• Communications of the Korean Mathematical Society
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• v.13 no.4
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• pp.889-901
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• 1998

Numerical approximations by pseudospectral method are obtained for the damped Boussinesq equation which is a modification of the good Boussinesq equation. The consistency and stability of the method are obtained using the extended Lax-Richtmyer equivalence theorem, which imply the convergence of the method. We obtain error estimates of O(h$^{s}$ ＋ k$^2$) for a fully discrete pseudospectral method.

• Tribology and Lubricants
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• v.36 no.2
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• pp.68-74
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• 2020

In this study, the effect of the shape error of a guideway on the movement of a stage that uses an air bearing is analyzed. The shape error of moving parts supported by the air bearing is known not to affect the vibrations of moving parts as much as the magnitude of the shape error. This is called the "averaging effect." In this study, the effect of shape error on a guideway, as well as the averaging effect of an air-bearing system, is analyzed theoretically using a dynamic-analysis program. The dynamic-analysis program applies a commercially available code in COMSOL and solves the Reynolds equation between the stage and the guideway, along with the equation of motion of the stage. The stage is modeled as a two-degree-of-freedom system. The shape error is applied to the film thickness function in the form of a sine wave. The stage movement is analyzed using the fast Fourier transform process. The eccentricity and tilting are found to be proportional to the amplitude of the shape error of the guideway. Stage vibrations are less than 10% of the amplitude of the shape error on the guideway. This means that the averaging effect of the air bearing is verified quantitatively. Moreover, if the air supply position matches the shape error in the guideway, there is a notable change in eccentricity and tilting.

• Archives of Pharmacal Research
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• v.28 no.5
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• pp.598-603
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• 2005

The purpose of this study was to determine the influence of weight with gentamicin assay error on the Bayesian and nonlinear least squares regression analysis in 12 Korean appen dicitis patients. Gentamicin was administered intravenously over 0.5 h every 8 h. Three specimens were collected at 48 h after the first dose from all patients at the following times, just before regularly scheduled infusion, at 0.5 h and 2 h after the end of 0.5 h infusion. Serum gentamicin levels were analyzed by fluorescence polarization immunoassay technique with TDxFLx. The standard deviation (SD) of the assay over its working range had been determined at the serum gentamicin concentrations of 0, 2, 4, 8, 12, and 16 ${\mu}g$/mL in quadruplicate. The polynominal equation of gentamicin assay error was found to be SD (${\mu}g$/mL) = 0.0246-(0.0495C)+ (0.00203C$^2$). There were differences in the influence of weight with gentamicin assay error on pharmacokinetic parameters of gentamicin using the nonlinear least squares regression analysis but there were no differences on the Bayesian analysis. This polynominal equation can be used to improve the precision of fitting of pharmacokinetic models to optimize the process of model simulation both for population and for individualized pharmacokinetic models. The result would be improved dosage regimens and better, safer care of patients receiving gentamicin.

• YAKHAK HOEJI
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• v.57 no.1
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• pp.32-36
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• 2013

The purpose of this study was to determine the influence of assay error for improved pharmacokinetic modeling and simulation of vancomycin on the Bayesian and nonlinear least squares regression analysis in 24 Korean gastric cancer patients. Vancomycin 1.0 g was administered intravenously over 1 hr every 12 hr. Three specimens were collected at 72 hr after the first dose from all patients at the following times, at 0.5 hr before regularly scheduled infusion, at 0.5 hr and 2 hr after the end of 1 hr infusion. Serum vancomycin levels were analyzed by fluorescence polarization immunoassay technique with TDX-FLX. The standard deviation (SD) of the assay over its working range had been determined at the serum vancomycin concentrations of 0, 20, 40, 60, 80 and $120{\mu}g/ml$ in quadruplicate. The polynomial equation of vancomycin assay error was found to be SD $({\mu}g/ml)=0.0224+0.0540C+0.00173C^2$ ($R^2=0.935$). There were differences in the influence of weight with vancomycin assay error on pharmacokinetic parameters of vancomycin using the nonlinear least squares regression analysis but there were no differences on the Bayesian analysis. This polynomial equation can be used to improve the precision of fitting of pharmacokinetic models to optimize the process of model simulation both for population and for individualized pharmacokinetic models. The result suggests the improvement of dosage regimens for the better and safer care of patients receiving vancomycin.

• Journal of the Korean Society of Marine Environment & Safety
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• v.20 no.3
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• pp.323-333
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• 2014

In this paper, the wakes behind a square cylinder were simulated using two kinds of different turbulence models for the eddy viscosity concept such as the zero- and the one-equation model in which the former is the mixing length model and the latter is the k-equation model. For comparison between numerical and analytical solutions, we employed three skill assessments: the correlation coefficient(r) for the similarity of the wake shape, the error of maximum velocity difference(EMVD) for the accuracy of wake velocity and the ratio of drag coefficient(RDC) for the pressure distribution around the structure. On the basis of the numerical results, the feasibility of each model for wake simulation was discussed and a suitable value for the empirical constant was suggested in these turbulence models. The zero-equation model, known as the simplest turbulence model, overestimated the EMVD and its absolute mean error(AME) for r, EMVD and RDC was ranging from 20.3 % to 56.3 % for all test. But the AME by the one-equation model was ranging from 3.4 % to 19.9 %. The predicted values of the one-equation model substantially agreed with the analytical solutions at the empirical mixing length scale $L=0.6b_{1/2}$ with the AME of 3.4 %. Therefore it was concluded that the one-equation model was suitable for the wake simulation behind a square cylinder when the empirical constant for eddy viscosity would be properly chosen.

• Journal of the Korean Society of Tobacco Science
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• v.35 no.1
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• pp.1-6
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• 2013

Near InfraRed Spectroscopy(NIRS) is a quick and accurate analytical method to measure multiple components in tobacco manufacturing process. This study was carried out to develop calibration equation of near infrared spectroscopy for the prediction of the amount of chemical components and hot water solubles(HWS) of reconstituted tobacco leaf. Calibration samples of reconstituted tobacco leaf were collected from every lot produced during one year. The calibration equation was formulated as modified partial least square regression method (MPLS) by analyzing laboratory actual values and mathematically pre-treated spectra. The accuracy of the acquired equation was confirmed with the standard error of prediction(SEP) of chemical components in reconstituted tobacco leaf samples, indicated as coefficient of determination($R^2$) and prediction error of sample unacquainted, followed by the verification of model equation of laboratory actual values and these predicted results. As a result of monitoring, the standard error of prediction(SEP) were 0.25 % for total sugar, 0.03 % for nicotine, 0.03 % for chlorine, 0.16 % for nitrate, and 0.38 % for hot water solubles. The coefficient of determination($R^2$) were 0.98 for total sugar, 0.97 for nicotine, 0.96 for chlorine, 0.98 for nitrate and 0.92 for hot water solubles. Therefore, the NIRS calibration equation can be applicable and reliable for determination of chemical components of reconstituted tobacco leaf, and NIRS analytical method could be used as a rapid and accurate quality control method.

• Bulletin of the Korean Mathematical Society
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• v.47 no.6
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• pp.1225-1234
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• 2010

Numerical solutions for the fractional differential dispersion equations with nonlinear forcing terms are considered. The backward Euler finite difference scheme is applied in order to obtain numerical solutions for the equation. Existence and stability of the approximate solutions are carried out by using the right shifted Grunwald formula for the fractional derivative term in the spatial direction. Error estimate of order $O({\Delta}x+{\Delta}t)$ is obtained in the discrete $L_2$ norm. The method is applied to a linear fractional dispersion equations in order to see the theoretical order of convergence. Numerical results for a nonlinear problem show that the numerical solution approach the solution of classical diffusion equation as fractional order approaches 2.

• The Journal of the Acoustical Society of Korea
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• v.21 no.2E
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• pp.56-62
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• 2002

This paper describes a new method of stability evaluation for an estimated impulse response of a plant. It is difficult for the conventional stability evaluation equation to be used in an adaptive feedforward control system which uses an immeasurable acoustic transfer system of a real plant, because the equation requires an exact true impulse response of the plant. Therefore, the usefulness of the conventional equation is limited in a computer simulation. The proposed method is applicable to not only a computer simulation but also a real feedforward adaptive control system. It is found that the system is stable when the value of misadjustment is below -10 dB through computer simulations and experiments. And also, it is proved that the error signal is stable through the verification using filtered reference and filtered error LMS methods.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.42 no.10
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• pp.816-822
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• 2014

The estimation of the angular rate of a satellite has been discussed. A nonlinear observer has been proposed based on the state-dependent Riccati equation method. A sufficient stability condition for the convergence of estimation error has been presented. This condition is related to a state-dependent algebraic Riccati equation. It has been derived by transforming nonlinear error dynamics into a Lipschitz nonlinearity. An observer gain is obtained from this condition. Numerical simulations are presented to verify the proposed method.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.28-31
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• 1996

We propose an estimator design method of Stewart platform, which gives the 6DOF, positions and velcities of Stewart platform from the measured cylinder length. The solution of forward kinematics is not solved yet as a useful realtime application tool because of the complexity of the equation with multiple solutions. Hence we suggest an nonlinear estimator for the forward kinematics solution using Luenberger observer with nonlinear error correction term. But the way of residual gain selection of the estimator is not clear, so we suggest an algebraic Riccati equation for gain matrix using Lyapunov method. This algorithm gives the sufficient condition of the stability of error dynamics and can be extended to general nonlinear system.