• Structural Engineering and Mechanics
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• 제12권5호
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• pp.527-540
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• 2001

A new sort of learning algorithm named whole learning algorithm is proposed to simulate the nonlinear and dynamic behavior of RC members for the estimation of structural integrity. A mathematical technique to solve the multi-objective optimization problem is applied for the learning of the feedforward neural network, which is formulated so as to minimize the Euclidean norm of the error vector defined as the difference between the outputs and the target values for all the learning data sets. The change of the outputs is approximated in the first-order with respect to the amount of weight modification of the network. The governing equation for weight modification to make the error vector null is constituted with the consideration of the approximated outputs for all the learning data sets. The solution is neatly determined by means of the Moore-Penrose generalized inverse after summarization of the governing equation into the linear simultaneous equations with a rectangular matrix of coefficients. The learning efficiency of the proposed algorithm from the viewpoint of computational cost is verified in three types of problems to learn the truth table for exclusive or, the stress-strain relationship described by the Ramberg-Osgood model and the nonlinear and dynamic behavior of RC members observed under an earthquake.

• Structural Engineering and Mechanics
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• 제54권6호
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• pp.1153-1174
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• 2015

Deployable structures have gained more and more applications in space and civil structures, while it takes a large amount of computational resources to analyze this kind of multibody systems using common analysis methods. This paper presents a new approach for dynamic analysis of multibody systems consisting of both rigid bars and arbitrarily shaped rigid bodies. The bars and rigid bodies are connected through their nodes by ideal pin joints, which are usually fundamental components of deployable structures. Utilizing the Moore-Penrose generalized inverse matrix, equations of motion and constraint equations of the bars and rigid bodies are formulated with nodal Cartesian coordinates as unknowns. Based on the constraint equations, the nodal displacements are expressed as linear combination of the independent modes of the rigid body displacements, i.e., the null space orthogonal basis of the constraint matrix. The proposed method has less unknowns and a simple formulation compared with common multibody dynamic methods. An analysis program for the proposed method is developed, and its validity and efficiency are investigated by analyses of several representative numerical examples, where good accuracy and efficiency are demonstrated through comparison with commercial software package ADAMS.

• Journal of the Korean Statistical Society
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• 제22권2호
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• pp.249-258
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• 1993

It is well known that design matrix X for any factorial design can be represented by a product $X = TX_o$ where T is replication matrix and $X_o$ is the corresponding balanced design matrix. Since $X_o$ consists of regular arrangement of 0's and 1's, we can easily find the spectral decomposition of $X_o',X_o$. Also using this we propose an efficient algorithm for computing the orthogonal projection matrix for a balanced factorial design.

• 대한수학회논문집
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• 제10권1호
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• pp.163-173
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• 1995

Inspired in [2,9,10,17], pp. E. Ehrlich and S. B. Kim in [4] cultivated the Riccati equation related to the Raychaudhuri equation of General Relativity for the stable Jacobi tensor along the geodesics to extend the Hawking-Penrose conjugacy theorem to $$ f(t) = Ric(c(t)',c'(t)) + tr(\sigma(A)^2) $$ where $\sigma(A)$ is the shear tensor of A for the stable Jacobi tensor A with $A(t_0) = Id$ along the complete Riemannian or complete nonspacelike geodesics c.

• 대한수학회지
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• 제40권4호
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• pp.577-593
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• 2003

The Funk transform is defined by integrating a function on the two-sphere over its great circles. We use complex analysis to invert this transform.

• 대한수학회보
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• 제52권5호
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• pp.1669-1681
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• 2015

In this paper, we provide semi-convergence results of the parameterized inexact Uzawa method with singular preconditioners for solving singular saddle point problems. We also provide numerical experiments to examine the effectiveness of the parameterized inexact Uzawa method with singular preconditioners.

• 대한수학회보
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• 제37권2호
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• pp.401-409
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• 2000

In this paper, we determine the structure of ${\kappa}-potent$ elements and regular elements of the semigroup ${\Omega}_n$of doubly stochastic matrices of order n. In connection with this, we find the structure of the matrices X satisfying the equation AXA = A. From these, we determine a condition of a doubly stochastic matrix A whose Moore-Penrose generalized is also a doubly stochastic matrix.

• 대한수학회지
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• 제45권5호
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• pp.1417-1425
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• 2008

In this paper we consider the solvability and describe the set of the solutions of the operator equations $AX+X^{*}C=B$ and $AXB+B^{*}X^{*}A^{*}=C$. This generalizes the results of D. S. Djordjevic [Explicit solution of the operator equation $A^{*}X+X^{*}$A=B, J. Comput. Appl. Math. 200(2007), 701-704].

• 소음진동
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• 제7권5호
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• pp.773-780
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• 1997

Using Generalized Inverse Method presented by Udwadia and Kalaba in 1992, we can obtain equations to exactly describe the motion of constrained systems. When the differential equations are numerically integrated by any numerical integration scheme, the numerical results are generally found to veer away from satisfying constraint equations. Thus, this paper deals with the numerical integration of the differential equations describing constrained systems. Based on Baumgarte method, we propose numerical methods for reducing the errors in the satisfaction of the constraints.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제17권4호
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• pp.307-319
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• 2010

We provide a new semilocal convergence analysis of the Gauss-Newton method (GNM) for solving nonlinear equation in the Euclidean space. Using our new idea of recurrent functions, and a combination of center-Lipschitz, Lipschitz conditions, we provide under the same or weaker hypotheses than before [7]-[13], a tighter convergence analysis. The results can be extented in case outer or generalized inverses are used. Numerical examples are also provided to show that our results apply, where others fail [7]-[13].