• 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 $l$.

• 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.

• Korean Journal of Mathematics
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• v.7 no.1
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• pp.71-77
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• 1999

We show that if the stable rank of $B^{\alpha}$ is one, then the stable rank of B is less than or equal to the order of G for any action of a finite group G. Also we give a short proof to the known fact that if the action of a finite group on a $C^*$-algebra B is saturated then the canonical conditional expectation from B to $B^{\alpha}$ is of index-finite type and the crossed product $C^*$-algebra is isomorphic to the algebra of compact operators on the Hilbert $B^{\alpha}$-module B.

• Communications for Statistical Applications and Methods
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• v.10 no.3
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• pp.1007-1015
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• 2003

In this paper we introduced a new score generating function for the rank dispersion function in a general linear model. Based on the new score function, we derived the null asymptotic theory of the rank-based hypothesis testing in a linear model. In essence we showed that several rank test statistics, which are primarily focused on our new score generating function and new dispersion function, are mainly distribution free and asymptotically converges to a chi-square distribution.

• Journal of the Korean Mathematical Society
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• v.47 no.1
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• pp.71-81
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• 2010

We characterize linear operators that preserve sets of matrix ordered pairs which satisfy extreme cases with respect to maximal column rank inequalities of matrix multiplications over semirings.

• Journal of Korea Multimedia Society
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• v.21 no.1
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• pp.45-50
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• 2018

This research paper describes how to summarize music lyrics using the TextRank algorithm. This method can summarize music lyrics as important lyrics. Therefore, we recommend music more effectively than analyzing the number of words and recommending music.

• Journal of the Korean Mathematical Society
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• v.51 no.4
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• pp.867-879
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• 2014

It is known that the orbifold Euler characteristic $e_{orb}(S)$ of a log del Pezzo surface S of rank one satisfies the inequality $0{\leq}e_{orb}(S){\leq}3$. In this note, we show that the orbifold Euler characteristic of S is strictly positive, i.e., 0 < $e_{orb}(S)$. Moreover, we also show, by construction, the existence of log del Pezzo surfaces of rank one with arbitrarily small orbifold Euler characteristic.

• Communications for Statistical Applications and Methods
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• v.9 no.1
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• pp.101-113
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• 2002

In this paper we introduce a new score generating (unction for the rank regression in the linear regression model. The score function compares the $\gamma$'th and s\`th power of the tail probabilities of the underlying probability distribution. We show that the rank estimate asymptotically converges to a multivariate normal. further we derive the asymptotic Pitman relative efficiencies and the most efficient values of $\gamma$ and s under the symmetric distribution such as uniform, normal, cauchy and double exponential distributions and the asymmetric distribution such as exponential and lognormal distributions respectively.

• 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.

• Honam Mathematical Journal
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• v.33 no.3
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• pp.301-310
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• 2011

In this paper, we construct the sets of fuzzy matrix pairs. These sets are naturally occurred at the extreme cases for the zero-term rank inequalities derived from the multiplication of fuzzy matrix pairs. We characterize the linear operators that preserve these extreme sets of fuzzy matrix pairs.