• Kyungpook Mathematical Journal
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• 제43권4호
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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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• 제25권1_2호
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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.

• Kyungpook Mathematical Journal
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• 제55권2호
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• pp.251-258
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• 2015

Let $\mathcal{A}$ be a unital $C^*$-algebra, a, x and y are elements in $\mathcal{A}$. In this paper, we present the expression of the Moore-Penrose inverse and the group inverse of a-$xy^*$ under the conditions $x=aa^+x,y^*=y^*a^+a$, respectively.

• Journal of applied mathematics & informatics
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• 제27권1_2호
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• pp.267-273
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• 2009

A representation for the Drazin inverse of an arbitrary square matrix in terms of the eigenprojection was established by Rothblum [SIAM J. Appl. Math., 31(1976) :646-648]. In this paper perturbation results based on the representation for the Darzin inverse $A^D\;=\;(A-X)^{-1}(I-X)$ are developed. Norm estimates of $\parallel(A+E)^D-A^D\parallel_2/\parallel A^D\parallel_2$ and $\parallel(A+E)^#-A^D\parallel_2/\parallel A^D\parallel_2$ are derived when IIEI12 is small.

• Journal of the Korean Data and Information Science Society
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• 제20권2호
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• pp.459-465
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• 2009

For an inverse double Weibull distribution which is symmetric about zero, we obtain distribution and moment of ratio of independent inverse double Weibull variables, and also obtain the cumulative distribution function and moment of a skew-symmetric inverse double Weibull distribution. And we introduce a skew-symmetric inverse double Weibull generated by a double Weibull distribution.

• Journal of applied mathematics & informatics
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• 제11권1_2호
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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.

• 전기전자학회논문지
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• 제19권3호
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• pp.378-384
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• 2015

기존의 HEVC 코어 역변환기에서는 동일한 시간에 동일한 수의 화소를 처리하기 위해서 $2n{\times}2n$ 역변환기에 여분의 $n{\times}n$ 역변환기를 추가하여 한 개의 $2n{\times}2n$ 역변환기 또는 두 개의 $n{\times}n$ 역변환기로 동작하게 하였으나 여분의 $n{\times}n$ 역변환기 때문에 하드웨어 크기가 증가하는 단점이 있다. 이러한 문제점을 해결하기 위해 곱셈기를 재사용하여 여분의 $4{\times}4$ 역변환기를 없앤 새로운 $8{\times}8$ HEVC 코어 역변환기 구조가 제안되었으며, 본 논문에서는 이를 확장한 $16{\times}16$ HEVC 코어 역변환기 구조를 제안한다. 제안하는 $16{\times}16$ HEVC 역변환기는 $4{\times}4$ 역변환, $8{\times}8$ 코어 역 변환, $16{\times}16$ 코어 역변환에서 프레임 처리 시간이 모두 동일하며, 여분의 역변환기를 사용하는 아키텍쳐에 비해 게이트 수를 13% 줄일 수 있다.

• International Journal of Internet, Broadcasting and Communication
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• 제16권2호
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• pp.127-135
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• 2024

Recent studies have shown that inverse design using deep learning has the potential to rapidly generate the optimal design that satisfies the target performance without the need for iterative optimization processes. Unlike traditional methods, deep learning allows the network to rapidly generate a large number of solution candidates for the same objective after a single training, and enables the generation of diverse designs tailored to the objectives of inverse design. These inverse design techniques are expected to significantly enhance the efficiency and innovation of design processes in various fields such as aerospace, biology, medical, and engineering. We analyzes inverse design models that are mainly utilized in the nano and chemical fields, and proposes inverse design models based on supervised and unsupervised learning that can be applied to the engineering system. It is expected to present the possibility of effectively applying inverse design methodologies to the design optimization problem in the field of engineering according to each specific objective.

• Journal of applied mathematics & informatics
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• 제23권1_2호
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• pp.113-126
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• 2007

Let A and E be $m{\times}n$ matrices and W an $n{\times}m$ matrix, and let $A_{d,w}$ denote the W-weighted Drazin inverse of A. In this paper, a new representation of the W-weighted Drazin inverse of A is given. Some new properties for the W-weighted Drazin inverse $A_{d,w}\;and\;B_{d,w}$ are investigated, where B=A+E. In addition, the Banach-type perturbation theorem for the W-weighted Drazin inverse of A and B are established, and the perturbation bounds for ${\parallel}B_{d,w}{\parallel}\;and\;{\parallel}B_{d,w}-A_{d,w}{\parallel}/{\parallel}A_{d,w}{\parallel}$ are also presented. When A and B are square matrices and W is identity matrix, some known results in the literature related to the Drazin inverse and the group inverse are directly reduced by the results in this paper as special cases.

• 천문학회보
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• 제38권2호
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• pp.60.2-60.2
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• 2013

Electron magnetohydrodynamic (EMHD) turbulence provides a fluid-like description of small-scale magnetized plasmas. Most EMHD turbulence studies consider "balanced" EMHD turbulence. However, imbalanced EMHD turbulence has never been studied. In this study, we numerically study "imbalanced" EMHD turbulence. Imbalanced turbulence means that wave packets moving in one direction have high amplitudes or strong perturbations than the others. In driven imbalanced EMHD turbulence, non-zero magnetic helicity is injected. When magnetic helicity is injected at a scale, we expect to have inverse cascade of magnetic helicity, as well as magnetic energy, in three-dimensional (3D) EMHD turbulence. For no helicity injection, we do not observe inverse energy cascade. However, when magnetic helicity is injected, inverse cascade of magnetic helicity is clearly observed. Magnetic energy also shows inverse cascade. In EMHD turbulence, it is well known that magnetic energy on scales smaller than the energy injection scale is forward-cascading quantity and the magnetic energy spectrum follows a k^{-7/3} one. On the other hand, the inverse-cascading entity on scales larger than the energy injection scale is uncertain. If the magnetic helicity is inverse-cascading quantity, we will obtain a k^{-5/3} magnetic energy spectrum. In our simulations, we do observe energy spectrum consistant with k^{-5/3} on large scales. Therefore, we confirm that magnetic helicity indeed is the inverse-cascading entity in 3D EMHD turbulence.