• Honam Mathematical Journal
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• v.42 no.2
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• pp.235-249
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• 2020

Let Q and R be the well-known matrices associated with Fibonacci and Lucas numbers, and k, m, and n be any integers. It is mainly established all solutions of the matrix equations c₁Qⁿ + c₂Q^m = Q^k, c₁Qⁿ + c₂Q^m = RQ^k, and c₁Qⁿ + c₂RQ^m = Q^k with unknowns c₁, c₂ ∈ ℂ*. Moreover, using the obtained results, it is presented many identities, some of them are available in the literature, and the others are new, related to the Fibonacci and Lucas numbers.

• East Asian mathematical journal
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• v.29 no.3
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• pp.327-335
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• 2013

In this paper we consider the quadratic matrix equation which can be defined by $$Q(X)=AX^2+BX+C=0$$, where X is a $n{\times}n$ unknown complex matrix, and A, B and C are $n{\times}n$ given matrices with complex elements. We first introduce a couple of condition numbers of the equation Q(X) and present normwise condition numbers. Finally, we compare the results and some numerical experiments are given.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.4
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• pp.413-427
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• 2020

In this work we study 0-commuting matrix C(0) under relationships with the Pascal matrix C(1). Like kth power C(1)k is an arithmetic matrix of (kx+y)n with yx = xy (k ≥ 1), we express C(0)k as an arithmetic matrix of certain polynomial with yx = 0.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.27 no.8
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• pp.98-104
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• 2013

AC machines are in wide use in industry and d-q transformation from 3 phase of a, b, c is commonly used to analyze these kinds of machines. The equivalent circuits of d and q axis are, however, generally cross coupled and difficult to analyze. In this study, a modeling technique of AC machine including induction and PM synchronous motors using matrix vector is proposed. With that model, it can not only explain the AC machines physically but also make it simple to analyze them. The separating process of d and q components is not needed in this model and this model can be applied to analyze asymmetric motors like IPMSM machine. With this technique, the model becomes simple, easy to understand physically, and yields results that are the same as those from other models. These simulation results of the proposed model for induction motor are compared with those of other models to verify the method proposed.

• Journal of Broadcast Engineering
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• v.21 no.1
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• pp.60-65
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• 2016

This paper introduces the non-local means (NLM) algorithm for image denoising, and also introduces an improved algorithm which is based on the principal component analysis (PCA). To do the PCA, a covariance matrix of a given image should be evaluated first. If we let the size of neighborhood patches of the NLM S × S², and let the number of pixels Q, a matrix multiplication of the size S² × Q is required to compute a covariance matrix. According to the characteristic of images, such computation is inefficient. Therefore, this paper proposes an efficient method to compute the covariance matrix by sampling the pixels. After sampling, the covariance matrix can be computed with matrices of the size S² × floor (Width/l) × (Height/l).

• Journal of the Korean Mathematical Society
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• v.50 no.4
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• pp.755-770
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• 2013

One of the interesting nonlinear matrix equations is the quadratic matrix equation defined by $$Q(X)=AX^2+BX+C=0$$, where X is a $n{\times}n$ unknown real matrix, and A, B and C are $n{\times}n$ given matrices with real elements. Another one is the matrix polynomial $$P(X)=A_0X^m+A_1X^{m-1}+{\cdots}+A_m=0,\;X,\;A_i{\in}\mathbb{R}^{n{\times}n}$$. Newton's method is used to find the symmetric and bisymmetric solvents of the nonlinear matrix equations Q(X) and P(X). The method does not depend on the singularity of the Fr$\acute{e}$chet derivative. Finally, we give some numerical examples.

• Environmental Engineering Research
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• v.14 no.1
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• pp.63-67
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• 2009

Escherichia coli K-12 (E. coli K-12) is a representative indicator globally used for distinguishing and monitoring dynamic fates of pathogenic microorganisms in the environment. This study investigated how to most critically quantify lacZ ($\beta$-galactosidase) gene in E. coli K-12 by two different real-time polymerase chain reaction (real-time PCR) in association with three different DNA extraction practices. Three DNA extractions, i.e., sodium dodecyl sulfate (SDS)/proteinase K, magnetic beads and guanidium thiocyanate (GTC)/silica matrix were each compared for extracting total genomic DNA from E. coli K-12. Among them, GTC/silica matrix and magnetic beads beating similarly worked out to have the highest (22-23 ng/${\mu}L$) concentration of DNA extracted, but employing SDS/proteinase K had the lowest (10 ng/${\mu}L$) concentration of DNA retrieved. There were no significant differences in the quantification of the copy numbers of lacZ gene between SYBR Green I qPCR and QProbe-qPCR. However, SYBR Green I qPCR obtained somewhat higher copy number as $1{\times}10^8$ copies. It was decided that GTC/silica matrix extraction or magnetic beads beating in combination with SYBR Green I qPCR can be preferably applied for more effectively quantifying specific gene from a pure culture of microorganism.

• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.643-652
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• 2008

We construct the sets of Boolean matrix pairs, which are naturally occurred at the extreme cases for the Boolean rank inequalities relative to the sums and difference of two Boolean matrices or compared between their Boolean ranks and their real ranks. For these sets, we consider the linear operators that preserve them. We characterize those linear operators as T(X) = PXQ or $T(X)\;=\;PX^tQ$ with appropriate invertible Boolean matrices P and Q.

• Kyungpook Mathematical Journal
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• v.46 no.1
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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.

• Honam Mathematical Journal
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• v.30 no.4
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• pp.659-670
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• 2008

We denote by $\mathcal{Q}$(A) the set of all real matrices with the same sign pattern as a real matrix A. A matrix A is an SN-matrix provided there exists a set S of sign pattern such that the set of sign patterns of vectors in the -space of $\tilde{A}$ is S, for each ${\tilde{A}}{\in}\mathcal{Q}(A)$. Some properties of SN-matrices arc investigated.