• Journal of Ocean Engineering and Technology
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• v.24 no.1
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• pp.34-38
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• 2010

An analytical solution procedure for the dynamic response of beams with variable properties is developed by using an asymptotic solution and the Green's function. This asymptotic closed form solution is derived for the transverse vibration of beams under the assumption of slowly varying properties, such as mass, cross-section, tension etc., along the beam length. However, this solution is still found to be very accurate even in the case of large variation, such as step change in cross-section, mass, and tension. Therefore, this derived asymptotic closed form solution and the Green's function can be easily applied to find dynamic responses for various kind of beam vibration problems.

• Journal of electromagnetic engineering and science
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• v.12 no.1
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• pp.45-54
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• 2012

When the cylindrical wave is incident on a plane dielectric interface from a denser medium to a rarer one, the asymptotic solution for the transmitted wave in the near region is different from the one in the far region. In this paper, we have derived a novel uniform asymptotic solution represented by using the parabolic cylinder function for the transmitted and scattered waves observed in the rarer medium when the cylindrical wave is incident on the plane dielectric interface from the denser medium. The validity of the uniform asymptotic solution has been confirmed by comparing with the reference solution calculated numerically. It has been clarified that the transition wave plays an important role to connect smoothly the asymptotic solution in the near region to the one in the far region through the transition region. We have shown the very interesting phenomenon that the lateral wave type transmitted wave is observed in the far and shallow region.

• Korean Journal of Mathematics
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• v.4 no.1
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• pp.39-43
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• 1996

Large-time asymptotic behavior of the solutions of interacting population reaction-diffusion systems are considered. Polynomial stability was proved.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.51 no.5
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• pp.1357-1368
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• 2014

This paper is concerned with a reaction-diffusion single species model with harvesting on n-dimensional isotropically growing domain. The model on growing domain is derived and the corresponding comparison principle is proved. The asymptotic behavior of the solution to the problem is obtained by using the method of upper and lower solutions. The results show that the growth of domain takes a positive effect on the asymptotic stability of positive steady state solution while it takes a negative effect on the asymptotic stability of the trivial solution, but the effect of the harvesting rate is opposite. The analytical findings are validated with the numerical simulations.

• Journal of the Korean Mathematical Society
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• v.48 no.2
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• pp.223-240
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• 2011

In this paper, the problem on periodic solutions of the bidirectional associative memory neural networks with both periodic coefficients and periodic time-varying delays is discussed. By using degree theory, inequality technique and Lyapunov functional, we establish the existence, uniqueness, and global asymptotic stability of a periodic solution. The obtained results of stability are less restrictive than previously known criteria, and the hypotheses for the boundedness and monotonicity on the activation functions are removed.

• The Proceeding of the Korean Institute of Electromagnetic Engineering and Science
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• v.2 no.4
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• pp.33-37
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• 1991

The problem of radiation from a flanged parallel-plate waveguide is re-examined. The technique of the Fourier transform is used to represent the radiation fields in the spectral domain. The simultaneous equations for the radiation field coefficients are formulated and solved to give an asymptotic seolution. The asymptotic series solution is compared with other results, thus clarifying the discrepancy among different numerical approaches.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.37-51
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• 2004

In this paper, we consider the asymptotic behavior of solutions of the forced nonlinear neutral difference equation $\Delta[x(n)-\sumpi(n)x(n-k_i)]+\sumqj(n)f(x(n-\iota_j))=r(n)$ with sign changing coefficients. Some sufficient conditions for every solution of (*) to tend to zero are established. The results extend and improve some known theorems in literature.

• Journal of the Korean Statistical Society
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• v.31 no.3
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• pp.329-342
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• 2002

We deal with asymptotic properties of Maximum Likelihood Estimator(MLE) for the parameters appearing in a Hilbert space-valued Stochastic Differential Equation(SDE) and a Stochastic Partial Differential Equation(SPDE). In paractice, the available data are only the finite dimensional projections to the solution of the equation. Using these data we obtain MLE and consider the asymptotic properties as the dimension of projections increases. In particular we explore a relationship between the conditions for the solution and asymptotic properties of MLE.

• The Pure and Applied Mathematics
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• v.20 no.4
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• pp.259-267
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• 2013

We present a high-order potential flow model for the motion of hydrodynamic unstable interfaces in cylindrical geometry. The asymptotic solutions of the bubbles in the gravity-induced instability and the shock-induced instability are obtained from the high-order model. We show that the model gives significant high-order corrections for the solution of the bubble.