propose a new method to construct an assembly model at the component-level by extracting joint mating features from the kinematics constraints specified between components. The assembly model constructed using the proposed method includes hierarchical and relational assembly models, component/sub-assembly positions and degrees of freedom information. The proposed method is more intuitive and natural way of assembly design and it guarantees the topological robustness of assembly modification such as component replacement and modification.

• International Journal of CAD/CAM
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• v.2 no.1
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• pp.55-67
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• 2002

In many areas of industry, it is desirable to have fast and reliable systems in order to quickly obtain suitable solid models for computer- aided analyses. Nevertheless it is well known that the data exchange process between CAD modelers and CAE packages can require significative efforts. This paper presents an approach for geometrical data exchange through triangulated boundary models. The proposed framework is founded on the use of STL file specification as neutral format file. This work is principally focused on data exchange among CAD modelers and FEA packages via STL. The proposed approach involves the definition of a topological structure suitable for the STL representation and the development of algorithms for topology and geometry data processing in order to get a solid model suitable for finite element analysis or other computer aided engineering purposes. Different algorithms for model processing are considered and their pros and cons are discussed. As a case study, a prototype modeler which supports an exporting filter for a commercial CAE package has been implemented.

• Korean Journal of Child Studies
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• v.3
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• pp.35-48
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• 1982

The purpose of this study is to investigate the Piaget's theory of the child's conception of space, which explains the stage of child's congnitive development. This thesis consists of 4 Chapters, including introduction, which examines the concept of space perception, and the development of arithmetic conception, and suggests the outline of this study. In the Chapter II, the brief history of topological Psychology, and the current situation of this theory has been explained. According to Piaget's theory of the conception of space, the child's development of the conception of space develops orderly three stages, that is to say, the stage of conception of space by the topological relations, the stage of projective conception of space, and finally the stage of the Euclidian, conception of space. Children's development of the conception of space continuously, and orderly has been made by these stages. Also, in this Chapter, Piaget's experiment about the development of child's conception of space has been explained. In the Chapter III, the children's conception of geometry has been examined. Here explains the development of space representation, and of seriation or classification. In the Chapter IV, some theories of the conception of space has been examined, and some points of view has been made as a conclusion.

• Journal of Ship and Ocean Technology
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• v.5 no.2
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• pp.14-26
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• 2001

This paper presents a novel design approach that could generate structural design alternatives having different topologies and then, select the optimum structure from them with simulataneously determining its optimum design variables related to geometry and the member size subjected to the multiple objective design environments. For this purpose, a specialized genetic algorithm, called StrGA_DeAl + MOGA, which can handle the design alternatives and multi-criteria problems very effectively, is developed for the optimal structural design. To validate the developed method, method, plain truss design problems are considered as illustrative example. To begin with, some possible topological of the truss structure are suggested based on the stability criterion that should be satisfied under the given loading condition. Then, with the consideration of the given multi-criteria, several different topology forms are selected as design alternatives for the second step of the conceptual design process. Based on the chosen topolgy of truss structures, the sizing or shaping optimization process starts to determine the optimum design parameters. Ten-bar truss problems are given in the paper to confirm the above concept and methodology.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.15 no.1
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• pp.33-42
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• 2002

A method of automatic 3D tunnel modeling is proposed. The proposed method used the parametric representation of geometry and a hierarchical and relational data structure. These two bases provide the generalization and extension for 3D tunnel modeling. Especially, these two fundamentals ion the basis iota representing the characteristics of the tunnel structure for analysis. The constant-curvature characteristic is exploited to generate 3D mesh on the tunnel surface. This is attributed to the advantage that any 2D automatic mesh generation algorithm can be applied to 3D mesh modeling.