• The Korean Journal of Applied Statistics
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• v.28 no.2
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• pp.211-219
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• 2015

Generalized linear mixed models are used to analyze longitudinal categorical data. Random effects specify the serial dependence of repeated outcomes in these models; however, the estimation of a random effects covariance matrix is challenging because of many parameters in the matrix and the estimated covariance matrix should satisfy positive definiteness. Several approaches to model the random effects covariance matrix are proposed to overcome these restrictions: modified Cholesky decomposition, moving average Cholesky decomposition, and partial autocorrelation approaches. We review several approaches and present potential future work.

• The Korean Journal of Applied Statistics
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• v.30 no.1
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• pp.103-117
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• 2017

In longitudinal data analysis, the serial correlation of repeated outcomes must be taken into account using covariance matrix. Modeling of the covariance matrix is important to estimate the effect of covariates properly. However, It is challenging because there are many parameters in the matrix and the estimated covariance matrix should be positive definite. To overcome the restrictions, several Cholesky decomposition approaches for the covariance matrix were proposed: modified autoregressive (AR), moving average (MA), ARMA Cholesky decompositions. In this paper we review them and compare the performance of the approaches using simulation studies.

• Journal of applied mathematics & informatics
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• v.38 no.1_2
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• pp.175-187
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• 2020

Recently Salkuyeh and Rahimian in (Comput. Math. Appl. 74 (2017) 2940-2949) proposed a modification of the generalized shift-splitting (MGSS) method for solving singular saddle point problems. In this paper, we present the spectral analysis of the MGSS preconditioner when it is applied to precondition the singular saddle point problems with the (1, 1) block being symmetric. Some eigenvalue bounds for the spectrum of the preconditioned matrix are given. We show that all the real eigenvalues of the preconditioned matrix are in a positive interval and all nonzero eigenvalues having nonzero imaginary part are contained in an intersection of two circles.

• Journal of Nutrition and Health
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• v.46 no.1
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• pp.26-33
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• 2013

The purpose of this study was to investigate the sodium intake of office workers using 24-hour urine analysis and to analyze the correlation matrix between variables. The sodium intake of the subjects (n = 137), based on a 24-hr sodium excretion period, was male (n = 56) 6072.4 mg and female (n = 81) 5,168.2 mg. Urinary sodium excretion showed significant positive correlation with BMI, frequency of eating out, expenditure of eating out, salty taste assessment and high-salt dietary behavior. Analysis of urinary sodium excretion showed significant positive correlation with intake frequencies of cabbage kimchi, broiled fish, feast noodle and rice with leaf wraps. Based on the results of multiple regression, urinary sodium excretion was found to be related to intake frequencies of cabbage kimchi, broiled fish, rice with leaf wraps and high score of high-salt dietary behavior.

• Carbon letters
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• v.1 no.1
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• pp.1-5
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• 2000

The effect of surface free energy on the positive temperature coefficient (PTC) of carbon black/thermoplastic resin composites was investigated. The thermoplastic resins such as EVA, LDPE, LLDPE and HDPE were used with the addition of 30 wt.% of the carbon black. The surface free energy of the composites was studied in the context of two-liquid contact angle measurements, i.e., deionized water and diiodomethane. It was observed that the resistivity on PTC composites Was greatly increased near the crystalline melting temperature, due to the thermal expansion of polymeric matrix. From the experimental results, it was proposed that the decrease of surface free energy induced by interactions between carbon black surfaces and polymer chains is an important factor to the fabrication of a PTC composite made of carbon black and polymeric matrix.

• Proceedings of the Korea Air Pollution Research Association Conference
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• 2002.11a
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• pp.189-190
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• 2002

PMF(Positive Matrix Factorization) 모텔은 기존의 인자분석 모델이 갖는 인자부하량의 음수 문제를 해결하기 위해 인자부하량과 공통인자를 양수로 제한하여 결과 해석에 명확성을 주었다. 또한 환경연구에서 많이 나타나는 outlier와 log-normal분포모형을 선택사항으로 도입하고 있어 현재 환경관련 연구에 응용성이 높다. 본 연구에서는 대전 1, 2 공단 지역의 PM 10 중 미량금속과 이온성분의 농도를 분석하고 PMF를 이용하여 오염원을 확인하고자 한다. (중략)

• Korean Journal of Mathematics
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• v.29 no.2
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• pp.371-386
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• 2021

This paper investigates two discrete time queueing inventory models with positive service time and lead time. Customers arrive according to a Bernoulli process and service time and lead time follow geometric distributions. The first model under discussion based on replenishment of order upto S policy where as the second model is based on order placement by a fixed quantity Q, where Q = S - s, whenever the inventory level falls to s. We analyse this queueing systems using the matrix geometric method and derive an explicit expression for the stability condition. We obtain the steady-state behaviour of these systems and several system performance measures. The influence of various parameters on the systems performance measures and comparison on the cost analysis are also discussed through numerical example.

• Communications of the Korean Mathematical Society
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• v.17 no.4
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• pp.577-581
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• 2002

The incidence matrices corresponding to a nil-algebra of finite index % can be used to determine the nilpotency. We find the smallest positive integer n such that the sum of the incidence matrices Σ$\_$p/$\^$p/ is invertible. In this paper, we give a different proof of the case that the nil-algebra of index 2 has nilpotency less than or equal to 4.

• Korean Management Science Review
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• v.19 no.2
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• pp.155-168
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• 2002

In this paper, some efficient implementation techniques for the multifrontal method, which can be used to compute the Cholesky factor of a symmetric positive definite matrix, are presented. In order to use the cache effect in the cache-based computer architecture, a hybrid method for factorizing a frontal matrix is considered. This hybrid method uses the column Cholesky method and the submatrix Cholesky method alternatively. Experiments show that the hybrid method speeds up the performance of the supernodal multifrontal method by 5%～10%, and it is superior to the Cholesky method in some problems with dense columns or large frontal matrices.

• Journal of the Korean Mathematical Society
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• v.43 no.3
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• pp.539-552
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• 2006

For an $n{\times}n$ Boolean matrix A, A is called nilpotent if $A^m=O$ for some positive integer m. We consider the set of $n{\times}n$ nilpotent Boolean matrices and we characterize linear operators that strongly preserve nilpotent matrices over Boolean algebras.