• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.299-318
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• 2023

This article devises an exponentially fitted method for the numerical solution of two parameter singularly perturbed parabolic boundary value problems. The proposed scheme is able to resolve the two lateral boundary layers of the solution. Error estimates show that the constructed scheme is parameter-uniformly convergent with a quadratic numerical rate of convergence. Some numerical test examples are taken from recently published articles to confirm the theoretical results and demonstrate a good performance of the current scheme.

• Kyungpook Mathematical Journal
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• v.52 no.2
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• pp.167-177
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• 2012

In this article, we propose exponentially fitted error correction methods(EECM) which originate from the error correction methods recently developed by the authors (see [10, 11] for examples) for solving nonlinear stiff initial value problems. We reduce the computational cost of the error correction method by making a local approximation of exponential type. This exponential local approximation yields an EECM that is exponentially fitted, A-stable and L-stable, independent of the approximation scheme for the error correction. In particular, the classical explicit Runge-Kutta method for the error correction not only saves the computational cost that the error correction method requires but also gives the same convergence order as the error correction method does. Numerical evidence is provided to support the theoretical results.

• Communications of the Korean Mathematical Society
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• v.37 no.1
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• pp.303-326
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• 2022

Our aim is to construct Hermite-type exponentially fitted interpolation formulas that use not only the pointwise values of an 𝜔-dependent function f but also the values of its first derivative at three unequally spaced nodes. The function f is of the form, f(x) = g₁(x) cos(𝜔x) + g₂(x) sin(𝜔x), x ∈ [a, b], where g₁ and g₂ are smooth enough to be well approximated by polynomials. To achieve such an aim, we first present Hermite-type exponentially fitted interpolation formulas I_N built on the foundation using N unequally spaced nodes. Then the coefficients of I_N are determined by solving a linear system, and some of the properties of these coefficients are obtained. When N is 2 or 3, some results are obtained with respect to the determinant of the coefficient matrix of the linear system which is associated with I_N. For N = 3, the errors for I_N are approached theoretically and they are compared numerically with the errors for other interpolation formulas.

• Journal of applied mathematics & informatics
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• v.31 no.5_6
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• pp.677-693
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• 2013

We construct exponentially fitted interpolation formulas using the values of the ${\omega}$-dependent function $f$ as well as its derivatives up to the $n$th order at a finite number of nodes on a closed interval ${\Omega}$. The function $f$ is of the form, $$f(x)=f_1(x)cos({\omega}x)+f_2(x)sin({\omega}x),x{\in}{\Omega}$$, where $f_1$ and $f_2$ are smooth enough to be approximated by polynomials on ${\Omega}$. Some properties of the formulas are newly found. The properties are numerically investigated and reexamined by producing some figures.

• Journal of applied mathematics & informatics
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• v.34 no.3_4
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• pp.207-220
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• 2016

Our goal is to construct a two-frequency-dependent formula $I_N$ which interpolates a product f of two functions with different frequencies at some N points. In the beginning, it is not clear to us that the formula $I_N$ satisfies $I_N=f$ at the points. However, it is later shown that $I_N$ satisfies the above equation. For this theoretical development, a one-frequency-dependent formula is introduced, and some of its characteristics are explained. Finally, our newly constructed formula $I_N$ is compared to the classical Lagrange interpolating polynomial and the one-frequency-dependent formula in order to show the advantage that is obtained by generating the formula depending on two frequencies.

• The Korean Journal of Applied Statistics
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• v.37 no.2
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• pp.177-189
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• 2024

The run length is defined as the number of samples or subgroups taken before the control chart statistic exceeds the control limits. Because the distribution of run length is typically asymmetric and has a large variability, it may not be appropriate to use ARL (average run length) alone to design control charts and evaluate performance. In this paper, we introduce the concept of percentile (PL)-based design of control charts, and propose the procedure for PL-based design of EWMA (exponentially weighted moving average) charts. For the PL-based design of EWMA, we present a fitted function for the control chart coefficient, given specific percentile parameters. Additionally, we perform simulations to compare the proposed design with the ARL-based design. The simulation results show that the proposed design yields improvements in monitoring in-control processes while maintaining the ability to detect out-of-control performance.

• Journal of Korean Society for Atmospheric Environment
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• v.17 no.5
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• pp.385-393
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• 2001

We have developed a Differential Absortion LIDAR (DIAL) method for the measurement of lower tropospheric ozone concentration. We used two laser beams from quadrupled Nd:YAG (266 nm) for the resonance wavelength and dye lasers (299.5 nm) for non -resonance wavelength. Aerosol extinction coefficients in the lower troposphere was computed by both Klett and Slope methods. To correct the SIN (Signal -Induced Noise) effect caused by photo detector, we subtracted a new-fitted baseline on the background part of a LIDAR signal, after the subtraction of the DC level. This is because SIN can be treated as an exponentially decaying tail. Using theme results, ozone profiles were obtained approximately 2km at daytime and 3km at nighttime. We compared the results derided by the Slope method with those measured by UV spectrometer. The computed results are in mostly good agreement with experimental results. In the measurement of the vertical layer, we observed the variation of the ozone profiles around the top mixed layer.

• Journal of Biosystems Engineering
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• v.23 no.4
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• pp.335-342
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• 1998

The objectives of this study were to evaluate respiration characteristics and develop empirical respiratory rate equations for short gain rough rice. The carbon dioxide concentrations generated from mush rice at four level temperatures(10, 20, 30, 4$0^{\circ}C$) and 4 level moisture contents(17.2, 21.5, 25.9, 31.6％, d.b.) were measured by gas chromatography. The respiratory rates' increased exponentially with gain temperature and also with moisture content The relationship between respiratory rate and gain temperature fitted the Arrehenius' and Core's equations very well. Two empirical respiratory rate equations were presented as a function of gain temperature and moisture content. The values of determination coefficient for the developed respiratory rate equations were 0.999, and the result of t-test showed that there were no significant differences between predicted and measured respiratory rates on significance level of 1%. Therefore, it appeared that respiratory rates predicted by the respiratory rate equations agreed well with measured values. An equation for predicting dry matter losses of rough rice during storage was presented by modifying the respiratory rate equations based on chemical reaction of decomposition of carbohydrate.

• IE interfaces
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• v.17 no.1
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• pp.1-12
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• 2004

In a modern semiconductor device manufacturing industry, statistical bin limits on wafer level test bin data are used for minimizing value added to defective product as well as protecting end customers from potential quality and reliability excursion. Most wafer level test bin data show skewed distributions. By Monte Carlo simulation, this paper evaluates methods and sample size effect regarding determination of statistical bin limits. In the simulation, it is assumed that wafer level test bin data follow the Poisson distribution. Hence, typical shapes of the data distribution can be specified in terms of the distribution's parameter. This study examines three different methods; 1) percentile based methodology; 2) data transformation; and 3) Poisson model fitting. The mean square error is adopted as a performance measure for each simulation scenario. Then, a case study is presented. Results show that the percentile and transformation based methods give more stable statistical bin limits associated with the real dataset. However, with highly skewed distributions, the transformation based method should be used with caution in determining statistical bin limits. When the data are well fitted to a certain probability distribution, the model fitting approach can be used in the determination. As for the sample size effect, the mean square error seems to reduce exponentially according to the sample size.

• Journal of the Korean Society for Precision Engineering
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• v.16 no.4 s.97
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• pp.205-212
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• 1999

A three dimensional binary parallel robot manipulator uses actuators which have only two stable states and its structure is variable geometry truss. As a result, it has a finite number of states and fault tolerant mechanism because of kinematic redundancy. This kind of robot manipulator has some advantages compared to a traditional one. Feedback control is not required, task repeatability can be very high, and finite state actuators are generally inexpensive. Because the number of states of a binary robot manipulator grows exponentially with the number of actuators it is very difficult to solve and inverse kinematic problem. The goal of this paper is to develop an efficient algorithm to solve an inverse kinematic problem of three dimensional binary parallel robot manipulator using a backbone curve when the number of actuators are too much. We first derive the coordinate transformations associated with a three degree of freedom in-parallel actuated robot manipulator. The backbone curve is generated optimally by considering the maximum roll and pitch angles of the robot manipulator configuration and length of link. Then, the robot manipulator is fitted along the backbone curve with some criterion.