• Journal of the Korean Mathematical Society
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• v.51 no.4
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• pp.773-789
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• 2014

We consider linear operators on square matrices over antinegative semirings. Let ${\varepsilon}_k$ denote the set of all primitive matrices of exponent k. We characterize those linear operators which preserve the set ${\varepsilon}_1$ and the set ${\varepsilon}_2$, and those that preserve the set ${\varepsilon}_{n^2-2n+2}$ and the set ${\varepsilon}_{n^2-2n+1}$. We also characterize those linear operators that strongly preserve ${\varepsilon}_2$, ${\varepsilon}_{n^2-2n+2}$ or ${\varepsilon}_{n^2-2n+1}$.

• The Pure and Applied Mathematics
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• v.21 no.2
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• pp.121-128
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• 2014

The Boolean rank of a nonzero m $m{\times}n$ Boolean matrix A is the least integer k such that there are an $m{\times}k$ Boolean matrix B and a $k{\times}n$ Boolean matrix C with A = BC. In 1984, Beasley and Pullman showed that a linear operator preserves the Boolean rank of any Boolean matrix if and only if it preserves Boolean ranks 1 and 2. In this paper, we extend this characterization of linear operators that preserve the Boolean ranks of Boolean matrices. We show that a linear operator preserves all Boolean ranks if and only if it preserves two consecutive Boolean ranks if and only if it strongly preserves a Boolean rank k with $1{\leq}k{\leq}min\{m,n\}$.

• Bulletin of the Korean Mathematical Society
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• v.46 no.2
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• pp.373-385
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• 2009

An m${\times}$n Boolean matrix A is called regular if there exists an n${\times}$m Boolean matrix X such that AXA = A. We have characterizations of Boolean regular matrices. We also determine the linear operators that strongly preserve Boolean regular matrices.

• Archives of Reconstructive Microsurgery
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• v.20 no.2
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• pp.126-131
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• 2011

Purpose: The subcutaneous pocket graft of the thumb tip amputation across or proximal to the lunula is chosen in case of impossible microvascular anastomosis and in patient who strongly desired to preserve the thumb tip after failed replantation. Materials and Methods: Two patients who underwent a subcutaneous pocket graft for a thumb tip reconstruction between August 2008 and November 2009 were reviewed retrospectively. They were all males with a mean age at the time of surgery of 48 years and had sustained complete thumb tip amputations across or proximal to the lunula. In one case, the microsurgical replantation was not feasible and the other one revealed arterial insufficiency at the 7th day after microsurgical replantation. Results: Authors had experienced 2 cases of flaps which survived completely. The results of sensibility was good, the range of motion at interphalangeal joint and tip to tip pinch was acceptable and color mismatch and loss of thumb finger nail was unacceptable after more than 1 year follow up with conventional successful thumb tip replantation. Conclusion: The subcutaneous pocket graft could be chosen in thumb tip amputation in case of impossible microvascular anastomosis as well as who strongly desires to preserve thumb tip after failed replantation.

• Kyungpook Mathematical Journal
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• v.54 no.4
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• pp.619-627
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• 2014

Let $\mathcal{M}(S)$ denote the set of all $m{\times}n$ matrices over a semiring S. For $A{\in}\mathcal{M}(S)$, zero-term rank of A is the minimal number of lines (rows or columns) needed to cover all zero entries in A. In [5], the authors obtained that a linear operator on $\mathcal{M}(S)$ preserves zero-term rank if and only if it preserves zero-term ranks 0 and 1. In this paper, we obtain new characterizations of linear operators on $\mathcal{M}(S)$ that preserve zero-term rank. Consequently we obtain that a linear operator on $\mathcal{M}(S)$ preserves zero-term rank if and only if it preserves two consecutive zero-term ranks k and k + 1, where $0{\leq}k{\leq}min\{m,n\}-1$ if and only if it strongly preserves zero-term rank h, where $1{\leq}h{\leq}min\{m,n\}$.

• Bulletin of the Korean Mathematical Society
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• v.57 no.3
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• pp.535-545
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• 2020

Let A be an m × n matrix over nonnegative integers. The isolation number of A is the maximum number of isolated entries in A. We investigate linear operators that preserve the isolation number of matrices over nonnegative integers. We obtain that T is a linear operator that strongly preserve isolation number k for 1 ≤ k ≤ min{m, n} if and only if T is a (P, Q)-operator, that is, for fixed permutation matrices P and Q, T(A) = P AQ or, m = n and T(A) = P A^tQ for any m × n matrix A, where A^t is the transpose of A.

• Bulletin of the Korean Mathematical Society
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• v.39 no.2
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• pp.283-287
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• 2002

In this paper, we will investigate the set of linear operators on real square matrices that strongly preserve multivariate majorisation without any additional conditions on the operator. This answers earlier conjecture on nonnegative matrices in [3] .

• Journal of the Korean Mathematical Society
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• v.43 no.3
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• pp.539-552
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• 2006

For an $n{\times}n$ Boolean matrix A, A is called nilpotent if $A^m=O$ for some positive integer m. We consider the set of $n{\times}n$ nilpotent Boolean matrices and we characterize linear operators that strongly preserve nilpotent matrices over Boolean algebras.

• Journal of the Korean Geographical Society
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• v.34 no.3
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• pp.247-264
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• 1999

In this study, I investigate how city parks have been created, and what are some characteristics of the location and function of 69 city parks in Tokyo. The city parks in Tokyo have been made in three patterns. The first is planned parks which have been created as a urban facilities considering the scales and types. The second is memorial parks which have been made to memorialize the national monumental event or to preserve natural and cultural resources. The third is public property parks which have been made by occurrence of public vacant land which is resulted from the grant of Royal Garden, restoration of public rented ground, producton of reclaimed land, utilization of dry river bed. The city parks can be classified in five patterns according to distance from CBD and park area. The first is central parks which have historical characteristics strongly. The second is planned parks that are specialized functionally. The third is large scale urban edge parks which are located in the edge of 23-Gu(district) in Tokyo. The fourth is hill parks which have natural characteristics strongly. The fifth is waterside parks that are located along a lake, a pond, a river, or artificial waterside facilities. From this study I have found out that a great effort has been made to activate the utilization of parks for residents in Tokyo, through mnagement goals and ways of parks, composition and chatacteristics of park facility resources, various Events, residents participation in undertaking of parks.

• Journal of the Korean Mathematical Society
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• v.52 no.3
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• pp.625-636
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• 2015

The Boolean rank of a nonzero $m{\times}n$ Boolean matrix A is the least integer k such that there are an $m{\times}k$ Boolean matrix B and a $k{\times}n$ Boolean matrix C with A = BC. We investigate the structure of linear transformations T : $\mathbb{M}_{m,n}{\rightarrow}\mathbb{M}_{p,q}$ which preserve Boolean rank. We also show that if a linear transformation preserves the set of Boolean rank 1 matrices and the set of Boolean rank k matrices for any k, $2{\leq}k{\leq}$ min{m, n} (or if T strongly preserves the set of Boolean rank 1 matrices), then T preserves all Boolean ranks.