• Proceedings of the Korean Operations and Management Science Society Conference
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• 1995.04a
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• pp.656-666
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• 1995

본 논문에서는 물체위로 투사된 line stripe으로부터 물체의 표면 정보를 추출하기 위해 2-D Grip paper를 이용해 캘리브레이션하는 방법이 제안되었다. 카메라의 이미지평면과 카메라의 가시범위에 있는 3차원 실세계간의 Projective Tranformation과정에서는 목표물과 이미지 평면사이의 거리나 각도 등이 정보를 실제로 측정해서 알고 있어야만 카메라와 실세계간의 캘리브레이션을 수행할 수 있다. 그러나 이미 크기나 거리를 알고 있는 Grid paper를 이용하면 카메라의 파라미터들에 대한 추정이나 카메라와 실세계간의 측정을 하지 않고서도 목표물위로 투사된 line stripe에 대한 정보를 얻을 수 있고 이를 이용해 물체의 표면에 대한 정보를 얻을 수 있다. 이미 지평면에 투영된 격자패턴에서 구한 교차점들의 위치를 이용해 실제 위치를 찾아낸다. 실제로 레이져스캐너를 이용해 물체위로 line stripe을 투사한 후, 위에서 제시한 방법을 통해 3차원 정보를 구하는 실험결과는 양호하였다.

• Journal of the Korean Mathematical Society
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• v.39 no.4
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• pp.593-609
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• 2002

The order of speciality of an ample invertible Sheaf L on a curve is the least integer m so that $L^{ m}$ is nonspecial. There is a reasonable upper bound of the order of speciality for a simple invertible sheaf in terms of its degree and projective dimension. We study the case where it reaches the upper bound. Moreover we for mulate Castelnuovo's genus bound involving the order of speciality.ality.

• Bulletin of the Korean Mathematical Society
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• v.41 no.3
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• pp.419-426
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• 2004

Let R be a commutative Noetherian ring and let M be an Artinian R-module. Let M${\subseteq}$M′ be submodules of M. Suppose F is an R-module which is projective relative to M. Then it is shown that $Att_{R}$($Hom_{A}$ (F,M′) :$Hom_{A}$(F,M) $In^n$), n ${\in}$N and $Att_{R}$($Hom_{A}$(F,M′) :$Hom_{A}$(F,M) In$^n$ $Hom_{A}$(F,M") :$Hom_{A}$(F,M) $In^n$),n ${\in}$ N are ultimately constant.

• Journal of the Korean Mathematical Society
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• v.39 no.5
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• pp.665-680
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• 2002

For a smooth projective irreducible algebraic curve C of odd gonality, the maximal possible dimension of the variety of special linear systems ${W^r}_d$(C) is d－3r by a result of M. Coppens et at. [4]. This bound also holds if C does not admit an involution. Furthermore it is known that if dim ${W^r}_d(C)qeq$ d-3r-1 for a curve C of odd gonality, then C is of very special type of curves by a recent progress made by G. Martens [11] and Kato-Keem [9]. The purpose of this paper is to pursue similar results for curves of even gonality which does not admit an involution.

• Bulletin of the Korean Mathematical Society
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• v.48 no.6
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• pp.1315-1327
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• 2011

Let M be a real hypersurface of a complex space form with almost contact metric structure (${\phi}$, ${\xi}$, ${\eta}$, g). In this paper, we study real hypersurfaces in a complex space form whose structure Jacobi operator $R_{\xi}=R({\cdot},\;{\xi}){\xi}$ is ${\xi}$-parallel. In particular, we prove that the condition ${\nabla}_{\xi}R_{\xi}=0$ characterizes the homogeneous real hypersurfaces of type A in a complex projective space or a complex hyperbolic space when $R_{\xi}{\phi}S=R_{\xi}S{\phi}$ holds on M, where S denotes the Ricci tensor of type (1,1) on M.

• Bulletin of the Korean Mathematical Society
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• v.54 no.2
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• pp.391-397
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• 2017

In this note we extend our previous result about the structure of the dual of a crossed product $C^*$-algebra $A{\rtimes}_{\sigma}G$, when G is a finite group. We consider the space $\tilde{\Gamma}$ which consists of pairs of irreducible representations of A and irreducible projective representations of subgroups of G. Our goal is to endow $\tilde{\Gamma}$ with a topology so that the orbit space e $G{\backslash}{\tilde{\Gamma}}$ is homeomorphic to the dual of $A{\rtimes}_{\sigma}G$. In particular, we will show that if $\widehat{A}$ is Hausdorff then $G{\backslash}{\tilde{\Gamma}}$ is homeomorphic to $\widehat{A{\rtimes}_{\sigma}G}$.

• Communications of the Korean Mathematical Society
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• v.35 no.2
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• pp.591-602
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• 2020

There is a well-known class of compact, complex, non-Kählerian manifolds constructed by Bosio, called the LVMB manifolds, which properly includes the Hopf manifold, the Calabi-Eckmann manifold, and the LVM manifolds. As in the case of LVM manifolds, these LVMB manifolds can admit a regular holomorphic foliation 𝓕. Moreover, later Meersseman showed that if an LVMB manifold is actually an LVM manifold, then the regular holomorphic foliation 𝓕 is actually transverse Kähler. The aim of this paper is to deal with a converse question and to give a simple and new proof of a well-known result of Cupit-Foutou and Zaffran. That is, we show that, when the holomorphic foliation 𝓕 on an LVMB manifold N is transverse Kähler with respect to a basic and transverse Kähler form and the leaf space N/𝓕 is an orbifold, N/𝓕 is projective, and thus N is actually an LVM manifold.

• Bulletin of the Korean Mathematical Society
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• v.57 no.4
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• pp.933-943
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• 2020

Let M be a Fano manifold, and H^🟉(M; ℂ) be the quantum cohomology ring of M with the quantum product 🟉. For 𝜎 ∈ H^🟉(M; ℂ), denote by [𝜎] the quantum multiplication operator 𝜎🟉 on H^🟉(M; ℂ). It was conjectured several years ago [7,8] and has been proved for many Fano manifolds [1,2,10,14], including our cases, that the operator [c₁(M)] has a real valued eigenvalue 𝛿₀ which is maximal among eigenvalues of [c₁(M)]. Galkin's lower bound conjecture [6] states that for a Fano manifold M, 𝛿₀ ≥ dim M + 1, and the equality holds if and only if M is the projective space ℙⁿ. In this note, we show that Galkin's lower bound conjecture holds for Lagrangian and orthogonal Grassmannians, modulo some exceptions for the equality.

• Bulletin of the Korean Mathematical Society
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• v.29 no.1
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• pp.73-80
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• 1992

We discuss transverse harmonic fields on compact foliated Riemannian manifolds, and give a necessary and sufficient condition for a transverse field to be a transverse harmonic one and the non-existence of transverse harmonic fields. 1. On a foliated Riemannian manifold, geometric transverse fields, that is, transverse Killing, affine, projective, conformal fields were discussed by Kamber and Tondeur([3]), Molino ([5], [6]), Pak and Yorozu ([7]) and others. If the foliation is one by points, then transverse fields are usual fields on Riemannian manifolds. Thus it is natural to extend well known results concerning those fields on Riemannian manifolds to foliated cases. On the other hand, the following theorem is well known ([1], [10]): If the Ricci operator in a compact Riemannian manifold M is non-negative everywhere, then a harmonic vector field in M has a vanishing covariant derivative. If the Ricci operator in M is positive-definite, then a harmonic vector field other than zero does not exist in M.

• Bulletin of the Korean Mathematical Society
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• v.54 no.4
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• pp.1323-1330
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• 2017

For a nondegenerate projective irreducible variety $X{\subset}{\mathbb{P}}^r$, it is a natural problem to find an upper bound for the value of $${\ell}_{\beta}(X)=max\{length(X{\cap}L){\mid}L={\mathbb{P}}^{\beta}{\subset}{\mathbb{P}}^r,\;{\dim}(X{\cap}L)=0\}$$ for each $1{\leq}{\beta}{\leq}e$. When X is locally Cohen-Macaulay, A. Noma in [10] proves that ${\ell}_{\beta}(X)$ is at most $d-e+{\beta}$ where d and e are respectively the degree and the codimension of X. In this paper, we construct some surfaces $S{\subset}{\mathbb{P}}^5$ of degree $d{\in}\{7,{\ldots},12\}$ which satisfies the inequality $${\ell}_2(S){\geq}d-3+{\lfloor}{\frac{d}{2}}{\rfloor}$$. This shows that Noma's bound is no more valid for locally non-Cohen-Macaulay varieties.