• Journal of applied mathematics & informatics
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• 제29권3_4호
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• pp.641-651
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• 2011

In this paper, with use of the displacement matrix, two special matrices are constructed. By these special matrices the block decompositions of the block symmetric Hankel matrix and the inverse of the Hankel matrix are derived. Hence, the algorithms according to these decompositions are given. Furthermore, the numerical tests show that the algorithms are feasible.

• 한국멀티미디어학회논문지
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• 제17권8호
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• pp.953-960
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• 2014

In Shamir's (t,n)-threshold based secret image sharing schemes, there exists a problem that the secret image can be reconstructed when an arbitrary attacker becomes aware of t secret image pieces, or t participants are malicious collusion. It is because that utilizes linear combination polynomial arithmetic operation. In order to overcome the problem, we propose a secret image sharing scheme using matrix decomposition and adversary structure. In the proposed scheme, there is no reconstruction of the secret image even when an arbitrary attacker become aware of t secret image pieces. Also, we utilize a simple matrix decomposition operation in order to improve the security of the secret image. In experiments, we show that performances of embedding capacity and image distortion ratio of the proposed scheme are superior to previous schemes.

• 응용통계연구
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• 제33권3호
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• pp.281-296
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• 2020

같은 개체로부터 반복 측정한 자료를 경시적 자료(longitudinal data)라고 한다. 이러한 자료를 분석하려면 흔히 사용되는 횡단 자료 분석과는 다른 분석 방법이 필요하다. 즉, 경시적 자료에서 공변량의 효과를 추정할 때에는 반복 측정된 결과 간의 상관성을 고려해야 하며, 따라서 공분산행렬을 모형화 하는 것이 매우 중요하다. 그러나 추정해야 할 모수가 많고, 추정된 공분산행렬이 양정치성을 만족해야 하므로 공분산 행렬의 모형화는 쉽지 않다. 특히 다변량 경시적 자료분석을 위한 공분산행렬의 모형화는 더욱더 심층적인 방법론을 사용해야 한다. 본 논문은 다변량 경시적 자료분석을 위한 공분산행렬을 모형화하기 위해 두 가지 방법론을 고찰한다. 두 방법 모두 수정된 콜레스키 분해(modified Cholesky decomposition)를 이용하여 시간에 따른 응답변수들의 상관관계를 설명하고 있다. 하지만 같은 시간에서 관측된 응답변수들간의 상관관계를 설명하는 방법이 다르다. 첫 번째 방법론에서는 향상된 선형 공분산 모형(enhanced linear covariance models)을 사용하여 공분산행렬이 양정치성을 만족하도록 한다. 두 번째 방법론에서는 분산-공분산 분해(variance-correlation decomposition)와 초구분해(hypersphere decomposition)을 이용하여 공분산 행렬을 모형화 한다. 이 두 방법론의 성능을 비교하고자 모의실험을 진행한다.

• Journal of applied mathematics & informatics
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• 제28권3_4호
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• pp.913-921
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• 2010

The derivative influence measure is adapted to the Cholesky decomposition of a covariance matrix. Formulas for the derivative influence of observations on the Cholesky root and the inverse Cholesky root of a sample covariance matrix are derived. It is easy to implement this influence diagnostic method for practical use. A numerical example is given for illustration.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2003년도 하계종합학술대회 논문집 V
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• pp.2705-2708
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• 2003

In this paper, we propose a method that applies matrix decomposition technique to the connection of actuator capabilities of each robot to object acceleration limits for multiple cooperative robot systems. The robot systems under consideration are composed of several robot manipulators and each robot contacts a single object to carry the object while satisfying the constraints described in kinematics as well as dynamics. By manipulating kinematic and dynamic equations of both robots and objects, we at first derive a matrix relating joint torques with object acceleration, manipulate the null space of the matrix, and then we decompose the matrix into three parts representing indeterminancy, connectivity, and redundancy. With the decomposed matrix we derive the boundaries of object accelerations from given joint actuators. To show the validity of the proposed method some examples are given in which the results can be expected by intuitive observation.

• Communications for Statistical Applications and Methods
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• 제25권1호
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• pp.61-70
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• 2018

Modeling of the random effects covariance matrix in generalized linear mixed models (GLMMs) is an issue in analysis of longitudinal categorical data because the covariance matrix can be high-dimensional and its estimate must satisfy positive-definiteness. To satisfy these constraints, we consider the autoregressive and moving average Cholesky decomposition (ARMACD) to model the covariance matrix. The ARMACD creates a more flexible decomposition of the covariance matrix that provides generalized autoregressive parameters, generalized moving average parameters, and innovation variances. In this paper, we analyze longitudinal count data with overdispersion using GLMMs. We propose negative binomial loglinear mixed models to analyze longitudinal count data and we also present modeling of the random effects covariance matrix using the ARMACD. Epilepsy data are analyzed using our proposed model.

• 응용통계연구
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• 제28권2호
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• pp.211-219
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• 2015

일반화 선형혼합모델은 일반적으로 경시적 범주형 자료를 분석하는데 사용된다. 이 모델에서 임의효과는 반복 측정치들의 시간에 따른 의존성을 설명한다. 임의효과 공분산행렬의 추정은 여러가지 제약조건들 때문에 쉽지 않은 문제이다. 제약조건으로는 행렬의 모수들의 수가 많으며, 또한 추정된 공분산행렬은 양정치성을 만족하여야 한다. 이러한 제한을 극복하기 위해, 임의효과 공분산행렬의 모형화를 위한 여러가지 방법이 제안되었다: 수정 단냠레스키분해, 이동평균 단냠레스키분해와 부분 자기상관행렬을 이용한 방법이 있다. 이 논문에서 위의 제안된 방법들을 소개한다.

• Journal of the Korean Data and Information Science Society
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• 제14권4호
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• pp.1007-1012
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• 2003

A recursive procedure for finding the Cholesky root of the inverse of sample covariance matrix, leading to a direct solution for the inverse of a positive definite matrix, is developed using the likelihood equation for the maximum likelihood estimation of the Cholesky root under normality assumptions. An example of the Hilbert matrix is considered for an illustration of the procedure.

• The Korean Journal of Ceramics
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• 제2권4호
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• pp.231-237
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• 1996

Mullite ceramics can be sintered by rf plasma sintering to densities as high as 97% compared to the theoretical density of the mullite, while SiC whisker-reinforced mullite matrix ceramic composites were not sintered by plasma sintering. Decomposition of mullite occurs in a superficial regins at the outside surface of the specimen by volatilization of SiO at elevated temperature by plasma. SiC whiskers were destroyed, and the matrix was converted to alumina from SiC-whisker reinforced mullite matrix ceramic composites during the plasma sintering. Accelerated volatilization from the SiC whisker in the mullite prevents sintering. The volatile species are mainly SiC and CO gas species. The effects of plasma on mullite and SiC-whisker reinforced mullite matrix composites are interpreted by thermodynamic simulation of the volatile species in the plasma environment. The thermodynamic results show that the decomposition will not occur during hot pressing.

• International Journal of Control, Automation, and Systems
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• 제5권5호
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• pp.508-514
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• 2007

Properties and potential applications of the block pulse response circulant matrix (PRCM) and its singular value decomposition (SVD) are investigated in relation to MIMO control and identification. The SVD of the PRCM is found to provide complete directional as well as frequency decomposition of a MIMO system in a real matrix form. Three examples were considered: design of MIMO FIR controller, design of robust reduced-order model predictive controller, and input design for MIMO identification. The examples manifested the effectiveness and usefulness of the PRCM in the design of MIMO control and identification. irculant matrix, SVD, MIMO control, identification.