• Journal of the Korean Mathematical Society
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• v.35 no.2
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• pp.371-386
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• 1998

Let G be a compact Lie group and M a semialgebraic G space in some orthogonal representation space of G. We prove that if G is finite then M has an equivariant semialgebraic triangulation. Moreover this triangulation is unique. When G is not finite we show that M has a semialgebraic G CW complex structure, and this structure is unique. As a consequence compact semialgebraic G space has an equivariant simple homotopy type.

• Honam Mathematical Journal
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• v.39 no.1
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• pp.101-113
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• 2017

Let G be a semialgebraic group which is not necessarily compact. Let X be a proper semialgebraic G-set whose orbit space has a semialgebraic structure. In this paper we prove that X has a finite open straight G-CW complex structure.

• Bulletin of the Korean Mathematical Society
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• v.60 no.6
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• pp.1497-1522
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• 2023

In this paper we compute the Bredon homology of wallpaper groups with respect to the family of finite groups and with coefficients in the complex representation ring. We provide explicit bases of the homology groups in terms of irreducible characters of the stabilizers.

• Communications of the Korean Mathematical Society
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• v.21 no.1
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• pp.185-191
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• 2006

This paper observes that the induced homomorphisms on cohomology groups by a cyclic map are trivial. For a CW-complex X, we use the fact to obtain some conditions of X so that the n-th Gottlieb group $G_n(X)$ is trivial for an even positive integer n. As corollaries, for any positive integer m, we obtain $G_{2m}(S^{2m})\;=\;0\;and\;G_2(CP^m)\;=\;0$ which are due to D. H. Gottlieb and G. Lang respectively, where $S^{2m}$ is the 2m- dimensional sphere and $CP^m$ is the complex projective m-space. Moreover, we show that $G_4(HP^m)\;=\;0\;and\;G_8(II)\;=\;0,\;where\;HP^m$ is the quaternionic projective m-space for any positive integer m and II is the Cayley projective space.

• Bulletin of the Korean Mathematical Society
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• v.58 no.2
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• pp.445-449
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• 2021

We define the relative self-closeness number N��(g) of a map g : X → Y, which is a generalization of the self-closeness number N��(X) of a connected CW complex X defined by Choi and Lee [1]. Then we compare N��(p) with N��(X) for a fibration $X{\rightarrow}E{\rightarrow\limits^p}Y$. Furthermore we obtain its rationalized result.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.22 no.6
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• pp.931-936
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• 2013

Recently, the use of large-electron-beam polishing for polishing complex metal surfaces has been proposed. In this study, the temperature induced by a large electron beam was predicted using the heat transfer theory. A finite element (FE) model of a continuous wave (CW) electron beam was constructed assuming Gaussian distribution. The temperature distribution and melting depth of an SUS304 sample were predicted by changing electron-beam polishing process parameters such as energy density and beam velocity. The results obtained using the developed FE model were compared with experimental results for verifying the melting depth prediction capability of the developed FE model.