• Kyungpook Mathematical Journal
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• v.43 no.4
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• pp.605-616
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• 2003

In this paper, some rank equalities related to generalized inverses $A^{(2)}_{T,S}$ of a matrix are presented. As applications, a variety of rank equalities related to the M-P inverse, the Drazin inverse, the group inverse, the weighted M-P inverse, the Bott-Duffin inverse and the generalized Bott-Duffin inverse are established.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.407-413
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• 2007

In this paper, we definite a generalized weighted Moore-Penrose inverse $A^{+}_{M,N}$ of a given matrix A, and give the necessary and sufficient conditions for its existence. We also prove its uniqueness and give a representation of it. In the end we point out this generalized inverse is also a prescribed rang T and null space S of {2}-(or outer) inverse of A.

• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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• pp.765-771
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• 2014

Necessary and sufficient conditions for the existence of the group inverse of an anti-triangular block matrix in Banach algebras are presented. Using these results, we give the formulae for the generalized Drazin inverse of a block matrix.

• The Pure and Applied Mathematics
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• v.16 no.4
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• pp.369-382
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• 2009

In this paper we establish various relationships among the generalized integral transform, the generalized convolution product and the first variation for functionals in a Banach algebra S($L_{a,b}^2$[0, T]) introduced by Chang and Skoug in [14]. We then derive an inverse integral transform and obtain several relationships involving inverse integral transforms.

• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.155-164
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• 2003

The existence and representations of some generalized inverses, including ${A_{T,*}}^{(2)},\;{A_{T,*}}^{(1,2)},\;{A_{T,*}}^{(2,3)},\;{A_{*,S}}^{(2)},\;{A_{*,S}}^{(1,2)}\;and\;{A_{*,S}}^{(2,4)}$, are showed. As applications, the perturbation theory for the generalized inverse {A_{T,S}}^{(2)} and the perturbation bound for unique solution of the general restricted system $A_{x}$ = b(dim(AT)=dimT, $b{\in}AT$ and $x{\in}T$) are studied. Moreover, a characterization and representation of the generalized inverse ${A_{T,*}}^{(2)}$ is obtained.

• The Pure and Applied Mathematics
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• v.28 no.4
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• pp.281-296
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• 2021

In this paper, we suggest a representation for an inverse transform of the generalized Fourier-Feynman transform on the function space C_a,b[0, T]. The function space C_a,b[0, T] is induced by the generalized Brownian motion process with mean function a(t) and variance function b(t). To do this, we study the generalized Fourier-Feynman transform associated with the Gaussian process Ƶ_k of exponential-type functionals. We then establish that a composition of the Ƶ_k-generalized Fourier-Feynman transforms acts like an inverse generalized Fourier-Feynman transform.

• Bulletin of the Korean Mathematical Society
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• v.55 no.4
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• pp.1263-1271
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• 2018

We introduce new generalized inverses (named the WgDMP inverse and dual WgDMP inverse) for a bounded linear operator between two Hilbert spaces, using its Wg-Drazin inverse and its Moore-Penrose inverse. Some new properties of WgDMP inverse and dual WgDMP inverse are obtained and some known results are generalized.

• East Asian mathematical journal
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• v.21 no.1
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• pp.105-112
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• 2005

In this paper we show that we can extend the purity extension properties of left R-modules to the various generalized inverse polynomial modules.

• Journal of the Korean Institute of Intelligent Systems
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• v.24 no.2
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• pp.193-200
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• 2014

Piezoelectric actuators have been widely used in various applications because they have many advantages such as fast response time, repeatable nanometer motion, and high resolution. However Piezoelectric actuators have the strong hysteresis effect. The hysteresis effect can degrade the performance of the system using piezoelectric actuators. In past study, the parameters of the inverse hysteresis model are computed from the identified parameters using the Generalized Prandtl-Ishlinskii(GPI) model to cancel the hysteresis effect, however according to the identified parameters there exist the cases that can't form the inverse hysteresis loop. Thus in this paper the inverse hysteresis modeling mothod is proposed using the Inverse Generalized Prandtl-Ishlinskii(IGPI) model to handle that problem. The modeling results are verified by experimental results using various input signals.

• Communications of the Korean Mathematical Society
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• v.29 no.2
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• pp.227-237
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• 2014

For an $m{\times}n$ nonnegative integral matrix A, a generalized inverse of A is an $n{\times}m$ nonnegative integral matrix G satisfying AGA = A. In this paper, we characterize nonnegative integral matrices having generalized inverses using the structure of nonnegative integral idempotent matrices. We also define a space decomposition of a nonnegative integral matrix, and prove that a nonnegative integral matrix has a generalized inverse if and only if it has a space decomposition. Using this decomposition, we characterize nonnegative integral matrices having reflexive generalized inverses. And we obtain conditions to have various types of generalized inverses.