• Journal of the Korean Mathematical Society
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• v.47 no.4
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• pp.805-818
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• 2010

We classify linear maps which preserve idempotents on $n{\times}n$ matrices over some classes of semirings. Our results include many known semirings like the semiring of all nonnegative integers, the semiring of all nonnegative reals, any unital commutative ring, which is zero divisor free and of characteristic not two (not necessarily a principal ideal domain), and the ring of integers modulo m, where m is a product of distinct odd primes.

• Proceedings of the IEEK Conference
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• 2002.07a
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• pp.490-493
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• 2002

In this paper, the old Fourier-Motzkin method (abbreviated as the old FH method from now on) is first modified to the form which can derive all minimal vectors as well as all minimal support vectors of nonnegative integer homogeneous solutions (i.e., T-invariants) for a matrix equation $Ax=b=0^{m{\times}1}$, $A\epsilonZ^{m{\times}n}$ and $b\epsilonZ^{m{\times}1}$, of a given Petri net, where the old FM method is a well-known and direct method that can obtain at least all minimal support solutions for $Ax=0^{m{\times}1}$ from the incidence matrix . $A\epsilonZ^{m{\times}n}$, Secondly, for $Ax=b\ne0^{m{\times}n}$ a new extended FM method is given; i.e., all nonnegative integer minimal vectors which contain all minimal support vectors of not only homogeneous but also inhomogeneous solutions are systematically obtained by applying the above modified FH method to the augmented incidence matrix $\tilde{A}$ =〔A,-b〕$\epsilon$ $Z^{m{\times}(n＋1)}$ s.t. $\tilde{A}\tilde{x}$ = 0^{m{\times}1}$ However, note that for this extended FM method we need some criteria to obtain a minimal vector as well as a minimal support vector from both of nonnegative integer homogeneous and inhomogeneous solutions for Ax=b. Then those criteria are also discussed and given in this paper.

• The Journal of the Acoustical Society of Korea
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• v.37 no.6
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• pp.489-498
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• 2018

In this paper, a target detection method based on beamspace-domain multichannel nonnegative matrix factorization is studied when an echo of continuous-wave ping is received from a low-Doppler target in reverberant environment. If the receiver of the continuous-wave active sonar moves, the frequency range of the reverberation is broadened due to the Doppler effect, so the low-Doppler target echo is interfered by the reverberation in this case. The developed algorithm analyzes the multichannel spectrogram of the received signal into frequency bases, time bases, and beamformer gains using the beamspace-domain multichannel nonnnegative matrix factorization, then the algorithm estimates the frequency, time, and bearing of target echo by choosing a proper basis. To analyze the performance of the developed algorithm, simulations were performed in various signal-to-reverberation conditions. The results show that the proposed algorithm can estimate the frequency, time, and bearing, but the performance was degraded in the low signal-to-reverberation condition. It is expected that modifying the selection algorithm of the target echo basis can enhance the performance according to the simulation results.

• Journal of applied mathematics & informatics
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• v.7 no.2
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• pp.665-671
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• 2000

A matrix whose entries consist of the symbols +.- and 0 is called a sign pattern matrix . In 1994 , Eschenbach gave a graph theoretic characterization of irreducible sign idempotent pattern matrices. In this paper, we give a characterization of reducible sign idempotent matrices. We show that reducible sign idempotent matrices, whose digraph is contained in an irreducible sign idempotent matrix, has all nonnegative entries up to equivalences. this extend the previous result.

• Journal of applied mathematics & informatics
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• v.31 no.3_4
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• pp.545-558
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• 2013

In this paper, the formulas for calculating the extremal ranks and inertias of the Hermitian least squares solutions to matrix equation AX = B are established. In particular, the necessary and sufficient conditions for the existences of the positive and nonnegative definite solutions to this matrix equation are given. Meanwhile, the least squares problem of the above matrix equation with Hermitian R-symmetric and R-skew symmetric constraints are also investigated.

• Communications for Statistical Applications and Methods
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• v.27 no.5
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• pp.523-533
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• 2020

This paper suggests three available methods for finding nonnegative estimates of variance components of the random effects in mixed models. The three proposed methods based on the concepts of projections are called projection method I, II, and III. Each method derives sums of squares uniquely based on its own method of projections. All the sums of squares in quadratic forms are calculated as the squared lengths of projections of an observation vector; therefore, there is discussion on the decomposition of the observation vector into the sum of orthogonal projections for establishing a projection model. The projection model in matrix form is constructed by ascertaining the orthogonal projections defined on vector subspaces. Nonnegative estimates are then obtained by the projection model where all the coefficient matrices of the effects in the model are orthogonal to each other. Each method provides its own system of linear equations in a different way for the estimation of variance components; however, the estimates are given as the same regardless of the methods, whichever is used. Hartley's synthesis is used as a method for finding the coefficients of variance components.

• Journal of applied mathematics & informatics
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• v.30 no.1_2
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• pp.201-210
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• 2012

A modified multiplicative update algorithms is presented for computing the nearest correlation matrix. The convergence property is analyzed in details and a sufficient condition is given to guarantee that the proposed approach will not breakdown. A number of numerical experiments show that the modified multiplicative updating algorithm is efficient, and comparable with the existing algorithms.

• Kyungpook Mathematical Journal
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• v.48 no.3
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• pp.465-472
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• 2008

For a nonnegative real matrix A of rank 1, A can be factored as $ab^t$ for some vectors a and b. The perimeter of A is the number of nonzero entries in both a and b. If B is a matrix of rank k, then B is the sum of k matrices of rank 1. The perimeter of B is the minimum of the sums of perimeters of k matrices of rank 1, where the minimum is taken over all possible rank-1 decompositions of B. In this paper, we obtain characterizations of the linear operators which preserve perimeters 2 and k for some $k\geq4$. That is, a linear operator T preserves perimeters 2 and $k(\geq4)$ if and only if it has the form T(A) = UAV or T(A) = $UA^tV$ with some invertible matrices U and V.

• Bulletin of the Korean Mathematical Society
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• v.57 no.3
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• pp.535-545
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• 2020

Let A be an m × n matrix over nonnegative integers. The isolation number of A is the maximum number of isolated entries in A. We investigate linear operators that preserve the isolation number of matrices over nonnegative integers. We obtain that T is a linear operator that strongly preserve isolation number k for 1 ≤ k ≤ min{m, n} if and only if T is a (P, Q)-operator, that is, for fixed permutation matrices P and Q, T(A) = P AQ or, m = n and T(A) = P A^tQ for any m × n matrix A, where A^t is the transpose of A.

• Proceedings of the Korean Information Science Society Conference
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• 2011.06c
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• pp.393-396
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• 2011

In this paper, we propose a constrained alternating least squares nonnegative matrix factorization algorithm (cALSNMF) to detect active brain regions from single subject's task-related fMRI data. In cALSNMF, we define a new cost function which considers the uncorrelation and noisy problems of fMRI data by adding decorrelation and smoothing constraints in original Euclidean distance cost function. We also generate a novel training procedure by modifying the update rules and combining with optimal brain surgeon (OBS) algorithm. The experimental results on visuomotor task fMRI data show that our cALSNMF fits fMRI data better than original ALSNMF in detecting task-related brain activation from single subject's fMRI data.