• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.43-61
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• 2020

We extend the work of A. Beauville on rank 2 vector bundles on a smooth curve in several directions. We give families of examples with large dimension, add new existence and non-existence results and prove the existence of indecomposable limits with arbitrary rank. To construct the large dimensional families we use the examples of limits of rank 2 trivial bundles on ℙ² and ℙ³ due to C. Banica. We also consider a more flexible notion: limits of trivial bundles on nearby curves.

• Proceedings of the Korea Information Processing Society Conference
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• 2002.11b
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• pp.1575-1578
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• 2002

본 논문에서는 공간-시간 블록 부호디자인(Space-Time Block Code) 관점에서 직교-디자인(Orthogonal-design) 즉, 최소거리가 5이면서 완전-계수(Full-Rank)인 디자인을 비교대상으로 완전-계수(Full-Rank)가 아니면서 최소거리가 5와7인 두 부호에 관하여 연구되어졌다.

• Kyungpook Mathematical Journal
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• v.53 no.2
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• pp.273-283
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• 2013

In this paper, we consider the row rank inequalities derived from comparisons of the row ranks of the additions and multiplications of nonnegative integer matrices and construct the sets of nonnegative integer matrix pairs which is occurred at the extreme cases for the row rank inequalities. We characterize the linear operators that preserve these extreme sets of nonnegative integer matrix pairs.

• Journal of the Korean Association of Geographic Information Studies
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• v.9 no.1
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• pp.149-157
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• 2006

The purpose of this study is to search for location potential in Busan metropolitan city and to support decision-making in land use policy. As basis work for the analysis of the location potential, we build rank-map database by using the 11 index. And then by using rank-map, we carried out the location potential ($P_i$) analysis. As a result, we found that many commercial use located in Rank 1 to 2. Also, Rank 4-7 must be made an un-commercial use in assignment of land use zone. These data can be effectively used for land use plan in Busan metropolitan city as the basis data.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.35 no.8C
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• pp.709-712
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• 2010

In this paper, the two sample locally optimum rank detector is obtained in the weakly dependent noise with non-zero temporal correlation between noise observations. The test statistic of the locally optimum rank detector is derived from the Neyman-Pearson lemma suitable for the two sample observation models, where it is assumed that reference observations are available in addition to regular observations. Two-sample locally optimum rank detecter shows the same performance with the one-sample locally optimum rank detector asymptotically. The structure of the two-sample rank detector is simpler than that of the one-sample rank detector because the sign statistic is not processed separately.

• Journal of Periodontal and Implant Science
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• v.37 no.4
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• pp.849-857
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• 2007

Purpose: The purposes of this study were to compare and quantify the expressions of RANK and RANKL in the gingival tissues of non-periodontitis patient and patients with chronic periodontitis, in order to understand the contribution of these proteins to periodontal destruction. Material and methods: Gingival tissue samples were obtained during periodontal surgery or tooth extraction. According to the patient's systemic condition & clinical criteria of gingiva, each gingival sample was divided into two groups. Group 1 (n=8) is clinically healthy gingiva without bleeding and no evidence of bone resorption or periodontal pockets, obtained from non-periodontitis patients. Group 2 (n=8) is inflammed gingiva from patients with chronic periodontitis. Tissue samples were prepared and analyzed by Western blotting. The quantification of RANK and RANKL were performed using a densitometer and statistically analyzed by Student's t-Test. Results: The expression of RANK were similar in group 1 and 2. The difference between group 1 and 2 was not statistically significant. And the mean amount of RANKL was more increased in group 2 than group 1. The difference between group 1 and group 2 was statistically significant. Conclusion: The expression level RANK didn't show any significant difference between healthy tissue from non-periodontitis patients and inflamed tissue from chronic periodontitis, but the expression level of RANKL in inflammed tissue from chronic periodontitis showed significantly increased tendency compared to healthy gingiva from non-periodontitis patients. Therefore, characteristics of RANK and RANKL in progress of chronic periodontitis would be basis of further studies in diagnostic method and treatment index of the disease.

• Bulletin of the Korean Mathematical Society
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• v.42 no.3
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• pp.501-507
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• 2005

A Boolean matrix with rank 1 is factored as a left factor and a right factor. The perimeter of a rank-1 Boolean matrix is defined as the number of nonzero entries in the left factor and the right factor of the given matrix. We obtain new characterizations of rank preservers, in terms of perimeter, of Boolean matrices.

• Bulletin of the Korean Mathematical Society
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• v.53 no.1
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• pp.153-161
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• 2016

It is shown that the algebra $\mathfrak{H}^{\infty}$ of bounded Dirichlet series is not a coherent ring, and has infinite Bass stable rank. As corollaries of the latter result, it is derived that $\mathfrak{H}^{\infty}$ has infinite topological stable rank and infinite Krull dimension.

• Journal of the Korean Mathematical Society
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• v.51 no.1
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• pp.113-123
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• 2014

The term rank of a matrix A over a semiring $\mathcal{S}$ is the least number of lines (rows or columns) needed to include all the nonzero entries in A. In this paper, we characterize linear operators that preserve the sets of matrix ordered pairs which satisfy extremal properties with respect to term rank inequalities of matrices over nonbinary Boolean semirings.

• Journal of the Korean Mathematical Society
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• v.50 no.1
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• pp.127-136
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• 2013

The term rank of a matrix A is the least number of lines (rows or columns) needed to include all the nonzero entries in A. In this paper, we obtain a characterization of linear transformations that preserve term ranks of matrices over antinegative semirings. That is, we show that a linear transformation T from a matrix space into another matrix space over antinegative semirings preserves term rank if and only if T preserves any two term ranks $k$ and $l$.