• 대한수학회논문집
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• 제20권4호
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• pp.671-683
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• 2005

The set of all $m\;{\times}\;n$ matrices with entries in $\mathbb{Z}_+$ is de­noted by $\mathbb{M}{m{\times}n}(\mathbb{Z}_+)$. We say that a linear operator T on $\mathbb{M}{m{\times}n}(\mathbb{Z}_+)$ is a (U, V)-operator if there exist invertible matrices $U\;{\in}\; \mathbb{M}{m{\times}n}(\mathbb{Z}_+)$ and $V\;{\in}\;\mathbb{M}{m{\times}n}(\mathbb{Z}_+)$ such that either T(X) = UXV for all X in $\mathbb{M}{m{\times}n}(\mathbb{Z}_+)$, or m = n and T(X) = $UX^{t}V$ for all X in $\mathbb{M}{m{\times}n}(\mathbb{Z}_+)$. In this paper we show that a linear operator T preserves the rank of matrices over the nonnegative integers if and only if T is a (U, V)­operator. We also obtain other characterizations of the linear operator that preserves rank of matrices over the nonnegative integers.

• 한국콘텐츠학회:학술대회논문집
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• 한국콘텐츠학회 2006년도 춘계 종합학술대회 논문집
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• pp.459-461
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• 2006

모든 n차 정사각 불리언 행렬 사이의 연속곱셈은 D-클래스 계산과 같은 응용에서 기본적으로 요구되는 연산이다. 그러나 불리언 행렬에 대한 많은 연구에도 불구하고 이에 대한 연구는 아직 보이지 않고 있다. 본 논문은 하나의 n차 정사각 불리언 행렬과 모든 n차 정사각 불리언 행렬 사이의 이중 연속곱셈을 효율적으로 할 수 있는 이론을 제시하고, 이를 모든 n차 정사각 불리언 행렬 사이의 연속곱셈에 적용한 실행결과를 보인다.

• Journal of Multimedia Information System
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• 제4권4호
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• pp.219-224
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• 2017

This paper is to introduce an application of face recognition algorithm in parallel. We have experiments of 25 images with different motions and simulated the image recognitions; grouping of the image vectors, image normalization, calculating average image vectors, etc. We also discuss an analysis of the related eigen-image vectors and a parallel algorithm. To develop the parallel algorithm, we propose a new type of initial matrices for eigenvalue problem. If A is a symmetric matrix, initial matrices for eigen value problem are investigated: the "optimal" one, which minimize ${\parallel}C-A{\parallel}_F$ and the "super optimal", which minimize ${\parallel}I-C^{-1}A{\parallel}_F$. In this paper, we present a general new approach to the design of an initial matrices to solving eigenvalue problem based on the new optimal investigating C with preserving the characteristic of the given matrix A. Fast all resulting can be inverted via fast transform algorithms with O(N log N) operations.

• Journal of electromagnetic engineering and science
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• 제6권4호
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• pp.209-216
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• 2006

This paper investigates a distinct set of complex unitary matrices for QPSK differential space time coding. After properly selecting the initial transmission matrix and unitary matrices we find that the different combinations of them could lead different BER performance over slow/fast Rayleigh fading channels and antennas correlated channels. The numerical results show that the proper selection of the initial transmission matrix and the set of unitary matrices can efficiently improve the bit error rate performance, especially for the antennas correlated fading channel. The computer simulations are evaluated over slow and fast Rayleigh fading channels.

• Journal of applied mathematics & informatics
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• 제22권1_2호
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• pp.307-316
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• 2006

Incomplete LU factorization preconditioning techniques often have difficulty on indefinite sparse matrices. We present hybrid reordering strategies to deal with such matrices, which include new diagonal reorderings that are in conjunction with a symmetric nondecreasing degree algorithm. We first use the diagonal reorderings to efficiently search for entries of single element rows and columns and/or the maximum absolute value to be placed on the diagonal for computing a nonsymmetric permutation. To augment the effectiveness of the diagonal reorderings, a nondecreasing degree algorithm is applied to reduce the amount of fill-in during the ILU factorization. With the reordered matrices, we achieve a noticeable improvement in enhancing the stability of incomplete LU factorizations. Consequently, we reduce the convergence cost of the preconditioned Krylov subspace methods on solving the reordered indefinite matrices.

• Kyungpook Mathematical Journal
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• 제47권3호
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• pp.311-322
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• 2007

This paper deals with space Beltrami system with three characteristic matrices in even dimensions, which can be regarded as a generalization of space Beltrami system with one and two characteristic matrices. It is transformed into a nonhomogeneous $p$-harmonic equation $d^*A(x,df^I)=d^*B(x,Df)$ by using the technique of out differential forms and exterior algebra of matrices. In the process, we only use the uniformly elliptic condition with respect to the characteristic matrices. The Lipschitz type condition, the monotonicity condition and the homogeneous condition of the operator A and the controlled growth condition of the operator B are derived.

• 한국IT서비스학회지
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• 제5권1호
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• pp.191-198
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• 2006

Boolean matrices have been successfully used in various areas, and many researches have been performed on them. However, almost all the researches focus on the efficient multiplication of two boolean matrices and no research has been shown to deal with the multiplication of all boolean matrices and their consecutive multiplications. The paper suggests a mathematical theory that enables the efficient consecutive multiplications of all $l{\times}n,\;n{\times}m,\;and\;m{\times}k$ boolean matrices, and discusses its computational complexity and the execution results of the consecutive multiplication algorithm based on the theory.

• 한국IT서비스학회지
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• 제7권4호
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• pp.221-230
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• 2008

Green's relations are five equivalence relations that characterize the elements of a semigroup in terms of the principal ideals. The J relation is one of Green's relations. Although there are known algorithms that can compute Green relations, they are not useful for finding all J relations in the semigroup of all $n{\times}n$ Boolean matrices. Its computation requires multiplication of three Boolean matrices for each of all possible triples of $n{\times}n$ Boolean matrices. The size of the semigroup of all $n{\times}n$ Boolean matrices grows exponentially as n increases. It is easy to see that it involves exponential time complexity. The computation of J relations over the $5{\times}5$ Boolean matrix is left an unsolved problem. The paper shows theorems that can reduce the computation time, discusses an algorithm for efficient J relation computation whose design reflects those theorems and gives its execution results.

• 한국동물학회지
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• 제24권2호
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• pp.91-98
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• 1981

Deer mice, Peromyscus maniculatus, 의 성체 571마리의 30개 morphometric 형질들을 이용한 cluster analyses에서 두가지의 similarity 행렬식 (Average taxonomic distance와 Correlation coefficient 행렬식)을 이용한 dendrogram이 서로 다르다는 것이 확인되었다. 이들 두가지의 행렬식 중에서 taxarks의 형태적인 유연관계를 나타내는 하나의 dendrogram만을 선택하기 위한 한 객관적방법이 제안되었다. 즉 principal component analysis에 의한 결과를 비교할 표준결과로 이용하는 방법이다.

• 대한건축학회논문집:구조계
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• 제34권1호
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• pp.27-32
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• 2018

This work provides the analytical methods to represent the updated form of stiffness or flexibility matrices using the measurements of the first few natural frequencies and the corresponding mode shapes. This study derives the mathematical forms on the variance of stiffness or flexibility matrices to minimize the performance index in the satisfaction of the eigen-function including the residual force depending on the measured data. The proposed methods can be utilized in detecting damage and updating the parameter matrices deviated from the analytical parameter matrices. The validity of the proposed methods is investigated in a numerical experiment of truss structure and the numerical results of stiffness-based and flexibility-based methods are compared. The sensitivity to the external noise is also examined for applying to the practical work.