• 대한수학회지
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• 제33권3호
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• pp.495-505
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• 1996

Let $\Omega$ be a bounded domain in $R^d, d \geq 1$, with smooth boundary $\partial\Omega$, and let $0 < T < \infty$ be given.

• Journal of applied mathematics & informatics
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• 제7권1호
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• pp.61-82
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• 2000

In this paper two so-called regularized Green's functions are introduced to derive the optimal maximum norm error estimates for the unknown function and the adjoint vector-valued function for mixed finite element methods of Laplacian operator. One contribution of the paper is a demonstration of how the boundedness of $L^1$-norm estimate for the second Green's function ${\lambda}_2$ and the optimal maximum norm error estimate for the adjoint vector-valued function are proved. These results are seemed to be to be new in the literature of the mixed finite element methods.

• Journal of Radiation Protection and Research
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• 제39권4호
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• pp.159-167
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• 2014

국내에서는 2012년 천연방사성핵종이 포함된 가공제품의 규제를 위해 생활주변방사선 안전관리법이 시행되었지만, 해당 가공제품 사용에 대한 인체 피폭선량을 평가할 수 있는 기초자료나 피폭선량 평가기술이 미비하다. 따라서 본 연구는 사용자 피폭선량을 정량적으로 평가하기 위한 방법을 제안하고, 방사선의 종류 및 에너지에 따른 피폭선량 특성의 확인을 목적으로 한다. 피폭선량 평가를 위해서 몬테칼로 방법을 사용한 Monte Carlo N-Particle Extended (MCNPX) 코드를 통해 International Commission on Radiological Protection (ICRP)의 기준팬텀이 전산모사 되었으며, 대표적 천연방사성핵종인 우라늄 계열에서 발생되는 알파선, 베타선, 감마선의 최소, 중간, 최대 에너지가 선원항으로 사용되었다. 연간 유효선량은 가공제품 사용시간 및 사용위치를 고려한 피폭시나리오를 기반으로 평가되었다. 짧은 비정의 알파선 및 베타선은 대부분의 선량을 피부에 전달한 반면, 감마선은 대부분의 장기에 유사한 선량을 전달하였다. 방사능이 $1Bq{\cdot}g^{-1}$ 인 돌침대에 포함된 천연방사성핵종의 함유율이 10%라고 가정하고 한국인 평균 수면시간인 7시간 50분간 돌침대를 사용하였을 때 최대 연간 유효선량은 알파선, 베타선, 감마선에 대해서 각각 0.0222, 0.0836, $0.0101mSv{\cdot}y^{-1}$로 평가되었다.

• 대한수학회지
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• 제49권5호
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• pp.927-945
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• 2012

An approximation of singular source terms in elliptic problems is developed and analyzed. Under certain assumptions on the curve where the singular source is defined, the second order convergence in the maximum norm can be proved. Numerical results present its better performance compared to previously developed regularization techniques.

• 한국인터넷방송통신학회논문지
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• 제14권6호
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• pp.55-61
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• 2014

본 논문은 CMA 적응등화기에서 최소 disturbance 기법을 적용하여 진폭과 위상의 동시 보상이 가능한 ECMA (Enchanced CMA) 알고리즘의 성능에 관한 것이다. ECMA는 적응등화기 탭 계수의 변화량을 squared euclidean norm 관점에서 최소화하는 최소 disturbance 기법과 decision directed mode에 의한 gradient noise amplification 문제와 안정도 및 roburstness 성능을 알고리즘 연산량의 큰 증가없이 개선할 수 있고, 수신신호에서 진폭과 위상의 동시 보상이 가능하도록 새로운 비용함수를 제안하였다. 논문에서는 ECMA 알고리즘의 성능을 MCMA와 비교하기 위하여 컴퓨터 시뮬레이션을 수행하였다. 이를 위하여 수신측에서의 등화기 출력신호인 복원된 신호 성상도, 수렴 성능을 나타내는 성능지수인 잔류 isi 및 MD (Maximum Distortion), MSE 특성곡선과 채널과 등화기의 종합 주파수 특성을 성능 비교 지수로 사용하였다. 시뮬레이션 결과 ECMA가 복원성상도에서 진폭과 위상보상 능력 및 적응등화를 위한 수렴시간에서 MCMA보다 우월함을 알 수 있었다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제5권2호
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• pp.25-37
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• 2001

We consider the finite element method applied to nonlinear Sobolev equation with smooth data and demonstrate for arbitrary order ($k{\geq}2$) finite element spaces the optimal rate of convergence in $L_{\infty}\;W^{1,{\infty}}({\Omega})$ and $L_{\infty}(L_{\infty}({\Omega}))$ (quasi-optimal for k = 1). In other words, the nonlinear Sobolev equation can be approximated equally well as its linear counterpart. Furthermore, we also obtain superconvergence results in $L_{\infty}(W^{1,{\infty}}({\Omega}))$ for the difference between the approximate solution and the generalized elliptic projection of the exact solution.

• International journal of advanced smart convergence
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• 제7권4호
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• pp.92-100
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• 2018

This paper presents a link adaptation scheme for adaptive full duplex (AFD) systems. The signal modulation levels and communication link patterns are adaptively selected according to the changing channel conditions. The link pattern selection process consists of two successive steps such as a transmit-receive antenna pair selection based on maximum sum rate or minimum maximum symbol error rate, and an adaptive modulation based on maximum minimum norm. In AFD systems, the antennas of both nodes are jointly determined with modulation levels depending on the channel conditions. An adaptive algorithm with relatively low complexity is also proposed to select the link parameters. Simulation results show that the proposed AFD system offers significant bit error rate (BER) performance improvement compared with conventional full duplex systems with perfect or imperfect self-interference cancellation under the same fixed sum rate.

• 대한수학회논문집
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• 제34권3호
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• pp.1015-1027
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• 2019

A class of systems of singularly perturbed convection diffusion type equations with integral boundary conditions is considered. A numerical method based on a finite difference scheme on a Shishkin mesh is presented. The suggested method is of almost first order convergence. An error estimate is derived in the discrete maximum norm. Numerical examples are presented to validate the theoretical estimates.

• Journal of applied mathematics & informatics
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• 제39권3_4호
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• pp.419-435
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• 2021

This paper deals with numerical treatment of singularly perturbed differential equations involving small delays. The highest order derivative in the equation is multiplied by a perturbation parameter 𝜀 taking arbitrary values in the interval (0, 1]. For small 𝜀, the problem involves a boundary layer of width O(𝜀), where the solution changes by a finite value, while its derivative grows unboundedly as 𝜀 tends to zero. The considered problem contains delay on the convection and reaction terms. The terms with the delays are approximated using Taylor series approximations resulting to asymptotically equivalent singularly perturbed BVPs. Inducing exponential fitting factor for the term containing the singular perturbation parameter and using central finite difference for the derivative terms, numerical scheme is developed. The stability and uniform convergence of difference schemes are studied. Using a priori estimates we show the convergence of the scheme in maximum norm. The scheme converges with second order of convergence for the case 𝜀 = O(N^-1) and for the case 𝜀 ≪ N^-1, the scheme converge uniformly with first order of convergence, where N is number of mesh intervals in the domain discretization. We compare the accuracy of the developed scheme with the results in the literature. It is found that the proposed scheme gives accurate result than the one in the literatures.

• Journal of applied mathematics & informatics
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• 제36권1_2호
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• pp.135-154
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• 2018

In this paper, an almost second order overlapping Schwarz method for singularly perturbed third order convection-diffusion type problem is constructed. The method splits the original domain into two overlapping subdomains. A hybrid difference scheme is proposed in which on the boundary layer region we use the combination of classical finite difference scheme and central finite difference scheme on a uniform mesh while on the non-layer region we use the midpoint difference scheme on a uniform mesh. It is shown that the numerical approximations which converge in the maximum norm to the exact solution. We proved that, when appropriate subdomains are used, the method produces convergence of second order. Furthermore, it is shown that, two iterations are sufficient to achieve the expected accuracy. Numerical examples are presented to support the theoretical results. The main advantages of this method used with the proposed scheme are it reduce iteration counts very much and easily identifies in which iteration the Schwarz iterate terminates.