• 대한수학회보
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• 제51권1호
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• pp.139-156
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• 2014

In this paper, we investigate the error estimates of a quadratic elliptic control problem with pointwise control constraints. The state and the co-state variables are approximated by the order k = 1 Raviart-Thomas mixed finite element and the control variable is discretized by piecewise linear but discontinuous functions. Approximations of order $h^{\frac{3}{2}}$ in the $L^2$-norm and order h in the $L^{\infty}$-norm for the control variable are proved.

• 대한수학회지
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• 제51권3호
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• pp.545-565
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• 2014

In this paper we derive a priori $L^{\infty}(L^2)$ error estimates for expanded mixed finite element formulations of semilinear Sobolev equations. This formulation expands the standard mixed formulation in the sense that three variables, the scalar unknown, the gradient and the flux are explicitly treated. Based on this method we construct finite element semidiscrete approximations and fully discrete approximations of the semilinear Sobolev equations. We prove the existence of semidiscrete approximations of u, $-{\nabla}u$ and $-{\nabla}u-{\nabla}u_t$ and obtain the optimal order error estimates in the $L^{\infty}(L^2)$ norm. And also we construct the fully discrete approximations and analyze the optimal convergence of the approximations in ${\ell}^{\infty}(L^2)$ norm. Finally we also provide the computational results.

• 대한수학회지
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• 제55권2호
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• pp.471-506
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• 2018

In this article, some projection methods (or fractional-step methods) are proposed and analyzed for the micropolar Navier-Stokes equations (MNSE). These methods allow us to decouple the MNSE system into two sub-problems at each timestep, one is the linear and angular velocities system, the other is the pressure system. Both first-order and second-order projection methods are considered. For the classical first-order projection scheme, the stability and error estimates for the linear and angular velocities and the pressure are established rigorously. In addition, a modified first-order projection scheme which leads to some improved error estimates is also proposed and analyzed. We also present the second-order projection method which is unconditionally stable. Ample numerical experiments are performed to confirm the theoretical predictions and demonstrate the efficiency of the methods.

• 한국산학기술학회논문지
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• 제13권8호
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• pp.3660-3665
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• 2012

블라인드 등화에서 등화 초기에는 눈모형을 빠르게 여는 것이 필요하고, 이후에는 등화기 출력 신호의 오차 레벨을 낮추는 것이 중요하다. 본 논문에서는 특별하게 정해지는 신호점을 사용한 거친 오차 추정과 원 신호점을 사용한 미세 오차 추정을 동시에 산출하고, 두 오차 추정을 활용하는 방식을 제안한다. 두 오차 추정은 각각 눈모형이 닫힌 상태에서 눈모형을 빠르게 열거나, 눈모형이 열리기 시작한 이후 정상상태에서 오차 레벨을 낮추는데 효과적이다. 등화기의 수렴 상태에 따라 두 오차 추정 중 하나를 선택하거나, 두 오차 추정의 상대적 신뢰도에 따라 두 오차를 가중 결합하여 새로운 오차를 산출하는 두 블라인드 등화 알고리즘을 제안하고 그 성능을 비교한다.

• 산업기술연구
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• 제9권
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• pp.67-77
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• 1989

This study is concerned with the accuracy, the pattern of error with which subjects can interpolate the location of a pointer or a target between two graduation markers with various size on CRT display. Stimuli were graphic images on CRT with a linear, end-marked, ungraduated scales having a target for t base-line sizes. The location of a target is estimated in units over the range 1-99. Smallest error of estimates was at the near ends and middle of the base-line. The median error was less 2 units, modal error was 1, and most error(;99.6%) was within 10. Subjects had a more tendency to overestimate than to underestimate at the left-part of base-line in all siges, and an opposite tendency at the right-part. A proper size to minimize the interpolation error exists such that size 500. It is suggested that interpolation of fifths and even tenths will give a reguired accuracy for certain situations, and relative location and base-line size has a relevant attribute to interpolate.

• 전자공학회논문지
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• 제50권7호
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• pp.52-58
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• 2013

이 논문에서는 블라인드 등화에서 등화기 출력 신호를 조사하여 신호 상태에 적합한 오차 신호를 동적으로 발생시키는 방식의 적응 알고리즘을 제안한다. 제안 방식에서는 단일 모듈러스와 다중 모듈러스를 사용하여 각각 등화 초기와 정상상태에서 효과적인 오차 신호를 추정하고, 두 추정 오차로부터 새로운 오차 신호를 생성한다. 이때 두 오차 신호를 가중 결합하여 새로운 오차 신호를 발생시키고 이를 이용하여 등화기를 갱신하는 1-등화기 구조와, 두 오차 신호의 가중치에 따라 두 등화기를 각각 갱신하는 2-등화기 구조를 구현하고 성능을 비교하였다. 제안 방식에서는 초기 수렴 이전과 이후에서 각각 적합한 오차 신호를 생성함에 따라 등화기 갱신이 효과적으로 이루어짐을 모의실험을 통하여 확인하였다.

• 한국정밀공학회지
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• 제15권5호
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• pp.120-127
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• 1998

Differential inequalities occurring in problems of obstacle contact problems are recast into variational inequalities and analyzed by finite element methods. A new a posteriori error estimator, which is essential in adaptive finite element method, is introduced to capture the errors in finite element approximations of these variational inequalities. In order to construct a posteriori error estimates, saddle point problems are introduced using Lagrange parameters and upper bounds are provided. The global upper bound is localized by a special mixed formulation, which leads to upper bounds of the element errors. A numerical experiment is performed on an obstacle contact problem to check the effectivity index both in a local and a global sense.

• 품질경영학회지
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• 제35권1호
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• pp.10-19
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• 2007

ANOVA is widely, used for measurement system analysis. It assumes that the measurement error is normally distributed, which nay not be seen in some industrial cases. In this study the estimates of the measurement system variability and PTR (precision-to-tolerance ratio) are obtained by using weighted standard deviation for the case where the measurement error is non-normally distributed. The Standard Bootstrap method is used foy estimating confidence intervals of measurement system variability and PTR. The point and confidence interval estimates for the cases with normally distributed measurement error are compared to those with non-normally distributed measurement errors through computer simulation.

• Communications for Statistical Applications and Methods
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• 제13권3호
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• pp.745-754
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• 2006

It has been shown that LAD estimates are more efficient than LS estimates when the error distribution is double exponential in AR(1) model. In order to explore the performance of LAD estimates one can use bootstrap approaches. In this paper we consider the efficiencies of bootstrap methods when we apply LAD estimates with highly variable data. Monte Carlo simulation results are given for comparing generalized bootstrap, stationary bootstrap and threshold bootstrap methods.

• Journal of applied mathematics & informatics
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• 제4권2호
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• pp.341-378
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• 1997

We consider three classes of numerical methods for solv-ing the semi-explicit differential-algebraic equations of index 1 and higher. These methods use implicit multistep fixed stepsize methods and several iterative processes including simple iteration, full a2nd modified Newton iteration. For these methods we prove convergence theorems and derive error estimates. We consider different ways of choosing initial approximations for these iterative methods and in-vestigate their efficiency in theory and practice.