• Journal of the Korean Mathematical Society
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• v.31 no.4
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• pp.645-657
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• 1994

If S is a semiring of nonnegative reals, which linear operators T on the space of $m \times n$ matrices over S preserve the column rank of each matrix\ulcorner Evidently if P and Q are invertible matrices whose inverses have entries in S, then $T : X \longrightarrow PXQ$ is a column rank preserving, linear operator. Beasley and Song obtained some characterizations of column rank preserving linear operators on the space of $m \times n$ matrices over $Z_+$, the semiring of nonnegative integers in [1] and over the binary Boolean algebra in [7] and [8]. In [4], Beasley, Gregory and Pullman obtained characterizations of semiring rank-1 matrices and semiring rank preserving operators over certain semirings of the nonnegative reals. We considers over certain semirings of the nonnegative reals. We consider some results in [4] in view of a certain column rank instead of semiring rank.

• Communications of the Korean Mathematical Society
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• v.20 no.4
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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.

• Proceedings of the Korea Contents Association Conference
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• 2006.05a
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• pp.459-461
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• 2006

The successive multiplication of all $n{\times}n$ boolean matrices is necessary for applications such as D-class computation. But, no research has been performed on it despite many researches dealing with boolean matrices. The paper suggests a theory with which successively multiplying a $n{\times}n$ boolean matrix by all $n{\times}n$ boolean matrices can be done efficiently, applies it to the successive multiplication of all $n{\times}n$ boolean matrices and shows its execution results.

• Journal of Multimedia Information System
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• v.4 no.4
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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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• v.6 no.4
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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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• v.22 no.1_2
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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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• v.47 no.3
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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.

• Journal of Information Technology Services
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• v.5 no.1
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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.

• Journal of Information Technology Services
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• v.7 no.4
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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.

• The Korean Journal of Zoology
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• v.24 no.2
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• pp.91-98
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• 1981

It has been confirmed that two dendrograms resulted from two similarity matrices, average taxonomic distance and correlation coefficient matrices, are different with each other when cluster analyses were performed with 571 adults of deer mice, Peromyscus maniculatus using 30 morphometric characters. To choose one of two similarity matrices mentioned above in order to construct a dendrogram representing phenetic relationships among taxa, an objective method using the result from principal component analysis as a standard result to compare with two matrices has been suggested.