• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.371-384
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• 2022

Fix an integer n ≥ 1. Then the simplex Π_n, Birkhoff polytope Ω_n, and Latin square polytope Λ_n each yield projective geometries obtained by identifying antipodal points on a sphere bounding a ball centered at the barycenter of the polytope. We investigate conditions for homogeneous coordinates of points in the projective geometries to locate exact vertices of the respective polytopes, namely crisp distributions, permutation matrices, and quasigroups or Latin squares respectively. In the latter case, the homogeneous conditions form a crucial part of a recent projective-geometrical approach to the study of orthogonality of Latin squares. Coordinates based on the barycenter of Ω_n are also suited to the analysis of generalized doubly stochastic matrices, observing that orthogonal matrices of this type form a subgroup of the orthogonal group.

• Journal of the Korean Mathematical Society
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• v.59 no.4
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• pp.821-841
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• 2022

In this paper, we introduce and study regular rings relative to the hereditary torsion theory w (a special case of a well-centered torsion theory over a commutative ring), called w-regular rings. We focus mainly on the w-regularity for w-coherent rings and w-Noetherian rings. In particular, it is shown that the w-coherent w-regular domains are exactly the Prüfer v-multiplication domains and that an integral domain is w-Noetherian and w-regular if and only if it is a Krull domain. We also prove the w-analogue of the global version of the Serre-Auslander-Buchsbaum Theorem. Among other things, we show that every w-Noetherian w-regular ring is the direct sum of a finite number of Krull domains. Finally, we obtain that the global weak w-projective dimension of a w-Noetherian ring is 0, 1, or ∞.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.42 no.2 s.302
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• pp.113-120
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• 2005

3D reconstruction of a scene structure from un-calibrated image sequences has been long one of the central problems in computer vision. For 3D reconstruction in Euclidean space, projective reconstruction, which is classified into the merging method and the factorization, is needed as a preceding step. By calculating all camera projection matrices and structures at the same time, the factorization method suffers less from dia and error accumulation than the merging. However, the factorization is hard to analyze precisely long sequences because it is based on the assumption that all correspondences must remain in all views from the first frame to the last. This paper presents a new projective reconstruction method for recovery of 3D structure over long sequences. We break a full sequence into sub-sequences based on a quantitative measure considering the number of matching points between frames, the homography error, and the distribution of matching points on the frame. All of the projective reconstructions of sub-sequences are registered into the same coordinate frame for a complete description of the scene. no experimental results showed that the proposed method can recover more precise 3D structure than the merging method.

• Journal of the Korean Mathematical Society
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• v.45 no.4
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• pp.953-963
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• 2008

We find necessary and sufficient conditions for a para-$K{\ddot{a}}hlerian$ manifold to be paraholomorphically pseudosymmetric in terms of the paraholomorphic projective and Bochner curvatures. New examples of such spaces are proposed.

• Bulletin of the Korean Mathematical Society
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• v.42 no.1
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• pp.93-119
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• 2005

In this paper, we characterize some semi-invariant sub-manifolds of codimension 3 with almost contact metric structure ($\phi$, $\xi$, g) in a complex projective space $CP^{n+1}$ in terms of the structure tensor $\phi$, the Ricci tensor S and the Jacobi operator $R_\xi$ with respect to the structure vector $\xi$.

• Bulletin of the Korean Mathematical Society
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• v.49 no.4
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• pp.761-765
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• 2012

We prove that for a toric manifold (respectively, a quasitoric manifold) M, any graded ring isomorphism $H^*(M){\rightarrow}H^*({\Pi}_{i=1}^{m}\mathbb{C}P^{ni})$ can be realized by a diffeomorphism (respectively, a homeomorphism) ${\Pi}_{i=1}^{m}\mathbb{C}P^{ni}{\rightarrow}M$.

• Communications of the Korean Mathematical Society
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• v.10 no.1
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• pp.1-10
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• 1995

In this paper we show that for each divisor class c of degree zero on a projective curve C (not necessarily smooth), there exists a unique function $\hat{h}_c$ on C up to bounded functions. Section 1 contain basic definitions and a brief summary of classical results on Jacobians and heights. In section 2, we prove the existence of "canonical height" on a singular curves and in section 3 we prove the analogouse results on N$\acute{e}$ron functions for singular curves. This is a part of the author's doctorial thesis at Ewha Womens University under the guidence of professor Sung Sik Woo.g Sik Woo.

• Communications of the Korean Mathematical Society
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• v.29 no.4
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• pp.569-579
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• 2014

We consider a condition under which the projectivization $P(E^k)$ of a complex k-bundle $E^k{\rightarrow}M$ over an even-dimensional manifold M can have the hard Lefschetz property, affected by [10]. It depends strongly on the rank k of the bundle $E^k$. Our approach is purely algebraic by using rational Sullivan minimal models [5]. We will give some examples.

• 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 $\infty$.

• Review of KIISC
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• v.2 no.4
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• pp.17-29
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• 1992

본 논문에서는 시스템 내의 모든sote들에게 분산되어 있는 정보들을 수렴하여 일치를 이루고, 그 결과를 모든 site들이 알도록 하는 다중 일치 프로토콜을 위한 효과적인 통신 방법을 제안하고자 한다. 분산 시스템에 참여하는 computer 또는 site들의 수를 N이라 할때, $O(N^2)$의 message를 필요로하면서 한 round안에 일치를 이룰 수 있는 프로토콜은 message의 수가 너무 많다는 것이 단점이다. 이에 본 논문에서는 Finite Projective Planes을 이용하여 message의 수를 줄이면서 두 round 안에 일치를 이룰 수 있는 통신 방법을 제안한다. 이때, 각 round마다 필요한 message의 수는 O(N$)이다. 또한, 이 통신 방법에서 이용되는 Finite Projective Planes을 구축하는 알고리즘을 제안하고자한다.