• Bulletin of the Korean Chemical Society
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• 제32권4호
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• pp.1187-1194
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• 2011

The hydrogen abstraction reaction of $CF_3CH_2CHO$ + OH has been studied theoretically by dual-level direct dynamics method. Two stable conformers, trans- and cis-$CF_3CH_2CHO$, have been located, and there are four distinct OH hydrogen-abstraction channels from t-$CF_3CH_2CHO$ and two channels from c-$CF_3CH_2CHO$. The required potential energy surface information for the kinetic calculation was obtained at the MCG3-MPWB//M06-2X/aug-cc-pVDZ level. The rate constants, which were calculated using improved canonical transitionstate theory with small-curvature tunneling correction (ICVT/SCT) were fitted by a four-parameter Arrhenius equation. It is shown that the reaction proceeds predominantly via the H-abstraction from the -CHO group over the temperature range 200-2000 K. The calculated rate constants were in good agreement with the experimental data between 263 and 358 K.

• 소음진동
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• 제7권3호
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• pp.489-498
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• 1997

In this paper, chaotic motions of a curved pipe conveying oscillatory flow are theoretically investigated. The nonliear partial differential equation of motion is derived by Newton's method. The transformed nonlinear ordinary differential equation is a type of Hill's equation, which has the external and parametric excitation with a same frequency. Bifurcation curves of chaotic motion of the piping systems are obtained by applying Melnikov's method. Numerical simulations are performed to demonstrate theoretical results and show the strange attractor of the chaotic motion.

• 대한수학회보
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• 제55권1호
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• pp.297-310
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• 2018

In this paper, a nonlinear high-order difference scheme is proposed to solve the Extended-Fisher-Kolmogorov equation. The existence, uniqueness of difference solution and priori estimates are obtained. Furthermore, the convergence of the difference scheme is proved by utilizing the energy method to be of fourth-order in space and second-order in time in the discrete $L^{\infty}-norm$. Some numerical examples are given in order to validate the theoretical results.

• Journal of applied mathematics & informatics
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• 제22권1_2호
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• pp.317-329
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• 2006

In this paper, a singularly perturbed ordinary differential equation with non-smooth data is considered. The numerical method is generated by means of a Petrov-Galerkin finite element method with the piecewise-exponential test function and the piecewise-linear trial function. At the discontinuous point of the coefficient, a special technique is used. The method is shown to be first-order accurate and singular perturbation parameter uniform convergence. Finally, numerical results are presented, which are in agreement with theoretical results.

• 전기의세계
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• 제21권4호
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• pp.7-14
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• 1972

The author has established a general equation for the travelling magnetic field in air gap with the end effect taken into consideration, which constitutes the basics for the analysis of characteristics of linear induction motor. This equation is verified by comparison of the experimental values with the theoretically calculated values. The properties of the travelling wave with attenuation, which is contained in the travelling magnetic field of linear induction motor, have been verified, and consequently the practicable equation is established with these effects taken into consideration. This provides the solid foundation for the theoretical analysis of the characteristics of the linear induction motor.

• Journal of applied mathematics & informatics
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• 제23권1_2호
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• pp.43-55
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• 2007

In this paper, an $H^1-Galerkin$ mixed finite element method is used to approximate the solution as well as the flux of Burgers' equation. Error estimates have been derived. The results of the numerical experiment show the efficacy of the mixed method and justifies the theoretical results obtained in the paper.

• 전기의세계
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• 제16권1호
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• pp.14-18
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• 1967

To analyze th frequency modulation system the characteristic equation of the F-M system, i.e., Mathieu's equation, is derived from the equivalent circuits of direct modulation system. The analysis of F-M equation is undertaken by the Yonsei 101 Analog Computer. And the computer solution is compared with the theoretical solution. It is concluded that not only the frequency but also the amplitude of the carrier wave are changed by varying the modulation index and the system becomes unstable if the modulation index is increased near to unity.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 1996년도 추계학술대회논문집; 한국과학기술회관, 8 Nov. 1996
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• pp.288-294
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• 1996

In this paper, Chaotic motions of a curved pipe conveying oscillatory flow are theoretically investigated. The nonlinear partial differential equation of motion is derived by Newton's method. The transformed nonlinear ordinary differential equation is a type of Hill's equation, which have the parametric and external excitation. Bifurcation curves of chaotic motion of the piping systems are obtained by applying Melnikov's method. Poincare maps numerically demonstrate theoretical results and show transverse homoclinic orbit of the chaotic motion.

• 대한수학회지
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• 제59권2호
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• pp.279-298
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• 2022

In this paper, the existence and uniqueness for the global solution of neutral stochastic functional differential equation is investigated under the locally Lipschitz condition and the contractive condition. The implicit iterative methodology and the Lyapunov-Razumikhin theorem are used. The stability analysis for such equations is also applied. One numerical example is provided to illustrate the effectiveness of the theoretical results obtained.

• 한국환경과학회지
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• 제11권9호
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• pp.907-914
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• 2002

Various Eulerian-Lagrangian models for the one-dimensional longitudinal dispersion equation in nonuniform flow were studied comparatively. In the models studied, the transport equation was decoupled into two component parts by the operator-splitting approach; one part is governing advection and the other is governing dispersion. The advection equation has been solved by using the method of characteristics following fluid particles along the characteristic line and the results were interpolated onto an Eulerian grid on which the dispersion equation was solved by Crank-Nicholson type finite difference method. In the solution of the advection equation, Lagrange fifth, cubic spline, Hermite third and fifth interpolating polynomials were tested by numerical experiment and theoretical error analysis. Among these, Hermite interpolating polynomials are generally superior to Lagrange and cubic spline interpolating polynomials in reducing both dissipation and dispersion errors.