• Kyungpook Mathematical Journal
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• v.20 no.1
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• pp.47-51
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• 1980

• Kyungpook Mathematical Journal
• /
• v.20 no.1
• /
• pp.59-76
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• 1980

• Kyungpook Mathematical Journal
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• v.24 no.2
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• pp.115-125
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• 1984

• Kyungpook Mathematical Journal
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• v.25 no.1
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• pp.15-28
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• 1985

• Communications of the Korean Mathematical Society
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• v.2 no.1
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• pp.89-115
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• 1987

• Journal of the Korean Mathematical Society
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• v.45 no.6
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• pp.1635-1646
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• 2008

Schanuel's formula describes the distribution of rational points on projective space. In this paper we will extend it to algebraic points of bounded degree in the case of ${\mathbb{P}}^1$. The estimate formula will also give an explicit error term which is quite small relative to the leading term. It will also lead to a quasi-asymptotic formula for the number of points of bounded degree on ${\mathbb{P}}^1$ according as the height bound goes to $\infty$.

• East Asian mathematical journal
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• v.24 no.1
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• pp.97-103
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• 2008

New fixed point theorems for permissible maps between $Fr{\acute{e}}chet$ spaces are presented. The proof relies on index theory developed by Dzedzej and on viewing a $Fr{\acute{e}}chet$ space as the projective limit of a sequence of Banach spaces.

• The Pure and Applied Mathematics
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• v.16 no.1
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• pp.69-83
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• 2009

New Lefschetz fixed point theorems for compact absorbing contractive admissible maps between Frechet spaces are presented. Also we present new results for condensing maps with a compact attractor. The proof relies on fixed point theory in Banach spaces and viewing a Frechet space as the projective limit of a sequence of Banach spaces.

• Communications of the Korean Mathematical Society
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• v.13 no.1
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• pp.85-94
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• 1998

The purpose of this paper is to give sample characterizations of n-dimensional CR-submanifolds of (n-1) CR-semifolds of (n-1) CR-dimension immersed in a complex projective space $CP^{(n+p)/2}$ with Fubini-Study metric and we study an n-dimensional compact, orientable, minimal CR-submanifold of (n-1) CR-dimension in $CP^{(n+p)/2}$.

• Journal of the Korean Mathematical Society
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• v.58 no.2
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• pp.501-523
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• 2021

We study the geometry of the moduli space of elliptic stable maps to projective space. The main component of the moduli space of elliptic stable maps is singular. There are two different ways to desingularize this space. One is Vakil-Zinger's desingularization and the other is via the moduli space of logarithmic stable maps. Our main result is a proof of the direct geometric relationship between these two spaces. For degree less than or equal to 3, we prove that the moduli space of logarithmic stable maps can be obtained by blowing up Vakil-Zinger's desingularization.