• Communications of the Korean Mathematical Society
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• v.4 no.1
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• pp.47-57
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• 1989

• Bulletin of the Korean Mathematical Society
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• v.17 no.1
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• pp.1-7
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• 1980

• Kyungpook Mathematical Journal
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• v.32 no.2
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• pp.159-166
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• 1992

• The Mathematical Education
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• v.23 no.1
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• pp.35-38
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• 1984

• Journal of the Korean Mathematical Society
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• v.20 no.2
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• pp.201-207
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• 1983

• The Mathematical Education
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• v.25 no.1
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• pp.33-37
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• 1986

• Journal of Korean Institute of Industrial Engineers
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• v.26 no.3
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• pp.220-226
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• 2000

The problem (P) of optimizing a linear function $d^Tx$ over the set of efficient points for a multiple objective linear program (M) is difficult because the efficient set is nonconvex. There are some interesting properties between the objective linear vector d and the matrix of multiple objectives C and those properties lead us to establish criteria to solve (P) with a linear program. In this paper we investigate a system of the linear equations $C^T{\alpha}$ = d and construct two linearly independent positive vectors u, v such that ${\alpha}$ = u - v. From those vectors u, v, solving an weighted sum linear program for finding an efficient extreme point for the (M) is a way of getting an optimal solution of the problem (P). Therefore the theorems presented in this paper provided us an easy way of solving nonconvex program (P) with a weighted sum linear program.

• Journal of Institute of Control, Robotics and Systems
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• v.17 no.9
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• pp.897-901
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• 2011

This paper presents a TS (Takagi-Sugeno) type FLC (Fuzzy Logic Controller) with only 3 rules. The choice of parameters of FLC is very difficult job on design FLC controller. Therefore, the choice of appropriate linguistic variable is an important part of the design of fuzzy controller. However, since fuzzy controller is nonlinear, it is difficult to analyze mathematically the affection of the linguistic variable. So this choice is depend on the expert's experience and trial and error method. In the design of the system, we use a variety of response characteristics like stability, rising time, overshoot, settling time, steady-state error. In particular, it is important for a stable system design to predict the steady-state error because the system's steady-state response of the system is related to the overall quality. In this paper, we propose the method to choose the consequence linear equation's parameter of T-S type FLC in the view of steady-state error. The parameters of consequence linear equations of FLC are tuned according to the system error that is the input of FLC. The full equation of T-S type FLC is presented and using this equation, the relation between output and parameters can represented. As well as the FLC parameters of consequence linear equations affect the stability of the system, it also affects the steady-state error. In this study, The system according to the parameter of consequence linear equations of FLC predict the steady-state error and the method to remove the system's steady-state error is proposed using the prediction error value. The simulation is carried out to determine the usefulness of the proposed method.

• Journal of Biosystems Engineering
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• v.12 no.2
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• pp.38-43
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• 1987

An experimental study was conducted to develop a thin-layer rewetting equation of short grain rough rice of Akihikari variety. Four thin-layer rewetting equations were experimentally determined from $25^{\circ}C$ to $45^{\circ}C$ and 70%RH to 85%RH conditions. Diffusion, Henderson, Page, and Thompson equations widely used as thin-layer drying equations were selected. Experimental data were fitted to these equations using linear regression analysis except diffusion equation. The diffusivity in the diffusion equation was determined by optimization method. Four equations were highly significant. In order to compare the goodness of fit of each equation, the error mean square of each equawas calculated. The diffusion model was not a very good model because the error mean square was very large. The other three models showed the same level or error mean square and could predict satisfactorily the rewetting rate or short grain rough rice.

• Journal of Mechanical Science and Technology
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• v.17 no.4
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• pp.538-544
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• 2003

Although many methodologies exist for determining the constrained equations of motion, most of these methods depend on numerical approaches such as the Lagrange multiplier's method expressed in differential/algebraic systems. In 1992, Udwadia and Kalaba proposed explicit equations of motion for constrained systems based on Gauss's principle and elementary linear algebra without any multipliers or complicated intermediate processes. The generalized inverse method was the first work to present explicit equations of motion for constrained systems. However, numerical integration results of the equation of motion gradually veer away from the constraint equations with time. Thus, an objective of this study is to provide a numerical integration scheme, which modifies the generalized inverse method to reduce the errors. The modified equations of motion for constrained systems include the position constraints of index 3 systems and their first derivatives with respect to time in addition to their second derivatives with respect to time. The effectiveness of the proposed method is illustrated by numerical examples.