• Communications of the Korean Mathematical Society
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• v.9 no.3
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• pp.629-639
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• 1994

Loewner ([13]) showend the semigroup of the real non-singular totally positive matrices is generated by itsinfinitesimal elements, that is,s the set of all Jacobi matrices with non-negative off-diagonal elements. In general, a semigroup is not completely recreated from the set of its infinitesimal elements. We extend Loewner's work and show that the semi-group of all invertible upper (or lower) triangular stochastic matrices is generated by the set of its infinitesimal elements.

• Communications of the Korean Mathematical Society
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• v.33 no.4
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• pp.1097-1102
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• 2018

Let A and B be matrices which are polynomials in r pairwise commuting nilpotent matrices over a field. We give a sufficient condition for the null space of $A^i$ to equal that of $B^i$ for all i, in particular, for A and B to be similar.

• Honam Mathematical Journal
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• v.35 no.2
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• pp.211-223
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• 2013

We consider permanent function on the faces of the polytope of certain doubly stochastic matrices, whose nonzero entries coincide with those of fully indecomposable square (0, 1)-matrices containing identity submatrix. We determine the minimum permanents and minimizing matrices on the given faces of the polytope using the contraction method.

• Journal of applied mathematics & informatics
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• v.40 no.5_6
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• pp.979-982
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• 2022

This paper covers some important operator inequalities connected with traces of matrices, from the classical inequalities we obtained new inequalities connected with traces of matrices which are better than the others.

• Journal of Information Technology Services
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• v.9 no.4
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• pp.219-229
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• 2010

The Green's equivalence relations have played a fundamental role in the development of semigroup theory. They are concerned with mutual divisibility of various kinds, and all of them reduce to the universal equivalence in a group. Boolean matrices have been successfully used in various areas, and many researches have been performed on them. Studying Green's relations on a monoid of boolean matrices will reveal important characteristics about boolean matrices, which may be useful in diverse applications. Although there are known algorithms that can compute Green relations, most of them are concerned with finding one equivalence class in a specific Green's relation and only a few algorithms have been appeared quite recently to deal with the problem of finding the whole D or J equivalence relations on the monoid of all $n{\times}n$ Boolean matrices. However, their results are far from satisfaction since their computational complexity is exponential-their computation requires multiplication of three Boolean matrices for each of all possible triples of $n{\times}n$ Boolean matrices and the size of the monoid of all $n{\times}n$ Boolean matrices grows exponentially as n increases. As an effort to reduce the execution time, this paper shows an isomorphism between the R relation and L relation on the monoid of all $n{\times}n$ Boolean matrices in terms of transposition. introduces theorems based on it discusses an improved algorithm for the J relation computation whose design reflects those theorems and gives its execution results.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.20 no.10
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• pp.946-952
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• 2010

A method for the identification of structural characteristic parameters of a steel bar in the matrices form such as stiffness matrices and mass matrices from frequency response function(FRF) by genetic algorithm is proposed. As the method is based on the finite element method(FEM), the obtained matrices have perfect physical meanings if the FRFs got from the analysis and the FRFs from the experiments were well coincident each other. The identified characteristic matrices from the FRFs with maximun 40 % of random errors by the genetic algorithm are coincident with the characteristic matrices from exact FEM FRFs well each other. The fitted element diameters by using only 2 points experimental FRFs are similar to the actual diameters of the bar. The fitted FRFs are good accordance with the experimental FRFs on the graphs. FRFs of the rest 9 points not used for calculating could be fitted even well.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.20 no.10
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• pp.923-930
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• 2010

Finite element models of dynamic systems can be updated in two stages. In the first stage, mass and stiffness matrices are updated neglecting damping, and in the second stage, damping matrices are estimated with the mass and stiffness matrices fixed. Three methods to estimate damping matrices for this purpose are proposed in this paper. The methods include one for proportional damping systems and two for non-proportional damping systems. Method 1 utilizes orthogonality of normal modes and estimates damping matrices using the modal parameters extracted from the measured responses. Method 2 estimates damping matrices from impedance matrices which are the inverse of FRF matrices. Method 3 estimates damping using the equation which relates a damping matrix to the difference between the analytical and measured FRFs. The characteristics of the three methods are investigated by applying them to simulated discrete system data and experimental cantilever beam data.

• The Journal of the Korea Contents Association
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• v.6 no.2
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• pp.27-33
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• 2006

Boolean matrices are applied to a variety of areas and used successfully in many applications, and there are many researches on boolean matrices. Most researches deal with the multiplication of boolean matrices, but all of them focus on the multiplication of two boolean matrices and very few researches deal with the multiplication between many n$\times$m boolean matrices and all m$\times$k boolean matrices. The paper discusses the existing optimal algorithms for the multiplication of two boolean matrices are not suitable for the multiplication between a n$\times$m boolean matrix and all m$\times$k boolean matrices, establishes a theory that enables the efficient multiplication of a n$\times$m boolean matrix and all m$\times$k boolean matrices, and shows the execution results of a multiplication algorithm designed with this theory.

• The Korean Journal of Applied Statistics
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• v.22 no.3
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• pp.443-461
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• 2009

In order to overcome the lack of Korean credit rating migration data, we consider an empirical Bayes procedure to estimate credit rating migration matrices. We derive the posterior probabilities of Korean credit rating transitions by utilizing the Moody's rating migration data and the credit rating assignments from Korean rating agency as prior information and likelihood, respectively. Metrics based upon the average transition probability are developed to characterize the migration matrices and compare our Bayesian migration matrices with some given matrices. Time series data for the metrics show that our Bayesian matrices are stable, while the matrices based on Korean data have large variation in time. The bootstrap tests demonstrate that the results from the three estimation methods are significantly different and the Bayesian matrices are more affected by Korean data than the Moody's data. Finally, Monte Carlo simulations for computing the values of a portfolio and its credit VaRs are performed to compare these migration matrices.

• Mass Spectrometry Letters
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• v.5 no.2
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• pp.49-51
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• 2014

The effectiveness of tertiary matrices composed of the combination of three common matrices (dihydrobenzoic acid (DHB), ${\alpha}$-cyano-4-hydroxycinnamic acid (CHCA), and sinapinic acid (SA)) was compared with that of single or binary matrices in the analysis of polyethylene glycol (PEG) polymers ranging from 1400 to 10000 Da using matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF MS). A tertiary matrix of 2,5-DHB+CHCA+SA was the most effective in terms of S/N ratios. CHCA and CHCA+SA produced the highest S/N ratios among the single matrices and the binary matrices, respectively. The improvement observed when using a tertiary matrix in analyses of PEG polymers by MALDI-TOF MS is believed to be due to the uniform morphology of the MALDI sample spots and synergistic effects arising from the mixture of the three matrix materials.