• 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 IKEEE
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• v.19 no.3
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• pp.378-384
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• 2015

In conventional HEVC inverse core transform architectures, extra $n{\times}n$ inverse transform block is added to $2n{\times}2n$ inverse transform block, and it operates as one $2n{\times}2n$ inverse transform block or two $n{\times}n$ inverse transform blocks. Thus, same number of pixels are processed in the same time, but it suffers from increased hardware size due to extra $n{\times}n$ inverse transform block. To avoid this problem, a novel $8{\times}8$ HEVC inverse core transform architecture was proposed to eliminate extra $4{\times}4$ inverse transform block based on multiplier reuse. This paper extends this approach and proposes a novel HEVC $16{\times}16$ inverse core transform architecture. Its frame processing time is same in $4{\times}4$, $8{\times}8$, and $16{\times}16$ inverse core transforms, and reduces gate counts by 13%.

• 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.

• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.541-547
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• 2008

Suppose R is an idempotence-diagonalizable ring. Let n and m be two arbitrary positive integers with $n\;{\geq}\;3$. We denote by $M_n(R)$ the ring of all $n{\times}n$ matrices over R. Let ($J_n(R)$) be the additive subgroup of $M_n(R)$ generated additively by all idempotent matrices. Let ($D=J_n(R)$) or $M_n(R)$. In this paper, by using an additive idem potence-preserving result obtained by Coo (see [4]), I characterize (i) the additive preservers of tripotence from D to $M_m(R)$ when 2 and 3 are units of R; (ii) the additive preservers of inverses (respectively, Drazin inverses, group inverses, {1}-inverses, {2}-inverses, {1, 2}-inverses) from $M_n(R)$ to $M_n(R)$ when 2 and 3 are units of R.

• International Journal of Internet, Broadcasting and Communication
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• v.16 no.2
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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 the Korean Data and Information Science Society
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• v.20 no.2
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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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• v.19 no.1_2
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• pp.297-310
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• 2005

The concept of the Moore-Penrose inverse in an indefinite inner product space is introduced. Extensions of some of the formulae in the Euclidean space to an indefinite inner product space are studied. In particular range-hermitianness is completely characterized. Equivalence of a weighted generalized inverse and the Moore-Penrose inverse is proved. Finally, methods of computing the Moore-Penrose inverse are presented.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.45-57
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• 2005

An efficient algorithm for finding the inverse and the group inverse of the FLS $\gamma-circulant$ matrix is presented by Euclidean algorithm. Extension is made to compute the inverse of the FLS $\gamma-retrocirculant$ matrix by using the relationship between an FLS $\gamma-circulant$ matrix and an FLS $\gamma-retrocirculant$ matrix. Finally, some examples are given.

• Journal of radiological science and technology
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• v.36 no.4
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• pp.319-326
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• 2013

The purpose of this study is to evaluate usefulness of Hybrid image and Inverse image about detection of tumor shadow in chest radiography using ROC analysis. Original images of 60 cases are selected from Standards digital image date base issued by the Japanese Society of Radiological Technology. Through computer language of C, Inverse images of 60 cases and Hybrid image of 30 cases are made. The continues reading experiment was conducted. In the case of inverse image were observed by 5 radiographer and 2 radiologist. In the case of In case of Hybrid image were observed by 3 student radiographer and 2 experienced radiographer. ROC curve are constructed using ROCKIT Program made by Metz. In Inverse image, a Az of average ROC curve was increases from 0.742 of original image to 0.775 of inverse image. In normal cases, the effect of the detrimental is same to that of the beneficial, however In abnormal cases, the beneficial effect is greater than detrimental effect. However in Hybrid image, a Az of average ROC curve was decreases from 0.5253 of original image to 0.4868 of Hybrid image. In Normal cases, the effect of the detrimental is greater than that of the Beneficial, however In abnormal cases, the Beneficial effect is greater than detrimental effect. The inverse image can be more positively considered for the detecting of tumor than the hybrid image.

• Communications for Statistical Applications and Methods
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• v.11 no.2
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• pp.275-285
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• 2004

We explore classification analysis using graphical methods such as sliced inverse regression and sliced average variance estimation based on dimension reduction. Some useful information about classification analysis are obtained by sliced inverse regression and sliced average variance estimation through dimension reduction. Two examples are illustrated, and classification rates by sliced inverse regression and sliced average variance estimation are compared with those by discriminant analysis and logistic regression.