• Journal of the Korean Data Analysis Society
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• v.20 no.6
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• pp.2747-2757
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• 2018

We consider the MLE (maximum likelihood estimate) and Bayesian estimates of three-parameter bathtub-shaped lifetime distribution based on the progressive type II censoring with binomial removal. Jung, Chung (2018) proposed the three-parameter bathtub-shaped distribution which is the extension of the two-parameter bathtub-shaped distribution given by Zhang (2004). Jung, Chung (2018) investigated its properties and estimations. The maximum likelihood estimates are computed using Newton-Raphson algorithm. Also, Bayesian estimates are obtained under the balanced loss function using MCMC (Markov chain Monte Carlo) method. In particular, BSEL (balanced squared error loss) function is considered as a special form of balanced loss function given by Zellner (1994). For comparing theirs MLEs with the corresponding Bayes estimates, some simulations are performed. It shows that Bayes estimates is better than MLEs in terms of risks. Finally, concluding remarks are mentioned.

• International Journal of Highway Engineering
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• v.10 no.1
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• pp.145-154
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• 2008

The purpose of this study is to evaluate the quality of on-line departure time-based link travel time estimates. For this, accuracy (i.e. estimation error) and timeliness (i.e. degree of time lag) are proposed as MOE of the quality of on-line link travel time estimates. Then the relationship between quality of link travel time estimates and link length and level of congestion is analyzed. It was found that there is trade-off between the accuracy and timeliness of link travel time estimates. The estimation error was modeled to consist of two components: one is systematic error and the other is mean square error which reflects level of congestion. further, time lag was again segmented into three parts for the analysis purpose. There are minimum one, congestion-related one, and update interval-related one. From the real-world data using AVI system, it was revealed that regardless of the link length and level of congestion, 10 minutes of time lag occurs in general.

• Computational Structural Engineering
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• v.11 no.1
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• pp.261-274
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• 1998

In this paper, local and global error estimates for the element-free Galerkin (EFG) method are proposed. The essence of proposed error estimates is to use the difference between the values of the projected stress and these given directly by the EFG solution. The stress projection can be obtained simply by taking product of shape function based on a different domain of influence with the stresses at nodes. In this study, it was found that the effectivity index is optimized if the domain of influence in stress projection procedure is the smallest that retains regularity of the matrices in EFG. Numerical tests are shown for various 1D and 2D examples illustrating the good effectiveness of the proposed error estimator in the global energy norm and in the local error estimates.

• Bulletin of the Korean Mathematical Society
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• v.48 no.5
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• pp.897-915
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• 2011

In this paper, we develop a symmetric Galerkin method with interior penalty terms to construct fully discrete approximations of the solution for nonlinear Sobolev equations. To analyze the convergence of discontinuous Galerkin approximations, we introduce an appropriate projection and derive the optimal $L^2$ error estimates.

• Journal of the Korean Mathematical Society
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• v.34 no.3
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• pp.661-672
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• 1997

In this paper we introduce the semidiscrete solution of a single-phase nonlinear Stefan problem We analyze the optimal convergence of the semidiscrete solution in $H^1$ and $H^2$ normed spaces and also we derive the error estimates in $L^2$ normed space.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.6 no.2
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• pp.85-97
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• 2002

In this paper, finite volume element methods for nonlinear parabolic problems are proposed and analyzed. Optimal order error estimates in $W^{1,p}$ and $L_p$ are derived for $2{\leq}p{\leq}{\infty}$. In addition, superconvergence for the error between the approximation solution and the generalized elliptic projection of the exact solution (or and the finite element solution) is also obtained.

• Journal of the Ergonomics Society of Korea
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• v.9 no.1
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• pp.35-42
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• 1990

This study is concerned with the accuracy, of error with which subjects can interpolate the location of a target between two graduation markers with 4 orientations and 6 sizes CRT display. Stimuli were graphic images on CRT with a linear, end-markec, ungraduated scales having a target. The location of a target is estimated in units over te range 1-99. Smallest error of estimates was at the near ends and middle of the base-line. The median error was less than 2 units, modal error was 1, and the most error (; 99.7%) was within 10. A proper size to make an minimum error in interpolation exists such that size 400 pixels. Interpolation estimation is shown to be affected by the size, location and interaction (orientation x location, size x location). The accuracy, interpolation performance are discussed in relation to absolute error associated with visual performance.

• Journal of applied mathematics & informatics
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• v.32 no.5_6
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• pp.707-719
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• 2014

In this paper, we investigate a variational discretization approximation of elliptic optimal control problems with control constraints. The state and the co-state are approximated by piecewise linear functions, while the control is not directly discretized. By using some proper intermediate variables, we derive a second-order convergence in $L^2$-norm and superconvergence between the numerical solution and elliptic projection of the exact solution in $H^1$-norm or the gradient of the exact solution and recovery gradient in $L^2$-norm. Then we construct a posteriori error estimates by using the superconvergence results and do some numerical experiments to confirm our theoretical results.

• Proceedings of the KIEE Conference
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• 2007.11c
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• pp.160-164
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• 2007

MRAS observer, which is based on adaptive control theory, estimates speed and position by using optimal observer gains on the basis of Lyapunov stability theory. However, in case of MRAS theory, position estimation error is in existence because of non-linearity for inductance variation and limit cycles for position estimation. The adaptive sliding observer based on the variable structure control theory estimates the speed and position for zero of estimation error by using the sliding surface equal to the error between speed and position estimation. The binary observer estimates the rotor speed and rotor flux with alleviation of the high-frequency chattering, and retains the benefits achieved in the conventional sliding observer, such as robustness to parameter and disturbance variations. The speed and position sensorless control of SRM under the load and inductance variation is verified by the experimental results.

• Bulletin of the Korean Mathematical Society
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• v.51 no.1
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• pp.139-156
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• 2014

In this paper, we investigate the error estimates of a quadratic elliptic control problem with pointwise control constraints. The state and the co-state variables are approximated by the order k = 1 Raviart-Thomas mixed finite element and the control variable is discretized by piecewise linear but discontinuous functions. Approximations of order $h^{\frac{3}{2}}$ in the $L^2$-norm and order h in the $L^{\infty}$-norm for the control variable are proved.