• Kyungpook Mathematical Journal
• /
• v.56 no.2
• /
• pp.387-396
• /
• 2016

An $n{\times}n$ matrix A over a commutative ring is strongly clean provided that it can be written as the sum of an idempotent matrix and an invertible matrix that commute. Let R be an arbitrary commutative ring, and let $A(x){\in}M_n(R[[x]])$. We prove, in this note, that $A(x){\in}M_n(R[[x]])$ is strongly clean if and only if $A(0){\in}M_n(R)$ is strongly clean. Strongly clean matrices over quotient rings of power series are also determined.

• Journal of Korea Society of Industrial Information Systems
• /
• v.12 no.2
• /
• pp.68-78
• /
• 2007

D-class is defined as a set of equivalent $n{\times}n$ boolean matrices according to a given equivalence relation. The D-class computation requires the multiplication of three boolean matrices for each of all possible triples of $n{\times}n$ boolean matrices. However, almost all the researches on boolean matrices focused on the efficient multiplication of only two boolean matrices and a few researches have recently been shown to deal with the multiplication of all boolean matrices. The paper suggests a mathematical theory that enables the efficient multiplication for all possible boolean matrix triples and the efficient computation of all D-classes, and discusses algorithms designed with the theory and their execution results.

• Journal of the Korea Institute of Military Science and Technology
• /
• v.8 no.3 s.22
• /
• pp.124-130
• /
• 2005

In this paper, the effects of matrix hygrothermal aging and residual stress changes on $Avimid^{(R)}$ K3B/IM7 laminates in $80^{\circ}C$ water were studied. The factors causing the $80^{\circ}C$ water to degradation of the laminates could be the degradation of the matrix toughness, the change in residual stresses. After 500 hours fully saturated aging of the neat resin, the weight gain was 1.55% increase with the diffusion coefficient $7{\times}10^{-6}m^2/s$ and the fracture toughness was decreased about 41%. After 100 hours fully saturated aging of the $[+45/0/-45/90]_s$ K3B/IM7 laminates in $80^{\circ}C$ water, the weight gain was 0.41% increase with the diffusion coefficient $1{\times}10^{-6}m^2/s$ and the loss of the microcracking fracture toughness was 43.8% of the original toughness. To see whether the residual stress influenced the fracture toughness, two ply $[90^{\circ}/0^{\circ}]$ laminates were put in $80^{\circ}C$ water from 2 hours to 8 hours. The changes in residual stress in 8 hours are less than 3MPa. Because the 3MPa change is not sufficient to degrade the laminates, the main factor to degrade the microcracking fracture toughness was the degradation of the matrix fracture toughness.

• The Korean Journal of Cytopathology
• /
• v.8 no.2
• /
• pp.174-178
• /
• 1997

Matrix producing carcinoma of the breast is a variant of heterologous metaplastic carcinoma which is defined as "overt carcinoma with direct transition to a cartilaoenous and/or osseous stromal matrix without an intervening spindle cell zone or osteoclastic cells". This tumor is very rare, occuring in less than 0.2% of total breast carcinoma, but the prognosis is better than other metaplastic carcinoma. We experienced a case of fine needle aspiration(FNA) cytologic finding of matrix producing carcinoma of the breast. A 75-year old woman, who presented a right huge breast mass$(9{\times}8cm)$ during 10months, was examined. Mammography reveals right lateral mass with even density without calcification. Breast ultrasonography shows multifocal hypoechogenic cystic change in the huge mass, suggesting resolving hematoma or carcinoma or sarcoma with necrosis. On cytologic finding of FNA, myxoid matrix was the dominant feature and the rest of the material was composed of scanty isolated atypical cells with large irregular nuclei. The histologic finding was moderately differentiated adenocarcinoma with abundant cartilagenous matrix and focal squamous metaplasia.

• Proceedings of the Korean Information Science Society Conference
• /
• 2006.06a
• /
• pp.400-402
• /
• 2006

Matrix multiplication is an important problem in linear algebra. its main significance for combinatorial algorithms is its equivalence to a variety of other problems, such as transitive closure and reduction, solving linear systems, and matrix inversion. Thus the development of high-performance matrix multiplication implies faster algorithms for all of these problems. In this paper. we present a quantitative comparison of the theoretical and empirical performance of key matrix multiplication algorithms and use our analysis to develop a faster algorithm. We propose a Hybrid approach on Winograd's and Strassen's algorithms that improves the performance and discuss the performance of the hybrid Winograd-Strassen algorithm. Since Strassen's algorithm is based on a $2{\times}2$ matrix multiplication it makes the implementation very slow for larger matrix because of its recursive nature. Though we cannot get the theoretical threshold value of Strassen's algorithm, so we determine the threshold to optimize the use of Strassen's algorithm in nodes through various experiments and provided a summary shown in a table and graphs.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.20 no.2
• /
• pp.107-121
• /
• 2016

We analyze the complexity of the LLL algorithm, invented by Lenstra, Lenstra, and $Lov{\acute{a}}sz$ as a a well-known lattice reduction (LR) algorithm which is previously known as having the complexity of $O(N^4{\log}B)$ multiplications (or, $O(N^5({\log}B)^2)$ bit operations) for a lattice basis matrix $H({\in}{\mathbb{R}}^{M{\times}N})$ where B is the maximum value among the squared norm of columns of H. This implies that the complexity of the lattice reduction algorithm depends only on the matrix size and the lattice basis norm. However, the matrix structures (i.e., the correlation among the columns) of a given lattice matrix, which is usually measured by its condition number or determinant, can affect the computational complexity of the LR algorithm. In this paper, to see how the matrix structures can affect the LLL algorithm's complexity, we derive a more tight upper bound on the complexity of LLL algorithm in terms of the condition number and determinant of a given lattice matrix. We also analyze the complexities of the LLL updating/downdating schemes using the proposed upper bound.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.9 no.3
• /
• pp.1105-1120
• /
• 2015

With the proposed principle of two-dimensional matrix bar code design based on masks, the whole surface of a 2D bar code is used for creating graphic patterns. Masks are a method of overlaying certain information with complete preservation of encoded information. In order to ensure suitable mask performance, it is essential to create a set of masks (mask folder) which are similar to each other. This ultimately allows additional error correction on the whole code level which is proven mathematically through an academic example of a QR code with a matrix of size $9{\times}9$. In order to create a mask folder, this article will investigate parameters based on Weber's law. With the parameters founded in the research, this principle shows how QR codes, or any other 2D bar code, can be designed to display two different messages. This ultimately enables a better description of a 2D bar code, which will improve users' visual recognition of 2D bar code purpose, and therefore users' greater enjoyment and involvement.

• Kyungpook Mathematical Journal
• /
• v.59 no.2
• /
• pp.225-231
• /
• 2019

In a previous paper, the authors of this paper studied $2{\times}2$ matrices in upper triangular form, whose entries are operators on Hilbert spaces, and in which the the (1, 1) entry has a nontrivial hyperinvariant subspace. We were able to show, in certain cases, that the $2{\times}2$ matrix itself has a nontrivial hyperinvariant subspace. This generalized two earlier nice theorems of H. J. Kim from 2011 and 2012, and made some progress toward a solution of a problem that has been open for 45 years. In this paper we continue our investigation of such $2{\times}2$ operator matrices, and we improve our earlier results, perhaps bringing us closer to the resolution of the long-standing open problem, as mentioned above.

• Communications of the Korean Mathematical Society
• /
• v.9 no.4
• /
• pp.767-772
• /
• 1994

For an $n \times n$ complex matrix $A = [A_{ij}]$, the permanent of A, per A, is defined by $$ per A = \sub_{\sigma \in S_n}{a_{1 \sigma(1)} a_{2 \sigma(2)} \cdots a_{n \sigma(n)} $$ where $S_n$ stands for the symmetric group on the set {1, 2, ..., n}.

• Bulletin of the Korean Mathematical Society
• /
• v.33 no.1
• /
• pp.127-133
• /
• 1996

Let $\Omega_n$ be the polyhedron of $n \times n$ doubly stochastic matrices, that is, nonnegative matrices whose row and column sums are all equal to 1. The permanent of a $n \times n$ matrix $A = [a_{ij}]$ is defined by $$ per(A) = \sum_{\sigma}^ a_{1\sigma(a)} \cdots a_{n\sigma(n)} $$ where $\sigma$ runs over all permutations of ${1, 2, \ldots, n}$.