• 대한수학회논문집
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• 제38권1호
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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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• 제52권2호
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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.

• 대한수학회논문집
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• 제37권1호
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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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• 제31권5_6호
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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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• 제34권3_4호
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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.

• 응용통계연구
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• 제37권2호
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• pp.177-189
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• 2024

관리도에서 런길이는 관리 통계량이 관리한계를 벗어날 때까지 관측한 표본의 수로 정의한다. 일반적으로 런길이의 분포는 비대칭이 심하고 변동성이 크기 때문에 평균 런길이만 사용하여 관리도를 설계하고 성능을 평가하는 것은 적절하지 않을 수도 있다. 평균 런길이 기반 설계에 대한 대안으로 이 논문에서는 백분위수를 기반으로 한 관리도의 설계를 소개하고, 이를 지수가중이동평균 관리도의 설계에 적용하는 절차를 제안하고 있다. 이 절차는 백분위수 모수들이 주어진 경우, 모의실험을 통하여 적합된 함수를 사용하여 관리한계의 계수를 설정하는 것이다. 또한 모의실험을 수행하여 제안된 설계 절차를 평균 런길이 기반 설계와 비교하고 평가하였다. 모의실험 결과, 제안된 절차는 이상상태에서 탐지 능력은 거의 유지하면서 관리상태에서의 성능을 향상시킨다는 사실을 확인할 수 있었다.

• 한국대기환경학회지
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• 제17권5호
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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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• 제23권4호
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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.

• 산업공학
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• 제17권1호
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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.

• 한국정밀공학회지
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• 제16권4호통권97호
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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.