• Title/Summary/Keyword: the cubic equation

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ON THE GENERALIZED HYERS-ULAM STABILITY OF A CUBIC FUNCTIONAL EQUATION

  • Jun, Kil-Woung;Lee, Sang-Baek
    • Journal of the Chungcheong Mathematical Society
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    • v.19 no.2
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    • pp.189-196
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    • 2006
  • The generalized Hyers-Ulam stability problems of the cubic functional equation f(x + y + z) + f(x + y - z) + 2f(x - y) + 4f(y) = f(x - y + z) + f(x - y - z) +2f(x + y) + 2f(y + z) + 2f(y - z) shall be treated under the approximately odd condition and the behavior of the cubic mappings and the additive mappings shall be investigated. The generalized Hyers-Ulam stability problem for functional equations had been posed by Th.M. Rassias and J. Tabor [7] in 1992.

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FUZZY STABILITY OF QUADRATIC-CUBIC FUNCTIONAL EQUATIONS

  • Kim, Chang Il;Yun, Yong Sik
    • East Asian mathematical journal
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    • v.32 no.3
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    • pp.413-423
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    • 2016
  • In this paper, we consider the functional equation f(x + 2y) - 3f(x + y) + 3f(x) - f(x - y) - 3f(y) + 3f(-y) = 0 and prove the generalized Hyers-Ulam stability for it when the target space is a fuzzy Banach space. The usual method to obtain the stability for mixed type functional equation is to split the cases according to whether the involving mappings are odd or even. In this paper, we show that the stability of a quadratic-cubic mapping can be obtained without distinguishing the two cases.

Performance Comparison of Cubic Equations of State With Two Temperature Dependent Parameters (두 개의 온도 의존 매개변수가 있는 3차 상태방정식의 성능비교)

  • Kwon, Young-Wook;Park, Kyoung-Kuhn
    • Proceedings of the KSME Conference
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    • 2001.11b
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    • pp.205-210
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    • 2001
  • Cubic equations of state with two temperature dependent parameters are suggested and optimized using ASHRAE data for methane, propane, carbon dioxide, R-32 and R-134a. Appropriate simple functional forms are assumed for the temperature dependent parameters. The equations tested are Martin, Fuller, Harmens-Knapp, Schmidt-Wenzel. Among them modified Schmidt-Wenzel equation of state appears to be the choice for calculation of saturation properties such as vapor pressures, saturated liquid volumes, and saturated vapor volumes with an average absolute deviation of about one percent over the entire region excluding; the near cirtical.

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Numerical solution of linear elasticity by preconditioning cubic spline collocation

  • Lee, Yong-Hun
    • Communications of the Korean Mathematical Society
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    • v.11 no.3
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    • pp.867-880
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    • 1996
  • Numerical approximations to the linear elasticity are traditionally based on the finite element method. In this paper we propose a new formulation based on the cubic spline collocation method for linear elastic problem on the unit square. We present several numerical results for the eigenvalues of the matrix represented by cubic collocation method and preconditioner matrix which is preconditioned by FEM and FDM. Finally we present the numerical solution for some example equation.

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Hyers-Ulam stability problem for an approximately cubic mapping

  • 김학만;전길웅
    • Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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    • 2003.09a
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    • pp.17.2-17
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    • 2003
  • The purpose of this paper is to solve the generalized Hyers-Ulam stability problem for a cubic functional equation 8f(x-y/2)+8f(y-x/2)+2f(x+y)=9f(x)+9f(y) on the basis of a direct method.

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GENERALIZED CUBIC MAPPINGS OF r-TYPE IN SEVERAL VARIABLES

  • Kang, Dong Seung
    • Journal of the Chungcheong Mathematical Society
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    • v.20 no.1
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    • pp.37-45
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    • 2007
  • Let X, Y be vector spaces. In this paper, we investigate the generalized Hyers-Ulam-Rassias stability problem for a cubic function $f:X{\rightarrow}Y$ satisfies $$r^3f(\frac{\Sigma_{j=1}^{n-1}x_j+2x_n}{r})+r^3f(\frac{\Sigma_{j=1}^{n-1}x_j-2x_n}{r})+8\sum_{j=1}^{n-1}f(x_j)=2f{\sum_{j=1}^{n-1}}x_j)+4{\sum_{j=1}^{n-1}}(f(x_j+x_n)+f(x_j-x_n))$$ for all $x_1,{\cdots},x_n{\in}X$.

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ON THE STABILITY OF THE GENERAL SEXTIC FUNCTIONAL EQUATION

  • Chang, Ick-Soon;Lee, Yang-Hi;Roh, Jaiok
    • Journal of the Chungcheong Mathematical Society
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    • v.34 no.3
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    • pp.295-306
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    • 2021
  • The general sextic functional equation is a generalization of many functional equations such as the additive functional equation, the quadratic functional equation, the cubic functional equation, the quartic functional equation and the quintic functional equation. In this paper, motivating the method of Găvruta [J. Math. Anal. Appl., 184 (1994), 431-436], we will investigate the stability of the general sextic functional equation.

Transient Linear Elastodynamic Analysis by the Finite Element Method (유한요소법을 이용한 과도 선형 동탄성 해석)

  • Hwang, Eun-Ha;Oh, Guen
    • Journal of the Korean Society of Industry Convergence
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    • v.12 no.3
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    • pp.149-155
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    • 2009
  • A new finite element equation is derived by applying quadratic and cubic time integration scheme to the variational formulation in time-integral for the analysis of the transient elastodynamic problems to increase the numerical accuracy and stability. Emphasis is focused on methodology for cubic time integration scheme procedure which are never presented before. In this semidiscrete approximations of the field variables, the time axis is divided equally and quadratic and cubic time variation is assumed in those intervals, and space is approximated by the usual finite element discretization technique. It is found that unconditionally stable numerical results are obtained in case of the cubic time variation. Some numerical examples are given to show the versatility of the presented formulation.

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Comparison of the Results of Finite Difference Method in One-Dimensional Advection-Dispersion Equation (유한차분 모형에 의한 일차원 이송-확산방정식 계산결과의 비교)

  • 이희영;이재철
    • Water for future
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    • v.28 no.4
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    • pp.125-136
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    • 1995
  • ELM, a characteristic line based method, was applied to advection-dispersion equation, and the results obtained were compared with those of Eulerian schemes(Stone-Brian and QUICKEST). The calculation methods consisted of Lagrangian interpolation scheme and cubic spline interpolation scheme for the advection calculation, and the Crank-Nicholson scheme for the dispersion calculation. The results of numerical methods were as follows: (1) for Gaussian hill: ELM, using Lagrangian interpolation scheme, gave the most accurate computational result, ELM, using cubic spline interpolation scheme, and QUICKEST scheme gave numerical damping for Peclet number 50. Stone-Brian scheme gave phase shift introduced in the numerical solution for Peclet number 10 and 50. (2) for advanced front: All schemes gave accurate computational results for Peclet number 1 and 4. ELM, Lagrangian interpolation scheme, and Stone,Brian scheme gave dissipation error and ELM, using cubic spline interpolation scheme, and QUICKEST scheme gave numerical oscillation for Peclet number 50.

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Mach Reflection of Sinusoidally-Modulated Nonlinear Stokes Waves by a Thin Wedge

  • Choi, Hang-S.;Chee, Won-S.
    • Selected Papers of The Society of Naval Architects of Korea
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    • v.1 no.1
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    • pp.45-51
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    • 1993
  • By using multiple-scale expansion techniques, the Mach reflection of sinusoidally- modulated nonlinear Stokes waves by a stationary thin wedge has been studied within the framework of potential theory. It is shown that the evolution of diffracted wave amplitude can be described by the Zakharov equation to the loading order and that It reduces to the cubic Schrodinger equation with an additional linear term in the case of stable modulations. Computations are made for the cubic Schrodinger equation for different values of nonlinear and dispersion parameters. Numerical results reflect the experimental findings in terms of the amplitude and width of generated stem waves. Based on the computations it is concluded that the nonlinearity dominates the wave field, while the dispersion does not significantly affect the wave evolution.

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