• Honam Mathematical Journal
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• v.36 no.2
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• pp.291-303
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• 2014

In this paper, through a direct computation with subintervals partitioning [0, 1], we compute better a posteriori bounds for the average case error of the difference between the true value of $I(f)=\int_{0}^{1}f(x)dx$ with $f{\in}C^r$[0, 1] minus the composite trapezoidal rule and the composite trapezoidal rule minus the basic trapezoidal rule for $r{\geq}3$ by using zero mean-Gaussian.

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.365-372
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• 2003

We show that if ${\gamma}$ $\leq$ 2, the average error of the composite Trapezoidal rule on two consecutive intervals is proportional to h$\^$2h+3/ where h is the length of each subinterval of the interval [0, 1]. As a result, we show that the Trapezoidal rule with equally spaced points is optimal in the average case setting when ${\gamma}$ $\leq$ 2.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.33-55
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• 2005

The temporal discretisation of a moderate semilinear parabolic problem in an abstract setting by the two-step backward differentiation formula with variable step sizes is analysed. Stability as well as optimal smooth data error estimates are derived if the ratios of adjacent step sizes are bounded from above by 1.91.

• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.107-117
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• 2003

We study the integration problem in which one wants to compute the approximation to the definite integral in the average case setting. We choose the composite Newton- Cotes quadratures as our algorithm and the function values at equally spaced sample points on the given interval［0, 1］as information. We compute the average case error of composite Newton-Cotes quadratures and show that it is minimal (modulo a multi-plicative constant).

• Communications of the Korean Mathematical Society
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• v.13 no.4
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• pp.903-911
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• 1998

We show that if r $\leq$ 2, the average error of the Trapezoidal rule is proportional to $n^{-min{r＋l, 3}}$ where n is the number of mesh points on the interval [D, 1]. As a result, we show that the Trapezoidal rule with equally spaced points is optimal in the average case setting when r $\leq$ 2.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.7 no.2
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• pp.284-292
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• 2003

In this paper, we carried out the numerical examination of the initial value setting-up method to extend the range of optimal step parameter in a adaptive system which is controlled by LMS algorithm. For initial value setting-up methods, the general method which select the initial value randomly and the other method which applies the approximate value obtained from the direct method to initial value, were used. And then, we compared to the ranges of step parameter setting, the convergence speeds of mean-square-error, and the stabilities during the convergence process when the initial values were applied to the optimal directivity synthesis problem. According to the numerical simulation results, the initial value setting-up method by means of the direct method provides wider range for the step parameter, more efficient capability for convergence and stability, and more error correction ability than the general method.

• Journal of Korean Society for Quality Management
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• v.29 no.3
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• pp.66-78
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• 2001

This paper deals with problem of determining process target value under automated visual inspection(AVI) system. Three independent error sources - digitizing error, illumination error, and positional error - which have a close relationship with the performance of the AVI system, are considered. Assuming that digitizing error is uniformly or normally distributed and illumination and positional errors are normally distributed, respectively, the distribution function for the error of measured lengths is derived when the length of a product is measured by the AVI system. Then, Optimal target values under two error models of AVI system are obtained by minimizing the total expected cost function which consists of give away, rework and penalty cost. To validate two process setting models, AVI system for drinks filling process is made up and test results are discussed.

• Journal of the korean Society of Automotive Engineers
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• v.10 no.3
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• pp.31-37
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• 1988

A phase different method to evaluate the instrument error of roundness measuring instrument and the form error of specimens for the calibration of the instrument is used. An instrument with a rotary table supported by an air bearing was calibrated by using the standard balls as a standard. The calibration was carried out repeatedly by setting the same ball in 12 phase angles(per 30.deg.) on the table and by recording their roundness errors with a magnification of 100,000 times. As a result of data analysis of all the observations, readout at each of 144 orientations(per 2.5.deg.) from recorded data file, the error of performance of the instrument and the specimens are separated. In the particular instrument used in the present experiment, the error of the instrument was determined with the accuracy of 0.0164 (.mu.m) and the form error of the specimens was determined with the accuracy of 0.0264,0.0172(.mu.m), respectively. If the instrument was calibrated by using the above specimens, then the accuracy of the measurement of roundness error can be improved to about 0.017 (.mu.m).

• Journal of the Korean Society for Precision Engineering
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• v.21 no.6
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• pp.43-51
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• 2004

A method for form error prediction in side wall machining with a flat end mill is suggested. Form error is predicted directly from the tool deflection without surface generation by cutting edge locus with time simulation. Developed model can predict the surface form error about three hundred times faster than the previous method. Cutting forces and tool deflection are calculated considering tool geometry, tool setting error and machine tool stiffness. The characteristics and the difference of generated surface shape in up milling and down milling are discussed. The usefulness of the presented method is verified from a set of experiments under various cutting conditions generally used in die and mold manufacturing. This study contributes to real time surface shape estimation and cutting process planning for the improvement of form accuracy.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2008.05a
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• pp.734-737
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• 2008

This paper presents a new automatic TFT-LCD image quality optimization system. We also have developed new algorithms using 6-point programmable matching technique with reference gamma curve, and automatic power setting sequence. It optimizes automatically gamma adjustment and power setting registers in mobile TFT-LCD driver IC to reduce gamma correction error, adjusting time, and flicker. Developed algorithms and programs are generally applicable for most of the TFT-LCD modules. The proposed optimization system contains module-under-test (MUT, TFT-LCD module), control program, multimedia display tester for measuring luminance and flicker, and control board for interface between PC and TFT-LCD module. The control board is designed with DSP, and it supports various interfaces such as RGB and CPU. Developed automatic image quality optimization system showed significantly reduced gamma adjusting time, reduced flicker, and much less average gamma error than competing system. We believe that the proposed system is very useful to provide high image quality TFT-LCD and to reduce developing process time using optimized gamma-curve setting and automatic power setting.