• Kyungpook Mathematical Journal
• /
• 제43권4호
• /
• pp.605-616
• /
• 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
• /
• 제25권1_2호
• /
• pp.407-413
• /
• 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.

• 대한수학회보
• /
• 제51권3호
• /
• pp.765-771
• /
• 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.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제16권4호
• /
• pp.369-382
• /
• 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
• /
• 제11권1_2호
• /
• pp.155-164
• /
• 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.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제28권4호
• /
• pp.281-296
• /
• 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.

• 대한수학회보
• /
• 제55권4호
• /
• pp.1263-1271
• /
• 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
• /
• 제21권1호
• /
• pp.105-112
• /
• 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.

• 한국지능시스템학회논문지
• /
• 제24권2호
• /
• pp.193-200
• /
• 2014

압전 액추에이터(Piezoelectric actuator)는 빠른 응답 특성, 넓은 대역폭, 우수한 반복 정밀도, 그리고 높은 분해능의 특성으로 인하여 다양한 산업분야에서 폭넓게 사용되고 있다. 하지만, 압전 액추에이터에는 히스테리시스 효과(Hysteresis effect)가 발생되는 단점이 있으며, 이는 시스템의 성능을 저하시키는 주요한 원인으로 알려져 있다. Generalized Prandtl-Ishlinskii(GPI) model을 이용한 기존 연구에서는 히스테리시스 효과를 제거하기 위하여 히스테리시스를 수리적으로 모델링하고, 그 결과로부터 역 히스테리시스를 도출하였다. 하지만 모델링된 변수 값에 따라서는 역 히스테리시스 루프를 형성하지 못하는 치명적 문제점이 발생된다. 따라서 본 논문에서는 이러한 문제점을 해결하기 위하여 Inverse Generalized Prandtl-Ishlinskii(IGPI) model을 이용하여 역 히스테리시스를 직접 모델링하는 방법을 제안하였다. 또한 모델링 정밀도는 다양한 입력신호를 이용한 실험 결과를 기반으로 검증하였다.

• 대한수학회논문집
• /
• 제29권2호
• /
• pp.227-237
• /
• 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.