• 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.

• Journal of the Korean Mathematical Society
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• v.51 no.3
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• pp.545-565
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• 2014

In this paper we derive a priori $L^{\infty}(L^2)$ error estimates for expanded mixed finite element formulations of semilinear Sobolev equations. This formulation expands the standard mixed formulation in the sense that three variables, the scalar unknown, the gradient and the flux are explicitly treated. Based on this method we construct finite element semidiscrete approximations and fully discrete approximations of the semilinear Sobolev equations. We prove the existence of semidiscrete approximations of u, $-{\nabla}u$ and $-{\nabla}u-{\nabla}u_t$ and obtain the optimal order error estimates in the $L^{\infty}(L^2)$ norm. And also we construct the fully discrete approximations and analyze the optimal convergence of the approximations in ${\ell}^{\infty}(L^2)$ norm. Finally we also provide the computational results.

• Journal of the Korean Mathematical Society
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• v.55 no.2
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• pp.471-506
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• 2018

In this article, some projection methods (or fractional-step methods) are proposed and analyzed for the micropolar Navier-Stokes equations (MNSE). These methods allow us to decouple the MNSE system into two sub-problems at each timestep, one is the linear and angular velocities system, the other is the pressure system. Both first-order and second-order projection methods are considered. For the classical first-order projection scheme, the stability and error estimates for the linear and angular velocities and the pressure are established rigorously. In addition, a modified first-order projection scheme which leads to some improved error estimates is also proposed and analyzed. We also present the second-order projection method which is unconditionally stable. Ample numerical experiments are performed to confirm the theoretical predictions and demonstrate the efficiency of the methods.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.13 no.8
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• pp.3660-3665
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• 2012

For blind equalization, it is necessary to open an eye pattern quickly in the early stage of equalization, after that it is important to lower an error level of equalizer output signal. This paper discusses coarse error estimation using signal points specifically determined and fine error estimation using original signal constellation, and proposes two suggestions for how to take advantage of the two error estimation methods. The two error estimates, respectively, are effective to quickly open an eye pattern in the state of eye pattern closed, or to lower the level of an error in the steady-state after the eye pattern opening. Two blind equalization algorithms are proposed and their performances are compared, which select one of the two error estimates depending on the state of convergence of the equalizer, or combine two errors weightedly according to the relative reliabilities of the two error estimates, and calculate the new error.

• Journal of Industrial Technology
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• v.9
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• pp.67-77
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• 1989

This study is concerned with the accuracy, the pattern of error with which subjects can interpolate the location of a pointer or a target between two graduation markers with various size on CRT display. Stimuli were graphic images on CRT with a linear, end-marked, ungraduated scales having a target for t base-line sizes. The location of a target is estimated in units over the range 1-99. Smallest error of estimates was at the near ends and middle of the base-line. The median error was less 2 units, modal error was 1, and most error(;99.6%) was within 10. Subjects had a more tendency to overestimate than to underestimate at the left-part of base-line in all siges, and an opposite tendency at the right-part. A proper size to minimize the interpolation error exists such that size 500. It is suggested that interpolation of fifths and even tenths will give a reguired accuracy for certain situations, and relative location and base-line size has a relevant attribute to interpolate.

• Journal of the Institute of Electronics and Information Engineers
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• v.50 no.7
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• pp.52-58
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• 2013

This paper proposes an adaptive algorithm based on a method of dynamic error signal generation suitable for signal state by examining the equalizer output signal in blind equalization. In the proposed method, it estimates the error signals using single modulus and multiple modulus each effective to the early stage of equalization or steady-state, and it generates a new error signal from the two error estimates. Two equalizer structures are implemented and their performances are compared: 1-equalizer structure that generates a new error signal by combining the two error estimates weightedly and updates the equalizer using this, and 2-equalizer structure that updates two equalizers respectively depending on the weights of the two error signals. In the proposed method, as the error signals were generated optimally before and after the initial convergence respectively, it was confirmed by computer simulations that the equalizer was updated effectively.

• Journal of the Korean Society for Precision Engineering
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• v.15 no.5
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• pp.120-127
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• 1998

Differential inequalities occurring in problems of obstacle contact problems are recast into variational inequalities and analyzed by finite element methods. A new a posteriori error estimator, which is essential in adaptive finite element method, is introduced to capture the errors in finite element approximations of these variational inequalities. In order to construct a posteriori error estimates, saddle point problems are introduced using Lagrange parameters and upper bounds are provided. The global upper bound is localized by a special mixed formulation, which leads to upper bounds of the element errors. A numerical experiment is performed on an obstacle contact problem to check the effectivity index both in a local and a global sense.

• Journal of Korean Society for Quality Management
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• v.35 no.1
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• pp.10-19
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• 2007

ANOVA is widely, used for measurement system analysis. It assumes that the measurement error is normally distributed, which nay not be seen in some industrial cases. In this study the estimates of the measurement system variability and PTR (precision-to-tolerance ratio) are obtained by using weighted standard deviation for the case where the measurement error is non-normally distributed. The Standard Bootstrap method is used foy estimating confidence intervals of measurement system variability and PTR. The point and confidence interval estimates for the cases with normally distributed measurement error are compared to those with non-normally distributed measurement errors through computer simulation.

• Communications for Statistical Applications and Methods
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• v.13 no.3
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• pp.745-754
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• 2006

It has been shown that LAD estimates are more efficient than LS estimates when the error distribution is double exponential in AR(1) model. In order to explore the performance of LAD estimates one can use bootstrap approaches. In this paper we consider the efficiencies of bootstrap methods when we apply LAD estimates with highly variable data. Monte Carlo simulation results are given for comparing generalized bootstrap, stationary bootstrap and threshold bootstrap methods.

• Journal of applied mathematics & informatics
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• v.4 no.2
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• pp.341-378
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• 1997

We consider three classes of numerical methods for solv-ing the semi-explicit differential-algebraic equations of index 1 and higher. These methods use implicit multistep fixed stepsize methods and several iterative processes including simple iteration, full a2nd modified Newton iteration. For these methods we prove convergence theorems and derive error estimates. We consider different ways of choosing initial approximations for these iterative methods and in-vestigate their efficiency in theory and practice.