• Kyungpook Mathematical Journal
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• 제46권1호
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• pp.89-96
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• 2006

For a rank-1 matrix A, there is a factorization as $A=ab^t$, the product of two vectors a and b. We characterize the linear operators that preserve rank and some equivalent condition of rank-1 matrices over a chain semiring. We also obtain a linear operator T preserves the rank of rank-1 matrices if and only if it is a form (P, Q, B)-operator with appropriate permutation matrices P and Q, and a matrix B with all nonzero entries.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제10권2호
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• pp.103-118
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• 2003

We estimate the stable rank of twisted crossed products of $C^{*}-algebras$ by topological Abelian groups. As an application we estimate the stable rank of twisted crossed products of $C^{*}-algebras$ by solvable Lie groups. In particular, we obtain the stable rank estimate of twisted group $C^{*}-algebras$ of solvable Lie groups by the (reduced) dimension and (generalized) rank of groups.

• Kyungpook Mathematical Journal
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• 제47권2호
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• pp.203-219
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• 2007

We estimate the stable rank and connected stable rank of group $C^*$-algebra of certain disconnected solvable Lie groups such as semi-direct products of connected solvable Lie groups by the integers.

• 대한수학회논문집
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• 제21권2호
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• pp.219-226
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• 2006

We consider matrices whose entries can be viewed as elements of both nonnegative integers and nonnegative rational numbers. We determine the differences of factor rank of matrices over the two semirings.

• 한국지리정보학회지
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• 제9권1호
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• pp.149-157
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• 2006

본 연구는 부산시의 GIS 데이타베이스를 활용하여 먼저, 입지포텐셜 분석을 위한 지표를 설정하여 각 지표별 Rank-Map을 작성하였다. 다음으로 각 상업 업무시설이 입지할 가능성을 예측할 수 있는 입지 포텐셜 ($P_i$)을 분석하여 제안하였다. Rank 1, 2로 분류되는 존의 건물용도 현황을 보면, 상업시설 용도가 차지하는 비율이 높음을 알 수 있었다. Rank 4~7까지의 존은 환경보전적 차원에서 비 상업계 용도지역이 지정되고 관리될 필요가 있다고 사료된다. 또한, 본 연구에서 제안한 입지 포텐셜은 용도지역 지정시 상업계 용도지역 지정의 기초자료로서 활용할 수 있다고 사료되어진다.

• 한국정보과학회논문지:컴퓨팅의 실제 및 레터
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• 제11권3호
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• pp.268-274
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• 2005

페이지랭크 알고리즘은 웹 문서들을 효과적으로 랭킹(ranking)하는 것으로 알려져 있다. 페이지랭크 알고리즘은 그 유용함에도 불구하고 경우에 따라 문서의 페이지랭크 값을 본래 값보다 작게 계산하는 현상을 유발한다. 본 논문에서는 이러한 현상을 놈-누수(norm-leak)라 명명하고, 웹 문서의 페이지 랭크 값을 정확히 산출하는 개선된 페이지랭크 알고리즘과 효율적인 구현방법을 제시한다. 또한, 약 67,000,000개의 실제 웹 문서들에 기존의 페이지랭크 알고리즘과 개선된 페이지랭크 알고리즘을 적용하여 그 결과를 비교 평가한다.

• 대한수학회지
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• 제41권2호
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• pp.397-406
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• 2004

For a Boolean rank-l matrix $A\;=\;ab^{t}$, we define the perimeter of A as the number of nonzero entries in both a and b. We characterize the Boolean linear operators that preserve rank and perimeter of Boolean rank-l matrices.

• 대한수학회보
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• 제42권3호
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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.

• Communications for Statistical Applications and Methods
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• 제9권1호
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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.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제14권9호
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• pp.3745-3761
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• 2020

Low-rank representation methods already achieve many applications in the image reconstruction. However, for high-gradient image patches with rich texture details and strong edge information, it is difficult to find sufficient similar patches. Existing low-rank representation methods usually destroy image critical details and fail to preserve edge structure. In order to promote the performance, a new representation-based image super-resolution reconstruction method is proposed, which combines gradient domain guided image filter with the structure-constrained low-rank representation so as to enhance image details as well as reveal the intrinsic structure of an input image. Firstly, we extract the gradient domain guided filter of each atom in high resolution dictionary in order to acquire high-frequency prior information. Secondly, this prior information is taken as a structure constraint and introduced into the low-rank representation framework to develop a new model so as to maintain the edges of reconstructed image. Thirdly, the approximate optimal solution of the model is solved through alternating direction method of multipliers. After that, experiments are performed and results show that the proposed algorithm has higher performances than conventional state-of-the-art algorithms in both quantitative and qualitative aspects.