• Bulletin of the Korean Mathematical Society
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• v.35 no.3
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• pp.473-484
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• 1998

We consider a finite difference approximation to a singular boundary value problem arising in the study of a nonlinear circular membrane under normal pressure. It is proved that the rate of convergence is $O(h^2)$. To obtain the solution of the finite difference equation, an iterative scheme converging monotonically to the solution of the finite difference equation is introduced. And the numerical experiment of this method is given.

• Journal of applied mathematics & informatics
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• v.36 no.3_4
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• pp.271-283
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• 2018

In this paper, we introduce various first order (p, q)-difference equations. We investigate solutions to equations which are linear (p, q)-difference equations and nonlinear (p, q)-difference equations. We also find some properties of (p, q)-calculus, exponential functions, and inverse function.

• Journal of the Korean Society of Tobacco Science
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• v.27 no.1 s.53
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• pp.94-99
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• 2005

To correct the difference of filling volumn for various cut tobacco and puffed stem according to moisture contents, correction equation was estamated by a simple regression analysis. The $R^2$(coefficient of determination) of correction equation was above 0.95. To verify the precision of correction equation, we predicted correction equation of other samples. The filling volumns by the difference of $1\%$ moisture content were $0.018\;~\;0.022cc/g$ (cut tobacco) and 0.060cc/g (puffed stem). The precision of correction equation for various cut tobacco was very high, but that of puffed stem was low due to quality deviation of row stem according to a season.

• Geophysics and Geophysical Exploration
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• v.3 no.2
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• pp.39-47
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• 2000

A great deal of computing time and a large computer memory are needed to solve wave equation in a large complex subsurface layers using the finite difference method. The computing time and memory can be reduced by decreasing the number of grid points per minimum wave length. However, the decrease of grids may cause numerical dispersion and poor accuracy. In this study we performed the grid dispersion analysis for several rotated finite difference operators, which was commonly used to reduce grids per wavelength with accuracy in order to determine the solution for the acoustic wave equation in frequency domain. The rotated finite difference operators were to be extended to 81, 121 and 169 difference stars and studied whether the minimum grids could be reduced to 2 or not. To obtain accuracy (numerical errors less than $1\%$) the following was required: more than 13 grids for conventional 5 point difference stars, 9 grids for 9 difference stars, 3 grids for 25 difference stars, and 2.7 grids for 49 difference stars. After grid dispersion analysis for the new rotated finite difference operators, more than 2.5 grids for 81 difference stars, 2.3 grids for 121 difference stars and 2.1 grids for 169 difference stars were needed. However, in the 169 difference stars, there was no solution because of oscillation of the dispersion curves in the group velocity curves. This indicated that the grids couldn't be reduced to 2 in the frequency acoustic wave equation. According to grid dispersion analysis for the determination of grid points, the more rotated finite difference operators, the fewer grid points. However, the more rotated finite difference operators that are used, the more complex the difference equation terms.

• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.787-797
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• 2007

In this paper, the following fourth-order rational difference equation $$x_{n+1}=\frac{{x_n^b}+x_n-2x_{n-3}^b+a}{{x_n^bx_{n-2}+x_{n-3}^b+a}$$, n=0, 1, 2,..., where a, b ${\in}$ [0, ${\infty}$) and the initial values $X_{-3},\;X_{-2},\;X_{-1},\;X_0\;{\in}\;(0,\;{\infty})$, is considered and the rule of its trajectory structure is described clearly out. Mainly, the lengths of positive and negative semicycles of its nontrivial solutions are found to occur periodically with prime period 15. The rule is $1^+,\;1^-,\;1^+,\;4^-,\;3^+,\;1^-,\;2^+,\;2^-$ in a period, by which the positive equilibrium point of the equation is verified to be globally asymptotically stable.

• Research in Mathematical Education
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• v.13 no.2
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• pp.171-180
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• 2009

This study investigates relationships between 7th and 8th grade students' achievements in forming and solving equations of. Study was conducted on randomly selected 7th and 8th grade students of elementary schools in Konya City, Turkey. 145 students (99 female, 46 male) participated in the research. Data were collected by an 'Equation Test'. The test which is suitable for equation types in 7th Grade Elementary Mathematics Curriculum. It was developed by the researchers. The relationships between achievements in forming and solving equations were examined by dependent samples t-test. The t-test results show that there is a significant difference. This difference is in the favor of equation solving (p>0.05). In other word, students are more successful in equation solving. In addition, students' achievements about different types of equations were investigated. The results show that the students have the highest achievement in ax=b type and the lowest achievement in (ax+b)/c=(dx+e)/f type of equations.

• Journal of Environmental Science International
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• v.11 no.12
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• pp.1321-1326
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• 2002

A numerical model is investigated to predict a behavior of the gaseous volatile organic compounds and a subsurface contamination caused by them in the unsaturated zone. Two dimensional advective-dispersion equation caused by a density difference and two dimensional diffusion equation are computed by a finite difference method in the numerical model. A laboratory experiment is also carried out to compare the results of the numerical model. The dimensions of the experimental plume are 1.2m in length, 0.5m in height, and 0.05m in thickness. In comparing the result of 2 methods used in the numerical model with the one of the experiment respectively, the one of the advective-dispersion equation shows better than the one the diffusion equation.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.295-303
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• 2007

In this paper we investigate the boundedness character of the positive solutions of the rational difference equation of the form $$x_{n+1}=\frac{a_0+{{\sum}^k_{j=1}}a_jx_{n-j+1}}{b_0+{{\sum}^k_{j=1}}b_jx_{n-j+1}},\;\;n=0,\;1,...$$ where $k{\in}N,\;and\;a_j,b_j,\;j=0,\;1,...,\;k $, are nonnegative numbers such that $b_0+{{\sum}^k_{j=1}}b_jx_{n-j+1}>0$ for every $n{\in}N{\cup}\{0\}$. In passing we confirm several conjectures recently posed in the paper: E. Camouzis, G. Ladas and E. P. Quinn, On third order rational difference equations(part 6), J. Differ. Equations Appl. 11(8)(2005), 759-777.

• Nuclear Engineering and Technology
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• v.31 no.1
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• pp.80-87
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• 1999

An analytic axial xenon oscillation model was developed for pressurized water reactor analysis. The model employs an equation system for axial difference parameters that was derived from the two-group one-dimensional diffusion equation with control rod modeling and coupled with xenon and iodine balance equations. The spatial distributions of nu, xenon, and iodine were expanded by the Fourier sine series, resulting in cancellation of the flux-xenon coupled non-linearity. An inhomogeneous differential equation system for the axial difference parameters, which gives the relationship between power, iodine and xenon axial differences in the case of control rod movement, was derived and solved analytically. The analytic solution of the axial difference parameters can directly provide with the variation of axial power difference during xenon oscillation. The accuracy of the model is verified by benchmark calculations with one-dimensional reference core calculations.

• Bulletin of the Korean Mathematical Society
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• v.61 no.3
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• pp.745-762
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• 2024

In this paper, we study the existence of finite order meromorphic solutions of the following non-linear difference equation fⁿ(z) + P_d(z, f) = p₁e^α1z + p₂e^α2z + p₃e^α3z, where n ≥ 2 is an integer, P_d(z, f) is a difference polynomial in f of degree d ≤ n - 2 with small functions of f as its coefficients, p_j (j = 1, 2, 3) are small meromorphic functions of f and α_j (j = 1, 2, 3) are three distinct non-zero constants. We give the expressions of finite order meromorphic solutions of the above equation under some restrictions on α_j (j = 1, 2, 3). Some examples are given to illustrate the accuracy of the conditions.