• 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.

• Proceedings of the KIEE Conference
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• 1987.07a
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• pp.185-189
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• 1987

An analysis and design of large-scale linear multivariable systems often requires to be block triangularized form for good sensitivity of the systems when their poles and zeros are varied. But the decomposition algorithms presented up to now need a procedure of permutation, rescaling and a solution of nonlinear algebraic equations, which are usually burden. To avoid these problem, in this paper we develop a newly alternative block triangular decomposition algorithm which used the generalized matrix sign function on the Z-plane. Also, the decomposition algorithm demonstrated using the fifth order linear model of a distillation tower system.

• Applied Science and Convergence Technology
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• v.27 no.5
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• pp.86-89
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• 2018

Observations of neutrino oscillations are very strong evidence for the existence of neutrino masses and mixing. From recent experimental results on neutrino oscillation, we find that neutrino mixing angles are quite consistent with the so-called tri-bi-maximal mixing pattern, but the deviation from observational results is non-negligible. However, the tri-bi-maximal mixing pattern is still useful as a leading order approximation and provides a good guideline to search for the flavor symmetry in the neutrino sector. We introduce the $S_4$ permutation symmetry as a flavor symmetry to the standard model of particle physics with additional particle contents of heavy right-handed neutrinos and scalar fields. Finally, we obtain the tri-bi-maximal mixing pattern as a mixing matrix in the lepton sector within the suggested model. To derive the required unitary mixing matrix for the neutrino sector, the double seesaw mechanism is utilized.

• Kyungpook Mathematical Journal
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• v.58 no.4
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• pp.589-597
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• 2018

For $A,B{\in}M_2(\mathbb{C})$, let the Jordan product be AB + BA and G(A) the eigenvalue inclusion set, the Gershgorin set of A. Characterization is obtained for maps ${\phi}:M_2(\mathbb{C}){\rightarrow}M_2(\mathbb{C})$ satisfying $$G[{\phi}(A){\phi}(B)+{\phi}(B){\phi}(A)]=G(AB+BA)$$ for all matrices A and B. In fact, it is shown that such a map has the form ${\phi}(A)={\pm}(PD)A(PD)^{-1}$, where P is a permutation matrix and D is a unitary diagonal matrix in $M_2(\mathbb{C})$.

• Asian-Australasian Journal of Animal Sciences
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• v.24 no.11
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• pp.1504-1513
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• 2011

It is important to identify genetic interactions related to human diseases or animal traits. Many linear statistical models have been reported but they did not consider genetic interactions. Genotype matrix mapping (GMM) has been developed to identify genetic interactions. This study uses the GMM method to detect superior SNP combinations of the CCDC158 gene that influences average daily gain, marbling score, cold carcass weight and longissimus muscle dorsi area traits in Hanwoo. We evaluated the statistical significance of the major SNP combinations selected by implementing the permutation test of the F-measure. The effect of g.34425+102 A>T (AA), g.8778G>A (GG) and g.4102+36T>G (GT) SNP combinations produced higher performance of average daily gain, marbling score, cold carcass weight and the longissimus muscle dorsi area traits than the effect of a single SNP. GMM is a fast and reliable method for multiple SNP analysis with potential application in marker-assisted selection. GMM may prospectively be used for genetic assessment of quantitative traits after further development.

• Journal for History of Mathematics
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• v.25 no.4
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• pp.101-119
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• 2012

The removal of the Go Stones is a game that anyone can play through simple rules. It is not only an interesting game but also a mathematical game that requires comprehensive knowledge of several mathematical theories. Through analyzing the rules and theories of this game, students can get a new mathematical perspective and recognize something that they didn't realize as important before. Furthermore, this game is given to students as a mathematical problem unconsciously. This helps them get a mathematical approach to understanding the actual concept of the problem as well as the basic principle of the problem.

• School Mathematics
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• v.13 no.3
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• pp.405-422
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• 2011

In this study, we consider the meaning of one-to-one correspondence through theoretical background under operation of matrix. On algebraic point of view, its significance is 'through one-to-one correspondence from a set with given structure, become a methods in order to induce an algebraic system in to a new set.' That is a key idea making isomorphic structure. Such process experiences necessity of mathematical fact, as well as the deep understanding of one-to-one correspon -dence. Also that becomes a base for develop a various mathematical concepts, such as matrix, exponential laws, symmetric difference, permutation and so on. This study help teachers and students to understand of mathematical concepts meaningfully and to facilitate teacher's professional development.

• Proceedings of the Korea Multimedia Society Conference
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• 2002.11b
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• pp.216-219
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• 2002

정보통신의 발달과 인터넷의 확산으로 인해 정보보안의 필요성이 중요한 문제로 대두되면서 여러 종류의 암호 알고리즘이 개발되어 활용되고 있다. Substitution Permutation Networks(SPN)등의 블록 암호 알고리즘에서는 확산선형변환 행렬을 사용하여 안전성을 높이고 있다. 확산선형변환 행렬이 Maximum Distance Separable(MDS) 코드를 생성하면 선형 공격과 차분 공격에 강한 특성을 보인다. 본 논문에서는 선형변환 행렬이 MDS 코드를 생성하는 가를 판단하는 새로운 알고리즘을 제안한다. 입력 코드는 GF(2/sub□/)상의 원소들로 구성되며, 원소를 변수로 해석하여, 변수를 소거시키면서 선형변환행렬이 MDS 코드를 생성하는 가를 판단한다. 본 논문에서 제안한 알고리즘은 종래의 모든 정방 부분행렬이 정칙인가를 판단하는 알고리즘과 비교하여 연산 수행 시간을 크게 줄였다.

• Communications for Statistical Applications and Methods
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• v.8 no.3
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• pp.643-650
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• 2001

Some classical plots like scatterplot matrices and parallel coordinates are valuable tools for data visualization. These tools are extensively used in the modern data mining softwares to explore the inherent data structure, and hence to visually classify or cluster the database into appropriate groups. However, the interpretation of these plots are very sensitive to the arrangement of variables. In this work, we introduce two methods to arrange the variables for data visualization. First method is based on the work of Wegman (1999), and this is to arrange the variables using minimum distance among all the pairwise permutation of the variables. Second method is using the idea of principal components. We Investigate the effectiveness of these methods with parallel coordinates using real data sets, and show that each of the two proposed methods has its own strength from different aspects respectively.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.307-316
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• 2006

Incomplete LU factorization preconditioning techniques often have difficulty on indefinite sparse matrices. We present hybrid reordering strategies to deal with such matrices, which include new diagonal reorderings that are in conjunction with a symmetric nondecreasing degree algorithm. We first use the diagonal reorderings to efficiently search for entries of single element rows and columns and/or the maximum absolute value to be placed on the diagonal for computing a nonsymmetric permutation. To augment the effectiveness of the diagonal reorderings, a nondecreasing degree algorithm is applied to reduce the amount of fill-in during the ILU factorization. With the reordered matrices, we achieve a noticeable improvement in enhancing the stability of incomplete LU factorizations. Consequently, we reduce the convergence cost of the preconditioned Krylov subspace methods on solving the reordered indefinite matrices.