• 대한수학회지
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• 제32권1호
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• pp.115-139
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• 1995

Our purpose in this paper is to prove a new version of the nonlinear Chernoff theorem and to discuss the equivalence between resolvent consistency and converge nce for nonlinear algorithms acting on different Banach spaces. Such results are useful in the numerical treatment of partial differential equations via difference schemes.

• 대한수학회보
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• 제37권3호
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• pp.451-459
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• 2000

In this paper, we observe the relation between the attainability of contingent claims and solutions of associated difference-differential equations. And we find the lower bound estimate of fair price using the minimax statistical approach.

• 한국전산구조공학회논문집
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• 제31권6호
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• pp.331-337
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• 2018

본 논문은 MLS(moving least squares) 차분법의 1차 미분 근사함수를 바탕으로 시간에 따른 수치해석이 가능한 해석기법을 제시한다. 오직 1차 미분 근사함수로만 지배방정식을 이산화했으며, 근사함수를 조립하는 형태로 전체 시스템 방정식을 구성하여 차분법으로 이산화된 운동방정식이 유한요소법(finite element method)과 유사한 모습을 갖게 되었다. 운동방정식을 시간적분하기 위해서 중앙차분법(central difference method)을 사용하였다. 유한요소 알고리즘을 통해서 MLS 차분법과 유한요소법의 고유진동 해석을 수행하였으며, 두 해석결과를 비교하였다. 또한, 동적해석 결과를 기존의 2차 미분 근사함수를 활용한 해석결과와 함께 도시함으로써 제안된 수치기법의 정확성을 검증하였다. 1차 미분 근사함수를 조립하는 과정에서 해석결과의 떨림현상이 억제되었으며 상대적으로 균일한 응력분포를 구할 수 있었다.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제13권4호
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• pp.281-294
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• 2006

Many partial differential equations defined on a rectangular domain can be solved numerically by using a domain decomposition method. The most commonly used decompositions are the domain being decomposed in stripwise and rectangular way. Theories for non-overlapping domain decomposition(in which two adjacent subdomains share an interface) were often focused on the stripwise decomposition and claimed that extensions could be made to the rectangular decomposition without further discussions. In this paper we focus on the comparisons of the two ways of decompositions. We consider the unconditionally stable scheme, the MIP algorithm, for solving parabolic partial differential equations. The SOR iterative method is used in the MIP algorithm. Even though the theories are the same but the performances are different. We found out that the stripwise decomposition has better performance.

• Journal of the Optical Society of Korea
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• 제20권2호
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• pp.223-227
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• 2016

The impact of optical receiver configuration on in-band crosstalk-induced penalty has been investigated in both theoretical and experimental analyses, for differential phase-shift keying (DPSK) and differential quadrature phase-shift keying (DQPSK) signals. Previously it has been shown that DPSK signals are ~6 dB more tolerant to in-band crosstalk than on-off keying (OOK) signals. However, we find that the tolerance difference between the two signals is reduced to ~3 dB when the decision threshold of the receiver is optimized to minimize the bit-error rate for each signal. Then we derive simple equations for the in-band crosstalk-induced penalty in DPSK and DQPSK signals with two different optical receiver configurations: balanced and single-ended direct-detection receivers. We confirm that the penalties obtained from our simple equations agree well with the measured results.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2004년도 하계학술대회 논문집 D
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• pp.2438-2440
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• 2004

This study is concerned with development of 3-Dimensional simulator of a biped robot that has a prismatic balancing weight or a revolute balancing weight. The dynamic stability equation of a biped robot which have a prismatic balancing weight is conditional linear but a walking robot's stability equation with a revolute balancing weight is nonlinear. To get a stable gait of a biped robot, stabilization equations with ZMP (Zero Moment Point) are modeled as non-homogeneous second order differential equations for each balancing weight type. A trajectory of balancing weight can be directly calculated with the FDM (Finite Difference Method) solution of the linearized differential equation. In this paper, the 3-Dimensional graphic simulator is programmed to get and calculate the desired ZMP and the actual ZMP. Walking of 4 steps was simulated and verified. This balancing system will be applied to a biped humanoid robot, which consist Begs and upper body, at future work.

• 한국컴퓨터산업학회논문지
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• 제7권1호
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• pp.33-38
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• 2006

케이블 뿐 아니라 현수교의 운동은 비선형 미분방정식에 지배된다. 미분방정식은 비선형성 때문에 진폭이 큰 해가 존재한다. 유한차분법을 이용하여 비선형 방정식의 주기근을 구한다. 일노드의 힘과 힘의 약간 변형된 형태를 이용하여 방정식의 해를 구한다.

• Structural Engineering and Mechanics
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• 제4권6호
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• pp.589-600
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• 1996

An explicit 4th order time integration scheme for solving the convection-diffusion equation is discussed in this paper. A system of ordinary differential equations are derived first by discretizing the spatial derivatives of the relevant PDE using the finite difference method. The integration of the ODEs is then carried out using a 4th order scheme and a self-adaptive technique based on the spatial grid spacing. For a non-uniform spatial grid, different time step sizes are used for the integration of the ODEs defined at different spatial points, which improves the computational efficiency significantly. A numerical example is also discussed in the paper to demonstrate the implementation and effectiveness of the method.

• Food Science and Biotechnology
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• 제17권6호
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• pp.1352-1356
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• 2008

Bootstrap method, a computer-intensive statistical technique to estimate the distribution of a statistic was applied to deal with uncertainty and variability of the experimental data in stochastic prediction modeling of microbial growth on a chill-stored food. Three different bootstrapping methods for the curve-fitting to the microbial count data were compared in determining the parameters of Baranyi and Roberts growth model: nonlinear regression to static version function with resampling residuals onto all the experimental microbial count data; static version regression onto mean counts at sampling times; dynamic version fitting of differential equations onto the bootstrapped mean counts. All the methods outputted almost same mean values of the parameters with difference in their distribution. Parameter search according to the dynamic form of differential equations resulted in the largest distribution of the model parameters but produced the confidence interval of the predicted microbial count close to those of nonlinear regression of static equation.

• Journal of applied mathematics & informatics
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• 제27권5_6호
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• pp.1001-1015
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• 2009

In this paper, two hybrid difference schemes on the Shishkin mesh are constructed for solving a weakly coupled system of two singularly perturbed convection-diffusion second order ordinary differential equations with a small parameter multiplying the highest derivative. We prove that the schemes are almost second order convergence in the supremum norm independent of the diffusion parameter. Error bounds for the numerical solution and its derivative are established. Numerical results are provided to illustrate the theoretical results.