• Journal of the Korean Mathematical Society
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• v.48 no.1
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• pp.83-104
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• 2011

In this note, compound-commuting additive maps on matrix spaces are studied. We show that compound-commuting additive maps send rank one matrices to matrices of rank less than or equal to one. By using the structural results of rank-one nonincreasing additive maps, we characterize compound-commuting additive maps on four types of matrices: triangular matrices, square matrices, symmetric matrices and Hermitian matrices.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.2 no.2
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• pp.27-30
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• 1998

Let A and B be $m{\times}n$ matrices. A linear operator T preserves the set of matrices on which the rank is additive if rank(A+B) = rank(A)+rank(B) implies that rank(T(A) + T(B)) = rankT(A) + rankT(B). We characterize the set of all linear operators which preserve the set of pairs of $n{\times}n$ matrices on which the rank is additive.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.253-260
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• 2005

Denote the set of n ${\times}$ n complex Hermitian matrices by Hn. A pair of n ${\times}$ n Hermitian matrices (A, B) is said to be rank-additive if rank (A+B) = rank A+rank B. We characterize the linear maps from Hn into itself that preserve the set of rank-additive pairs. As applications, the linear preservers of adjoint matrix on Hn and the Jordan homomorphisms of Hn are also given. The analogous problems on the skew Hermitian matrix space are considered.

• Bulletin of the Korean Mathematical Society
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• v.55 no.5
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• pp.1587-1598
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• 2018

We study additive decompositions (and generalized additive decompositions with a zero-dimensional scheme instead of a finite sum of rank 1 tensors), which are not of minimal degree (for sums of rank 1 tensors with more terms than the rank of the tensor, for a zero-dimensional scheme a degree higher than the cactus rank of the tensor). We prove their existence for all degrees higher than the rank of the tensor and, with strong assumptions, higher than the cactus rank of the tensor. Examples show that additional assumptions are needed to get the minimally spanning scheme of degree cactus +1.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.15 no.11
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• pp.955-961
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• 1990

Test statistics are obtained for detection of weak signals in signal-dependent noise using rank statistics. A generalized model is used in this paper in order to consider non-additivenoise as well as purely-additive noise. Locally optimum rank detectors for the model are shown to have similarity to locally optimum detectors and to be generalizations of these for the purely-additive noise model. A similar result is obtained for multi-input cases.

• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.115-122
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• 2004

We characterize the additive operators preserving rank-additivity on symmetry matrix spaces. Let $S_{n}(F)$ be the space of all $n\;\times\;n$ symmetry matrices over a field F with 2, $3\;\in\;F^{*}$, then T is an additive injective operator preserving rank-additivity on $S_{n}(F)$ if and only if there exists an invertible matrix $U\;\in\;M_n(F)$ and an injective field homomorphism $\phi$ of F to itself such that $T(X)\;=\;cUX{\phi}U^{T},\;\forallX\;=\;(x_{ij)\;\in\;S_n(F)$ where $c\;\in;F^{*},\;X^{\phi}\;=\;(\phi(x_{ij}))$. As applications, we determine the additive operators preserving minus-order on $S_{n}(F)$ over the field F.

• Journal of the Korean Mathematical Society
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• v.45 no.2
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• pp.301-312
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• 2008

The spanning column rank of an $m{\times}n$ matrix A over a semiring is the minimal number of columns that span all columns of A. We characterize linear operators that preserve the sets of matrix pairs which satisfy additive properties with respect to spanning column rank of matrices over semirings.

• Communications for Statistical Applications and Methods
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• v.16 no.2
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• pp.325-334
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• 2009

In this research, we propose a nonparametric test procedure for the right censored and grouped data under the additive hazards model. For deriving the test statistics, we use the likelihood principle. Then we illustrate proposed test with an example and compare the performance with other procedure by obtaining empirical powers. Finally we discuss some interesting features concerning the proposed test.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.22 no.7
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• pp.1543-1549
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• 1997

In this paper, rank-based nonparmetric detection of composite signals in additive noise is considered. Based on signs and ranks of observations, the locally optimum detector is deived for weak-signal detection under any specified noise probability density funhction. This detector has similarities to the locally optimum detector for comjposite signals in additive noise. The asymptotic performance of this nonparametric detector is shown to be as good as that of the locally optimum detector.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.16 no.5
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• pp.445-448
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• 1991

The two-sample locally optimum rank detection scheme is obtained which uses rank and sign statistics for detection of random signals in additive noise. It is shown that the detector is similar in structure to the locally optimum detector for random signals and to the one-sample locally optimum rank detector for random signals. It is also shown that the detector is a generalization of the two-sample locally optimum rank detector for known signals. In addition , the problem of two-sample locally optimum rank detection of random signals in multiple input case is considered briefly.