• Journal of applied mathematics & informatics
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• 제13권1_2호
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• pp.11-27
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• 2003

A fourth order in time and second order in space scheme using a finite-difference method is developed for the non-linear Boussinesq equation. For the solution of the resulting non-linear system a predictor-corrector pair is proposed. The method is analyzed for local truncation error and stability. The results of a number of numerical experiments for both the single and the double-soliton waves are given.

• Journal of applied mathematics & informatics
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• 제5권1호
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• pp.23-40
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• 1998

Mixed finite element method is developed to approxi-mate the solution of the initial-boundary value problem for a strongly nonlinear second-order hyperbolic equation in divergence form. Exis-tence and uniqueness of the approximation are proved and optimal-order $L\infty$-in-time $L^2$-in-space a priori error estimates are derived for both the scalar and vector functions approximated by the method.

• Journal of applied mathematics & informatics
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• 제19권1_2호
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• pp.385-395
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• 2005

A finite element scheme is considered for the viscous Cahn-Hilliard equation with the nonconstant gradient energy coefficient. The scheme inherits energy decay property and mass conservation as for the classical solution. We obtain the corresponding error estimate using the extended Lax-Richtmyer equivalence theorem.

• Journal of applied mathematics & informatics
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• 제29권1_2호
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• pp.23-37
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• 2011

In this paper, we use a modified Tikhonov regularization method to solve the Fredholm integral equation of the first kind. Under the assumption that measured data are contaminated with deterministic errors, we give two error estimates. The convergence rates can be obtained under the suitable choices of regularization parameters and the number of measured points. Some numerical experiments show that the proposed method is effective and stable.

• East Asian mathematical journal
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• 제35권1호
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• pp.99-108
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• 2019

In this paper, we introduce a numerical approach to solve heat-diffusion equation with discontinuous diffusion coefficients in the three dimensional rectangular domain. First, we study the support operator method and suggest a new method, the continuous velocity method. Further, we apply both methods to a diffusion process for neurotransmitter release in an individual synapse and compare their results.

• 한국운동역학회지
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• 제27권1호
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• pp.53-58
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• 2017

Objective: The purpose of this study was to compare the accuracy of stride time and stride length provided by a commercial APDM inertial sensor system (APDM) with the results of three dimensional motion capture system (3D motion) during treadmill walking. Method: Five healthy men participated in this experiment. All subjects walked on the treadmill for 3 minutes at their preferred walking speed. The 3D motion and the APDM were simultaneously used for extracting gait variables such as stride time and stride length. Mean difference and root mean squared (RMS) difference were used to compare the measured gait variables from the two measurement devices. The regression equation derived from the range of motion of the lower limb was also applied to correct the error of stride length. Results: The stride time extracted from the APDM was almost the same as that from the 3D motion (the mean difference and RMS difference were less than 0.0001 sec and 0.0085 sec, respectively). For stride length, mean difference and RMS difference were less than 0.1141 m and 0.1254 m, respectively. However, after correction of the stride length error using the derived regression equation, the mean difference and the RMS difference decreased to 0.0134 m and 0.0556 m or less, respectively. Conclusion: In this study, we confirmed the possibility of using the temporal variables provided from the APDM during treadmill walking. By applying the regression equation derived only from the range of motion provided by the APDM, the error of the spatial variable could be reduced. Although further studies are needed with additional subjects and various walking speeds, these results may provide the basic data necessary for using APDM in treadmill walking.

• 농업과학연구
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• 제46권1호
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• pp.137-149
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• 2019

Accurate estimation of reference evapotranspiration (RET) is important to quantify crop evapotranspiration for sustainable water resource management in hydrological, agricultural, and environmental fields. It is estimated by different methods from direct measurements with lysimeters, or by many empirical equations suggested by numerous modeling using local climatic variables. The potential to use some such equations depends on the availability of the necessary meteorological parameters for calculating the RET in specific climatic conditions. The objective of this study was to determine the proper RET equations using limited climatic data and to analyze the temporal and spatial trends of the RET in South Korea. We evaluated the FAO-56 Penman-Monteith equation (FAO-56 PM) by comparing several simple RET equations and observed small fan evaporation. In this study, the modified Penman equation, Hargreaves equation, and FAO Penman-Monteith equation with missing solar radiation (PM-Rs) data were tested to estimate the RET. Nine weather stations were considered with limited climatic data across South Korea from 1973 - 2017, and the RET equations were calculated for each weather station as well as the analysis of the mean error (ME), mean absolute error (MAE), and root mean square error (RMSE). The FAO-56 PM recommended by the Food Agriculture Organization (FAO) showed good performance even though missing solar radiation, relative humidity, and wind speed data and could still be adapted to the limited data conditions. As a result, the RET was increased, and the evapotranspiration rate was increased more in coastal areas than inland.

• 복식문화연구
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• 제7권2호
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• pp.275-288
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• 1999

The purpose of this is providing a simple, relatively errorless body surface area calculation. Subjects were 10 married women and 10 singles women whose age was 20 to 29 years old. The Gypsum method has applied for the sampling of body surface. The Weight method has been used to measure body surface by means of transferring gypsum shape on uniform plane polypropylene films. In this study, compare analyzed errors between the traditional formulas for measuring body surface area and measuring data in this experiment. More than all, it has been to induce a regression equation for measuring body surface area, which is so simple to calculate with less errors, with variable factors as weight and height. The results of this experiment as follows : 1. In the traditional formulas, weight formula was shown high average error : Niya\`s height formula. which was modified K value as 0.62 in the height formula (S = KH) is shown lower average error than Lassabliere\`s Height formula. 2. In the weight-height formula (S=K √WH), it was shown high average error according to the increasing of K value. Kawanami\`s formula, which 5.378 as K value, was shown low average error both the singles and the married women. 3. Dubois weight-heingt formula (S=W/sup a/·H/sub b/·K) was shown low average error than the weight, height, weight-height (S=K√WH) formula. 4. The regression equations with variable factors as weight and height are 156.74W + 86.05H - 660.25 (Single women) and 136.02W + 90.57H - 6241.32 (Married women) the average error and absolute average error to the singles are 0.09%, 0.94% and resoectively -0.13%, 1.16% for the married women.

• 한국정밀공학회지
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• 제18권2호
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• pp.152-160
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• 2001

Six degrees of freedom measurement systems are required in many fields: Precision machine control. precision assembly, vibration analysis, and so on. This paper presents a new six degrees of freedom measurement system utilizing typical features of a diffraction grating. It is composed of a laser source, three position sensitive detectors, a diffraction grating target, and several optical components. Six degrees of freedom displacement is calculated kinematically from the coordinates of diffracted rays on the detectors. Optical measurement error was caused by the fact that a laser source had a Gaussian intensity distribution. This error was analyzed and compensated using simple equations. The performance of the compensation equation was verified in the experiment. The experimental results showed that the compensation equation could reduce the optical measurement error remarkably and the error in six degrees of freedom measurement less than $\pm$10$\mu$m for translation and $\pm$0.012$^{\circ}$for rotation.

• Journal of applied mathematics & informatics
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• 제7권2호
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• pp.409-438
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• 2000

In this paper we develop a new procedure to control stepsize for Runge- Kutta methods applied to both ordinary differential equations and semi-explicit index 1 differential-algebraic equation In contrast to the standard approach, the error control mechanism presented here is based on monitoring and controlling both the local and global errors of Runge- Kutta formulas. As a result, Runge-Kutta methods with the local-global stepsize control solve differential of differential-algebraic equations with any prescribe accuracy (up to round-off errors)