• Journal of the Korean Mathematical Society
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• v.33 no.3
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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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• v.7 no.1
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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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• v.39 no.4
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• pp.159-167
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• 2014

In Korea, July 2012, the law as called 'Act on Safety Control of Radioactive Rays Around Living Environment' was implemented to control the consumer product containing Naturally Occurring Radioactive Material (NORM), but, there are no appropriate database and effective dose calculation system. The aim of this study was to develop evaluation technique of the exposure dose with the use of the consumer products containing NORM and to understand the characteristics of the exposed dose according to the radiation type and energy. For the evaluate of exposure dose, the ICRP reference phantom was simulated by the MCNPX code based on Monte Carlo method, and the minimum, medium, maximum energy of alphas, betas, gammas from the representative NORM of Uranium decay series were used as the source term in the simulation. The annual effective doses were calculated by the exposure scenario of the consumer product usage time and position. Short range of the alpha and beta rays are mostly delivered the dose to the skin. On the other hand, the gamma rays mostly delivered the similar dose to all of the organs. The results of the annual effective dose with $1Bq{\cdot}g^{-1}$ radioactive stone-bed and 10% radioactive concentration were employed with the usage time of 7 hours 50 minute per day, the maximum annual effective dose of alphas, betas, gammas were calculated 0.0222, 0.0836, $0.0101mSv{\cdot}y^{-1}$, respectively.

• Journal of the Korean Mathematical Society
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• v.49 no.5
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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.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.14 no.6
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• pp.55-61
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• 2014

This paper related with the ECMA (Enchanced CMA) algorithm performance which is possible to simultaneously compensation of the amplitude and phase by appling the minimum disturbance techniques in the CMA adatpve equalizer. The ECMA can improving the gradient noise amplification problem, stability and roburstness performance by the minimum disturbance technique that is the minimization of the equalizer tap weight variation in the point of squared euclidiean norm and the decision directed mode, and then the now cost function were proposed in order to simultaneouly compensation of amplitude and phase of the received signal with the minimum increment of computational operations. The performance of ECMA algorithm was compared to present MCMA by the computer simulation. For proving the performance, the recovered signal constellation that is the output of equalizer output signal and the residual isi and Maximum Distortion charateristic and MSE learning curve that are presents the convergence performance in the equalizer and the overall frequency transfer function of channel and equalizer were used. As a result of computer simulation, the ECMA has more better compensation capability of amplitude and phase in the recovered constellation, and the convergence time of adaptive equalization has improved compared to the MCMA.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.5 no.2
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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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• v.7 no.4
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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.

• Communications of the Korean Mathematical Society
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• v.34 no.3
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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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• v.39 no.3_4
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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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• v.36 no.1_2
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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.