• Journal of electromagnetic engineering and science
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• 제12권1호
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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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• 제21권3호
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• pp.293-304
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• 2013

In this paper we analyze an error estimator for the lowest-order triangular Raviart-Thomas mixed finite element which is based on solution of local problems for the error. This estimator was proposed in [Alonso, Error estimators for a mixed method, Numer. Math. 74 (1996), 385{395] and has a similar concept to that of Bank and Weiser. We show that it is asymptotically exact for the Poisson equation if the underlying triangulations are uniform and the exact solution is regular enough.

• 대한화학회지
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• 제18권5호
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• pp.307-319
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• 1974

2-전향점 문제의 Uniform WKB 파동함수의 정밀도를 대응하는 수치해와 비교하고 검토한 결과 Uniform WKB 파동함수가 대단히 정밀하다는 것을 발견하였다. 그러한 파동함수의 응용의 예로서 model계에 대한 Franck-Condon 인자들을 계산하였으며 계산된 인자들의 정밀도도 역시 매우 높다는 것을 보였다. Uniform WKB파동함수를 이용하여 Franck-Condon 인자의 점근치를 검토하였으며 전환진동수에 대한 Mulliken 의 조건, $E'_{n'J'}-U'_{eff}(r_s)=E"_{n"J"}-U"_{eff}(r_s),$ 을 유도하였다.

• Kyungpook Mathematical Journal
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• 제45권3호
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• pp.433-443
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• 2005

In 1994, Lim-Xu asked whether the Maluta's constant D(X) < 1 implies the fixed point property for asymptotically nonexpansive mappings and gave a partial solution for this question under an additional assumption for T, i.e., weakly asymptotic regularity of T. In this paper, we shall prove that the result due to Lim-Xu is also satisfied for more general non-Lipschitzian mappings in reflexive Banach spaces with weak uniform normal structure. Some applications of this result are also added.

• 충청수학회지
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• 제24권3호
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• pp.561-568
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• 2011

We investigate the stability property and existence of almost periodic solutions of discrete Volterra equations with unbounded delay.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제12권3호
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• pp.169-178
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• 2005

In this paper we study the existence and local asymptotic limit of the topological Chern-Simons vortices of the CP(1) model in $\mathbb{R}^2$. After reducing to semilinear elliptic partial differential equations, we show the existence of topological solutions using iteration and variational arguments & prove that there is a sequence of topological solutions which converges locally uniformly to a constant as the Chern­Simons coupling constant goes to zero and the convergence is exponentially fast.

• Journal of applied mathematics & informatics
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• 제29권5_6호
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• pp.1081-1096
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• 2011

In this paper, a steady axisymmetric MHD flow of two dimensional incompressible fluids is studied under the influence of a uniform transverse magnetic field. The governing equations are reduced to nonlinear boundary value problem by applying the integribility conditions. Optimal Homotopy Asymptotic Method (OHAM) is applied to obtain solution of reduced fourth order nonlinear boundary value problem. For comparison, the same problem is also solved by Variational Iteration Method (VIM).

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제24권4호
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• pp.201-209
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• 2017

We prove convergence properties of the global solutions to the cooperative cross-diffusion system with the intra-specific cooperative pressures dominated by the inter-specific competition pressures and the inter-specific cooperative pressures dominated by intra-specific competition pressures. Under these conditions the $W^1_2-bound$ and the time global existence of the solution for the cooperative cross-diffusion system have been obtained in [10]. In the present paper the convergence of the global solution is established for the cooperative cross-diffusion system with large diffusion coefficients.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1993년도 봄 학술발표회논문집
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• pp.19-26
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• 1993

The p-version crack model based on integrals of Legendre polynomial and virtual crack extension method is proposed with its potential for application to stress intensity factor computations in linear elastic fracture mechanics. The main advantage of this model is that the data preparation effort is minimal because only a small number of elements are used and the high accuracy and the rapid rate of convergence can be achieved in the vicinity of crack tip. There are two important findings from this study. Firstly, the limit value, the strain energy of the exact solution can be estimated with successive three p-version approximations by ascertaining the approximations is entered the asymptotic range. Secondly, the rate of convergence of p-version model is almost twice that of h-version model on the basis of uniform or quasiuniform mesh refinement for the cracked panel problem subjected tension.

• 전산구조공학
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• 제6권4호
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• pp.57-66
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• 1993

적분형 르장드르 다항식과 가상균열확장법을 사용한 p-version균열모델이 선형 탄성파괴력학에서 응력확대계수를 산정할 수 있도록 제안되었다. 이 모델의 큰 장점은 소수의 요소를 사용하기 때문에 입력재료를 최소화 할 수 있고 균열선단 부근에서 높은 정확도와 빠른 수검율을 얻을 수 있다는 것이다. 이 연구를 통해 얻어진 두 가지 결론은 다음과 같다. 첫째, 변형에너지의 정해인 극한치가 수검구간에 있는 연속된 3개의 p-version 유한요소 결과로 부터 확정 할 수 있다는 것이다. 둘째, 인장력을 받는 균열판 해석에서 p-version의 수검율은 균등 또는 유사균등 요소분할에 근거를 둔 h-version모델에 비해 거의 2배 가량 빠름을 알 수 있다.