• 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.

• 대한수학회보
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• 제44권2호
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• pp.225-231
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• 2007

Given an injective envelope E of a left R-module M, there is an associative Galois group Gal$({\phi})$. Let R be a left noetherian ring and E be an injective envelope of M, then there is an injective envelope $E[x^{-1}]$ of an inverse polynomial module $M[x^{-1}]$ as a left R[x]-module and we can define an associative Galois group Gal$({\phi}[x^{-1}])$. In this paper we describe the relations between Gal$({\phi})$ and Gal$({\phi}[x^{-1}])$. Then we extend the Galois group of inverse polynomial module and can get Gal$({\phi}[x^{-s}])$, where S is a submonoid of $\mathbb{N}$ (the set of all natural numbers).

• Journal of applied mathematics & informatics
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• 제19권1_2호
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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.

• 제어로봇시스템학회논문지
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• 제21권5호
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• pp.434-441
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• 2015

In this paper, we propose an inverse optimal distributed protocol for the formation and velocity consensus of nonholonomic mobile robots. The communication among mobile robots is described by a simple undirected graph, and the mobile robots' kinematics are considered. The group of mobile robots driven by the proposed protocols asymptotically achieves the desired formation and group velocity in an inverse optimal fashion. The design of the protocols is based on dynamic feedback linearization and the proposed linear quadratic (LQ) inverse optimal second-order consensus protocol. A numerical simulation is given to verify the effectiveness of the proposed scheme.

• 대한수학회보
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• 제35권4호
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• pp.791-807
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• 1998

The purpose of this paper is to construct a ring with unity under the derived cup product on the cochain groups of the inverse system and an isomorphism which is useful as the computation of a derived group by deleting the suitable terms in the directed set D. Moreover we apply these results to the K-theory.

• 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.

• 한국광학회지
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• 제28권6호
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• pp.263-272
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• 2017

넓은 시야를 가지는 광학계에서는 전반부는 음의 굴절능, 후반부는 양의 굴절능을 가지는 inverted telephoto 구조가 일반적으로 사용되고 있고, 2반사광학계에서는 inverse Cassegrain system이 inverted telephoto 구조에 해당한다. 하지만 통상적인 회전대칭 구성의 inverse Cassegrain system에서는 시야가 가려지고 광선의 차폐가 심한 문제점이 있다. 이 연구에서는 이점을 고려하여 inverse Cassegrain system의 제2면에 조리개를 두어 시야를 넓히고, 광선의 차폐가 없는 비축시야만을 사용하는 광시야 비축 2반사광학계를 설계하였다.

• 한국인구학
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• 제12권2호
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• pp.56-68
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• 1989

The methodology in historical demography comprises the three core areas the family reconstitution method at the Institut National d' Ftudes Demographiques(I.N.E.D), the back projection at the Cambridge Group for the History of PopuJation and Social Struc-ture(HPSS). and the household-pattern analysis at the Cambridge Group and at the California Institute of Technology. The paper presents an outline of the family reconstitu-tion method and discusses the problems, both theoretical and methodological, arising from the problematic back projection vis-a-vis the usual inverse projection developed by Ronald D. Lee at Berkeley. Recent developments in the tield of the generalized inverse projection method designed 10 supplement the defects in the back projection and the inverse projection are presented. and for ease of explanation of the parish register data for the family reconstitution form (FRE). pre-modern Korean household register data are presented along with the parish register data of England and Wales that constitute the backbone of historical demography in pre-modern Europe. Possibilities of exploring the household pattern analysis method based on the Laslett-Hammel classification scheme for the mid-eighteenth-century Korean household register data are suggested.

• 호남수학학술지
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• 제21권1호
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• pp.157-169
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• 1999

For a k-connected inverse system $({\scr{X}},\;*)=((X_{\lambda},\;*),p_{{\lambda}{{\lambda}}^{\prime}},\;{\Lambda})$ of pointed topological spaces and pointed preserving weak fibrations, inducting epimorphic chain maps, over a directed set, we show that the homotopy group ${\pi}_k(lim{\scr{X}},\;*)$ of the inverse limit is isomorphic to the integral homology group $$H_k(lim{\scr{X}};\mathbb{Z})$. Using the result of S. $Marde{\check{s}}i{\acute{c}}$, we prove that the group of pure extension $Pext(colimH^n({\scr{X}},\;A)$ is isomorphic to the group of extension $Ext({\Delta}({\lambda}),\;Hom(H^n({\scr{X}}),\;A))$.

• 대한수학회지
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• 제50권6호
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• pp.1349-1367
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• 2013

The weighted Moore-Penrose inverse will be introduced and studied in the context of Banach algebras. In addition, weighted EP Banach algebra elements will be characterized. The Banach space operator case will be also considered.