• Communications for Statistical Applications and Methods
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• 제3권3호
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• pp.93-101
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• 1996

The unknown response function is usually approximated by a low order polynomial model. Such an approximation always accompanies bias due to model departure. The minimax Average MSE (AMSE) designs are suggested for estimating mean responses. A class of first order minimax AMSE designs is derived and a specific first order minimax AMSE design is selected from the class by optimizing the secondary criterion related to the power of the lack of fit test.

• 호남수학학술지
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• 제37권3호
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• pp.299-315
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• 2015

In this paper, we study the first-order system least-squares (FOSLS) spectral method for parabolic partial differential equations. There were lots of least-squares approaches to solve elliptic partial differential equations using finite element approximation. Also, some approaches using spectral methods have been studied in recent. In order to solve the parabolic partial differential equations in parallel, we consider a parallel numerical method based on a hybrid method of the frequency-domain method and first-order system least-squares method. First, we transform the parabolic problem in the space-time domain to the elliptic problems in the space-frequency domain. Second, we solve each elliptic problem in parallel for some frequencies using the first-order system least-squares method. And then we take the discrete inverse Fourier transforms in order to obtain the approximate solution in the space-time domain. We will introduce such a hybrid method and then present a numerical experiment.

• Journal of applied mathematics & informatics
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• 제27권3_4호
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• pp.463-473
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• 2009

A family of quasi-interpolatory wavelet system was introduced in [10], extending and unifing the biorthogonal Coiffman wavelet system. The corresponding refinable functions and wavelets have vanishing moment of a certain order (say, L), which is a key property for data representation and approximation. One of main advantages of this wavelet systems is that we can get optimal smoothness in the sense of smoothing factors in the scaling filters. In this paper, we first discuss the biorthogonality condition of the quisi-interpolatory wavelet system. Then, we study the properties of the scaling and wavelet filters, related to the polynomial reproduction and the vanishing moment respectively, which in fact determines the approximation orders of biorthogonal projections. In addition, we discuss the approximation orders of the wavelet projections.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제16권1호
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• pp.1-13
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• 2012

In this paper we present an a posteriori error estimator for the stabilized P1 nonconforming finite element method of the linear elasticity problem based on a nonsymmetric H(div)-conforming approximation of the stress tensor in the first-order Raviart-Thomas space. By combining the equilibrated residual method and the hypercircle method, it is shown that the error estimator gives a fully computable upper bound on the actual error. Numerical results are provided to confirm the theory and illustrate the effectiveness of our error estimator.

• 전자공학회논문지C
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• 제36C권7호
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• pp.1-9
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• 1999

본 논문에서는 칩 내부 회로 연결선의 모형으로 많이 사용되는 RC-class 회로에 대하여 시뮬레이션을 수행하지 않고 지연 시간을 계산할 수 있는 해석적 3차 근사 기법을 제시한다. 본 논문에서 제시하는 3차 근사 기법은 기존의 2차 근사 기법에 비해 크지 않은 수행 시간을 필요로 하면서도 보다 정확한 결과를 보장한다. 이 해석적 3차 근사 기법은 일반적인 q 차 AWE(Asymptotic Waveform Evaluation)기법의 계산 결과와 비교해 허용 가능한 수준의 오차를 보장하며, 계산 시간의 단축과 함께 수치적으로 안정된 값을 제공한다. 제안하는 기법의 첫 알고리즘은 3차의 근사를 위해 8개의 모멘트를 필요로 하며, 보다 정확한 지연 시간의 근사가 가능하다. 둘째 알고리즘은 3차의 근사를 위해 6개의 모멘트를 필요로 하며, 첫 알고리즘보다 정확도는 뒤지나 빠른 근사가 가능하다.

• Journal of applied mathematics & informatics
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• 제26권3_4호
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• pp.689-706
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• 2008

In this paper, a fifth order numerical method is presented for solving singularly perturbed two point boundary value problems with a boundary layer at one end point. The two point boundary value problem is transformed into general first order ordinary differential equation system. A discrete approximation of a fifth order compact difference scheme is presented for the first order system. An asymptotically equivalent first order equation of the original singularly perturbed two point boundary value problem is obtained from the theory of singular perturbations. It is used in the fifth order compact difference scheme to get a two term recurrence relation and is solved. Several linear and non-linear singular perturbation problems have been solved and the numerical results are presented to support the theory. It is observed that the present method approximates the exact solution very well.

• 한국음향학회지
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• 제25권5호
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• pp.229-238
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• 2006

본 논문에서는 수치 영역의 포물선 지배 방정식의 근사 차수와 수치 영역 경계의 비국소적 경계 조건의 근사 차수가 서로 다를 때 음파 해에 미치는 영향을 해석적으로 보였다. 우선 평면파 분석법을 이용해 비국소적 경계 조건을 반 무한 매질 영역으로 변환했다. 그리고 실제 수치 영역과 반 무한 매질 영역의 경계에서 해석적 반사 오차를 유도했다. 지배 방정식과 비국소적 경계 조건의 해석적 오차가 간단한 대수 식으로 표현 가능한 경우에 대해서는 대수적인 오차식을 유도하고 그 경향을 고찰했다. 지배 방정식이 일반적인 고차 포물선 방정식일 때는 대수적인 오차 식은 보다 복잡하게 표현되며 수치적 방법을 이용해 그 특성을 고찰했다. 최종적으로 지배 방정식의 차수에 따른 비국소적 경계 조건의 정밀도를 유도하고 해석적 반사 오차의 전반적인 특성에 대해 논의했다. 본 연구의 핵심 공헌은 포물선 방정식과 비국소적 경계 조건의 근사 차수가 다를 때 해석적 오차 추정 방법과 사용한계를 제시했다는데 있다.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2008년도 정기 학술대회
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• pp.72-77
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• 2008

Stability is a very important part which we must consider in structural design. In this paper, we take advantage of finite element method, and study about parametrical instability of star-dome structures, which is subjected to harmonically pulsating load. When calculating stiffness matrix, we consider elastic stiffness and geometrical stiffness simultaneously. In equation of motion, we represent displacements and accelerations by trigonometric series expansions, and then obtain Hill's infinite determinants. After first order approximation, we can get first and second order dynamic instability region finally.

• Bulletin of the Korean Chemical Society
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• 제34권1호
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• pp.243-245
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• 2013

Rate equations are exactly solved for the reversible consecutive reaction of the first-order and the time-dependence of concentrations is analytically determined for species in the reaction. With the assumption of pseudo first-order reaction, the calculation applies and determines the concentration of product accurately and explicitly as a function of time in the unimolecular decomposition of Lindemann and in the enzyme catalysis of Michaelis-Menten whose rate laws have been approximated in terms of reactant concentrations by the steady-state approximation.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제7권2호
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• pp.95-111
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• 2003

BDM mixed methods are obtained for a good approximation of velocity for flow equations. In this paper, we study an implementation issue of solving the algebraic system arising from the BDM mixed finite elements. First we discuss post-processing based on the use of Lagrange multipliers to enforce interelement continuity. Furthermore, we establish an equivalence between given mixed methods and projection finite element methods developed by Chen. Finally, we present the implementation of the first order BDM on rectangular grids and show it is as simple as solving the pressure equation.