• Journal of the Korean Statistical Society
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• 제14권1호
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• pp.29-38
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• 1985

Cyclic Factorial Association Scheme (CFAS) for incomplete block designs in a factorial experiment is defined. It is a generalization of EGD/($2^n-1$)-PBIB designs defined by Hinkelmann (1964) or Binary Number Association Scheme (BNAS) named by Paik and Federer (1973). A property of PBIB designs having CFAS is investigated and it is shown that the structural matrix NN' of such designs has a pattern of multi-nested block circulant matrix. The generalized inverse of (rI-NN'/k) is obtained. Generalized Cyclic incomplete block designs for factorial experiments introduced by John (1973) are presented as the examples of CFAS-PBIB designs. Finally, the relationship between CFAS and BNAS in block designs is briefly discussed.

• 대한수학회보
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• 제46권3호
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• pp.511-519
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• 2009

A matrix $P{\in}\mathbb{C}^{n{\times}n}$ is called a generalized reflection matrix if $P^*$ = P and $P^2$ = I. An $n{\times}n$ complex matrix A is said to be a reflexive (anti-reflexive) matrix with respect to the generalized reflection matrix P if A = PAP (A = -PAP). It is well-known that the reflexive and anti-reflexive matrices with respect to the generalized reflection matrix P have many special properties and widely used in engineering and scientific computations. In this paper, we give new necessary and sufficient conditions for the existence of the reflexive (anti-reflexive) solutions to the linear matrix equation AXB + CY D = E and derive representation of the general reflexive (anti-reflexive) solutions to this matrix equation. By using the obtained results, we investigate the reflexive (anti-reflexive) solutions of some special cases of this matrix equation.

• International Journal of Precision Engineering and Manufacturing
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• 제2권4호
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• pp.61-68
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• 2001

A new approach for motion control of constrained mechanical systems is proposed in this paper. The approach uses a new equations of motion which is proposed by Udwadia and Kalaba and named Udwadia-Kalaba's equations of motion in this paper. This paper reveals that the Udwadia-Kalaba's equations of motion is more adequate to model constrained mechanical systems rather than the famous Lagrange's equations of motion at least for control purpose. The proposed approach coverts most of constraints including holonomic and nonholonomic constraints. Comparison of simulation results of two systems which are well-known in the literature show the superiority of the proposed approach. Furthermore, a special constrained mechanical system which includes nonlinear generalized velocities in its constraint equations, which has been considered to be difficult to control, can be controlled easily. It shows the possibility of the proposed approach to being a general framework for motion control of constrained mechanical systems with various kinds of constraints.

• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.321-328
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• 2005

We investigate a matrix inequality on Schur complements defined by {1}-generalized inverses, and obtain simultaneously a necessary and sufficient condition under which the inequality turns into an equality. This extends two existing matrix inequalities on Schur complements defined respectively by inverses and Moore-Penrose generalized inverses (see Wang et al. [Lin. Alg. Appl., 302-303(1999)163-172] and Liu and Wang [Lin. Alg. Appl., 293(1999)233-241]). Moreover, the non-uniqueness of $\{1\}$-generalized inverses yields the complicatedness of the extension.

• 한국측량학회지
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• 제3권2호
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• pp.48-62
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• 1985

본 논문은 g-inverse를 이용한 자유망 조정으로서, 미지 Parameter를 이용한 해법에 있어서는 모든점의 좌표가 동일경중률에 의한 Parameter로 처리되기 때문에 정규방정식의 행열이 특이행열이 된다. 이 논문은 망조정에 있어서의 특이행열과 삼변측양에 있어서 기존방법의 정확도 분석 및 삼변자유망조정의 문제를 검토하였다. 본 삼변자유망 조정의 경우에 있어서는 조정좌표의 최소제곱근 오차가 심다변망에서 35.6%, 사변망에서 50.5%로 정확도가 향상되었고, 오차구원의 요소에 있어서도 최소제곱근오차가 유심다변망에서 a=24.5%, b=5.0%, 사변망에서는 a=42.6%, b＝49.2％로 감소하였다. 따라서 자유망조정 방법의 적용은 기준점의 수평위치결정에 있어서 상대오차의 개선을 위하여 필요한 것으로 사료된다.

• 한국인터넷방송통신학회논문지
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• 제15권3호
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• pp.25-33
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• 2015

양면을 뒤집어 입을 수 있는 Jacket처럼, 내부 및 외부 양 쪽 모두 호환이 가능한 행렬을 Jacket 행렬이라 한다. element-wise inverse와 block-wise inverse 과정을 통해 Jacket 행렬은 안 쪽 요소와 바깥쪽 요소 모두를 가진다. 이 개념은 1989년에 저자 중 한 명인 이문호 교수에 의해 이루어진 것으로서, 2000년에는 최종적으로 Jacket 행렬이라 부르게 되었다. 이것은 잘 알려진 Hadamard 행렬의 가장 일반적인 확장으로서, 직교와 비직교 행렬에 대한 성질을 포함하고 있다. Jacket 행렬은 정보 및 통신 분야 이론의 많은 문제들을 해석하는데 이용된다. 본 논문에서는 Jacket 행렬의 성질과 특성, 예를 들어 determinants와 eigenvalues, Kronecker product에 대해서 다룬다. 이 연산들은 신호 처리와 직교 코드 디자인에 매우 유용하다. 또한, 본 논문은 복잡성이 낮은 매우 간단한 수학적 모델을 통해 이들의 유용성을 계산한 결과를 제시한다.

• Journal of applied mathematics & informatics
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• 제20권1_2호
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• pp.35-59
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• 2006

In this paper, we generalized the results of [23, 26], and get the results of the condition number of the W-weighted Drazin-inverse solution of linear system W AW\chi=b, where A is an $m{\times}n$ rank-deficient matrix and the index of A W is $k_1$, the index of W A is $k_2$, b is a real vector of size n in the range of $(WA)^{k_2}$, $\chi$ is a real vector of size m in the range of $(AW)^{k_1}$. Let $\alpha$ and $\beta$ be two positive real numbers, when we consider the weighted Frobenius norm $\|[{\alpha}W\;AW,\;{\beta}b]\|$(equation omitted) on the data we get the formula of condition number of the W-weighted Drazin-inverse solution of linear system. For the normwise condition number, the sensitivity of the relative condition number itself is studied, and the componentwise perturbation is also investigated.

• Journal of applied mathematics & informatics
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• 제26권5_6호
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• pp.1011-1020
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• 2008

The problem of finding Cramer rule for solutions of some restricted linear equation Ax = b has been widely discussed. Recently Wang and Qiao consider the following more general problem AXB = D, $R(X){\subset}T$, $N(X){\supset}\tilde{S}$. They present the solution of above general restricted matrix equation by using generalized inverses and give an explicit expression for the elements of the solution matrix for the matrix equation. In this paper we re-consider the restricted matrix equation and give an equivalent matrix equation to it. Through the equivalent matrix equation, we derive condensed Cramer rule for above restricted matrix equation. As an application, condensed determinantal expressions for $A_{T,S}^{(2)}$ A and $AA_{T,S}^{(2)}$ are established. Based on above results, we present a method for computing the solution of a kind of restricted matrix equation.

• 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.

• Kyungpook Mathematical Journal
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• 제55권1호
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• pp.181-189
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• 2015

In this paper, we study Baire property of a family of spaces which contains properly the family of all topological spaces and generalize the existing results. Also, we study the images and inverse images of such spaces.