• 대한수학회보
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• 제58권3호
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• pp.609-616
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• 2021

We study the solvability of the Fermat's matrix equation in some classes of 2-by-2 matrices. We prove the Fermat's matrix equation has infinitely many solutions in a set of 2-by-2 positive semidefinite integral matrices, and has no nontrivial solutions in some classes including 2-by-2 symmetric rational matrices and stochastic quadratic field matrices.

• Kyungpook Mathematical Journal
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• 제63권4호
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• pp.561-569
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• 2023

An element a ∈ R is strongly rad-clean provided that there exists an idempotent e ∈ R such that a - e ∈ U(R), ae = ea and eae ∈ J(eRe). In this article, we completely determine when a 2 × 2 matrix over a commutative local ring is strongly rad clean. An application to matrices over power-series is also given.

• Journal of the Korean Data and Information Science Society
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• 제20권4호
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• pp.741-747
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• 2009

Properties of multivariate Shewhart and EWMA (Exponentially Weighted Moving Average) control charts for monitoring variance-covariance matrix of quality variables are investigated. Performances of the proposed charts are evaluated for matched fixed sampling interval (FSI) and variable sampling interval (VSI) charts in terms of average time to signal (ATS) and average number of samples to signal (ANSS). Average number of swiches (ANSW) of the proposed VSI charts are also investigated.

• Journal of the Korean Data and Information Science Society
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• 제15권4호
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• pp.1003-1010
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• 2004

Properties of the variable sampling interval(VSI) CUSUM chart for monitoring dispersion matrix of related quality characteristics are investigated. Performances of the proposed charts are evaluated for matched fixed sampling interval(FSI) and VSI charts in terms of average time to signal(ATS) and average number of samples to signal (ANSS). Average number of swiches(ANSW) of the proposed VSI Shewhart and CUSUM charts are also investigated.

• 한국경영과학회지
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• 제17권2호
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• pp.25-33
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• 1992

Manufacturing cell formation is one of the most important problems faced in designing cellular manufacturing systems. The purpose of this study is to design effective manufacturing cell systems by developing a method which forms machines/parts into optimal machine cells/part families. The 0-1 data matrix structure is used to form a basis for manufacturing cell formation. In this paper, we propose a CE method to reorder the 0-1 data matrix for manufacturing cell formation. The resulting solutions are shown to demonstrate the effectiveness of the CE method.

• Communications for Statistical Applications and Methods
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• 제2권1호
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• pp.48-54
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• 1995

A direct method for fitting analysis-of-variance models to unbalanced data is presented. This method exploits sparsity and rank deficiency of the matrix and is based on Gram-Schmidt orthogonalization of a set of sparse columns of the model matrix. The computational algorithm of the sum of squares for testing estmable hyphotheses is given.

• Journal of the Korean Data and Information Science Society
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• 제15권3호
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• pp.633-644
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• 2004

Exponentially Weighted Moving Average(EWMA) control chart for variance-covariance matrix of several quality characteristics based on accumulate-combine approach has proposed. Numerical computations show that multivariate EWMA chart based on accumulate-combine approach is more efficient than corresponding multivariate EWMA chart based on combine-accumulate approach.

• 한국신뢰성학회지:신뢰성응용연구
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• 제1권1호
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• pp.17-33
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• 2001

The characteristics of Weibull distribution are investigated as a function of shape parameter. The statistical estimation methods of the shape parameter and statistical comparison methods of two or more shape parameters are studied. Assuming Weibull distribution, statistical analysis of bending-strength data of alumina titanium carbide ceramic matrix composites machined two different methods are performed.

• Journal of the Korean Data and Information Science Society
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• 제22권6호
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• pp.1251-1256
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• 2011

Consider a p-variate ($p{\geq}4$) normal distribution with mean ${\theta}$ and identity covariance matrix. Using a simple property of noncentral chi square distribution, the generalized Bayes estimators dominating the Lindley estimator under quadratic loss are given based on the methods of Brown, Brewster and Zidek for estimating a normal variance. This result can be extended the cases where covariance matrix is completely unknown or ${\Sigma}={\sigma}^2I$ for an unknown scalar ${\sigma}^2$.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제11권3호
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• pp.135-142
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• 2011

Unlike using the sequence-based representation for a chromosome in previous genetic algorithms for Bayesian structure learning, we proposed a matrix representation-based genetic algorithm. Since a good chromosome representation helps us to develop efficient genetic operators that maintain a functional link between parents and their offspring, we represent a chromosome as a matrix that is a general and intuitive data structure for a directed acyclic graph(DAG), Bayesian network structure. This matrix-based genetic algorithm enables us to develop genetic operators more efficient for structuring Bayesian network: a probability matrix and a transpose-based mutation operator to inherit a structure with the correct edge direction and enhance the diversity of the offspring. To show the outstanding performance of the proposed method, we analyzed the performance between two well-known genetic algorithms and the proposed method using two Bayesian network scoring measures.