• Kyungpook Mathematical Journal
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• v.62 no.3
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• pp.557-581
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• 2022

The anisotropic-diffusion convection equation with exponentially variable coefficients is discussed in this paper. Numerical solutions are found using a combined Laplace transform and boundary element method. The variable coefficients equation is usually used to model problems of functionally graded media. First the variable coefficients equation is transformed to a constant coefficients equation. The constant coefficients equation is then Laplace-transformed so that the time variable vanishes. The Laplace-transformed equation is consequently written as a boundary integral equation which involves a time-free fundamental solution. The boundary integral equation is therefore employed to find numerical solutions using a standard boundary element method. Finally the results obtained are inversely transformed numerically using the Stehfest formula to get solutions in the time variable. The combined Laplace transform and boundary element method are easy to implement and accurate for solving unsteady problems of anisotropic exponentially graded media governed by the diffusion convection equation.

• Journal of applied mathematics & informatics
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• v.31 no.1_2
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• pp.229-239
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• 2013

This paper studies the generalized fifth-order KdV equation with variable coefficients using Lie symmetry methods.Lie group classification with respect to the time dependent coefficients is performed. Then we get the similarity reductions using the symmetry and give some exact solutions.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.143-152
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• 2010

Based on the Exp-function method and a suitable transformation, new generalized solitonary solutions including free parameters of the MDI and Sawada-Kotera equations with variable coefficients are obtained, form which solitary wave solutions and periodic solutions including some known solutions reported in open literature are derived as special cases. The free parameters in the obtained generalized solitonary solutions might imply some meaningful results in the physical models. It is shown that the Exp-function method provides a very effective and important new method for nonlinear evolution equations with variable coefficients.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.30 no.9C
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• pp.860-870
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• 2005

In this paper we propose a new method to derive GRM(Generalized Reed-Muller) coefacients for each $2^{n}$ polarities using cell of karnaugh map(k-map). Generally, there are the serial and parallel method to derive GRM coefficients. As a serial method, Green method generates GRM coefncients using transform matrix. And as a parallel method, Besslich algorithm produces GRM coefficients of each polarity using the generated anteriorly. Green's method generates GRM coefficients for n-variable by calculating transform matrix for one-variable and n-times kronecker product this matrix. And Besslich's method generates GRM coefficients of each polarity in order of Grey-code. But those methods have disadvantages that the number of variable exceeding four makes transform matrix large and there are so many operation steps. In this paper, GRM coefficients is generated by producing cell [$f_{i}$] minimizing variable on k-map and operating this cell [$f_{i}$] and transform matrix for one-variable. So, we can generate GRM coefficients of all polarities easily by using the proposed method.

• The Korean Journal of Applied Statistics
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• v.34 no.4
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• pp.589-597
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• 2021

In simple and multiple regression, there is a difference in the meaning of regression coefficients, and not only are the estimates of regression coefficients different, but they also have different signs. Understanding the relative contribution of explanatory variables in a regression model is an important part of regression analysis. In a standardized regression model, the regression coefficient can be interpreted as the change in the response variable with respect to the standard deviation when the explanatory variable increases by the standard deviation in a situation where the values of the explanatory variables other than the corresponding explanatory variable are fixed. However, the size of the standardized regression coefficient is not a proper measure of the relative importance of each explanatory variable. In this paper, the estimator of the regression coefficient in multiple regression is expressed as a function of the correlation coefficient and the coefficient of determination. Furthermore, it is considered in terms of the effect of an additional explanatory variable and additional increase in the coefficient of determination. We also explore the relationship between estimates of regression coefficients and correlation coefficients in various plots. These results are specifically applied when there are two explanatory variables.

• Journal of applied mathematics & informatics
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• v.6 no.1
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• pp.185-196
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• 1999

This paper is concerned with investigating the global asymptotic behavior of the solution to a nonlinear wave equation with variable coefficients. noreover an estimate of the rate of decay of the solution is obtained.

• Journal of the Korean Wood Science and Technology
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• v.34 no.5
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• pp.98-103
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• 2006

Radial and tangential diffusion coefficients of boron in wood under water leaching conditions were determined from the change of concentration profiles of boron. Egner's solution was used to obtain variable diffusion coefficients of boron because it has been known to be the only method to determine variable diffusion coefficients with no cumbersome assumption. The values of diffusion coefficients were between $0.18{\times}10^{-6}m^2/sec$ and $25.6{\times}10^{-6}cm^2/sec$. They increased with the increase of sample thicknesses, and decreased with the increase of leaching times. There was a region where Egner's method was not valid. However, Egner's solution illustrates a convenient way to evaluate diffusion characteristics of boron from wood under water leaching conditions. The diffusion coefficients at wood surface may be regarded as leaching coefficients.

• Proceedings of the IEEK Conference
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• 2002.07a
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• pp.686-689
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• 2002

This paper proposes a weighted least-squares(WLS) method for designing variable one-dimensional (1-D) FIR digital filters with simultaneously variable magnitude and variable non-integer phase-delay responses. First, the coefficients of a variable FIR filter are represented as the two-dimensional (2-D) polynomials of a pair of spectral parameters: one is for tuning the magnitude response, and the other is for varying its non-integer phase-delay response. Then the optimal coefficients of the 2-D polynomials are found by minimizing the total weighted squared error of the variable frequency response. Finally, we show that the resulting variable FIR filter can be implemented in a parallel form, which is suitable for high-speed signal processing.

• Kyungpook Mathematical Journal
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• v.61 no.2
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• pp.383-393
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• 2021

In this paper, numerical techniques are presented for solving initial value problems of fractional differential equations with variable coefficients. The method is derived by applying a Taylor vector approximation. Moreover, the operational matrix of fractional integration of a Taylor vector is provided in order to transform the continuous equations into a system of algebraic equations. Furthermore, numerical examples demonstrate that this method is applicable and accurate.

• The Korean Journal of Applied Statistics
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• v.18 no.2
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• pp.435-443
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• 2005

Coefficients of determination in logistic regression analysis are defined as various statistics, and their values are relatively smaller than those for linear regression model. These coefficients of determination are not generally used to evaluate and diagnose logistic regression model. Liao and McGee (2003) proposed two adjusted coefficients of determination which are robust at the addition of inappropriate predictors and the variation of sample size. In this work, these adjusted coefficients of determination are applied to variable selection method for logistic regression model and compared with results of other methods such as the forward selection, backward elimination, stepwise selection, and AIC statistic.