• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.1-28
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• 2004

We first apply a first order splitting to a semilinear reaction-diffusion equation and then discretize the resulting system by an $H^1$-Galerkin mixed finite element method in space. This semidiscrete method yields a system of differential algebraic equations (DAEs) of index one. A priori error estimates for semidiscrete scheme are derived for both differ-ential as well as algebraic components. For fully discretization, an implicit Runge-Kutta (IRK) methods is applied to the temporal direction and the error estimates are discussed for both components. Finally, we conclude the paper with a numerical example.

• Bulletin of the Korean Mathematical Society
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• v.57 no.1
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• pp.219-244
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• 2020

In this paper, we approximate the solution of the coupled nonlinear Schrödinger equations by using a fully discrete finite element scheme based on the standard Galerkin method in space and implicit midpoint discretization in time. The proposed scheme guarantees the conservation of the total mass and the energy. First, a priori error estimates for the fully discrete Galerkin method is derived. Second, the existence of the approximated solution is proved by virtue of the Brouwer fixed point theorem. Moreover, the uniqueness of the solution is shown. Finally, convergence orders of the fully discrete Crank-Nicolson scheme are discussed. The end of the paper is devoted to some numerical experiments.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.1267-1271
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• 2003

This paper proposes an indirect adaptive fuzzy controller for general SISO nonlinear systems. No a priori information on bounding constants of uncertainties including reconstruction errors and optimal fuzzy parameters is needed. The control law and the update laws for fuzzy rule structure and estimates of fuzzy parameters and bounding constants are determined so that the Lyapunov stability of the whole closed loop system is guaranteed. The computer simulation results for an inverted pendulum system show the performance of the proposed robust adaptive fuzzy controller.

• Proceedings of the KIEE Conference
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• 2003.07d
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• pp.2441-2443
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• 2003

This paper proposes an indirect adaptive fuzzy controller for general SISO nonlinear systems. No a priori information on bounding constants of uncertainties including reconstruction errors and optimal fuzzy parameters is needed. The control law and the update laws for fuzzy rule structure and estimates of fuzzy parameters and bounding constants are determined so that the Lyapunov stability of the whole closed loop system is guaranteed. The computer simulation results for an inverted pendulum system show the performance of the proposed robust adaptive fuzzy controller.

• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.1013-1024
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• 2007

In this paper we consider the uniform decay for the wave equation of Carrier model subject to memory condition at the boundary. We prove that if the kernel of the memory decays exponentially or polynomially, then the solutions for the problems have same decay rates.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.18 no.4
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• pp.337-350
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• 2014

In this paper, we consider discontinuous Galerkin finite element methods with interior penalty term to approximate the solution of nonlinear parabolic problems with mixed boundary conditions. We construct the finite element spaces of the piecewise polynomials on which we define fully discrete discontinuous Galerkin approximations using the Crank-Nicolson method. To analyze the error estimates, we construct an appropriate projection which allows us to obtain the optimal order of a priori ${\ell}^{\infty}(L^2)$ error estimates of discontinuous Galerkin approximations in both spatial and temporal directions.

• Korean Management Science Review
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• v.11 no.2
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• pp.1-27
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• 1994

A reliability data processing MPRDP (Multi-Purpose Reliability Data Processor) has been developed in FORTRAN language since Jan. 1992 at KAERI (Korean Atomic Energy Research Institute). The purpose of the research is to construct a reliability database(plant-specific as well as generic) by processing various kinds of reliability data in most objective and systematic fashion. To account for generic estimates in various compendia as well as generic plants' operating experience, we developed a 'three-stage' Bayesian procedure[1] by logically combining the 'two-stage' procedure[2] and the idea for processing generic estimates[3]. The first stage manipulates generic plant data to determine a set of estimates for generic parameters,e.g. the mean and the error factor, which accordingly defines a generic failure rate distribution. Then the second stage combines these estimates with the other ones proposed by various generic compendia (we call these generic book type data). This stage adopts another Bayesian procedure to determine the final generic failure rate distribution which is to be used as a priori distribution in the third stage. Then the third stage updates the generic distribution by plant-specific data resulting in a posterior failure rate distribution. Both running failure and demand failure data can be handled in this code. In accordance with the growing needs for a consistent and well-structured reliability database, we constructed a generic reliability database by the MPRDP code[4]. About 30 generic data sources were reviewed and available data were collected and screened from them. We processed reliability data for about 100 safety related components frequently modeled in PSA. The underlying distribution for the failure rate was assumed to be lognormal or gamma, according to the PSA convention. The dependencies among the generic sources were not considered at this time. This problem will be approached in further study.

• Korean Journal of Remote Sensing
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• v.33 no.4
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• pp.445-454
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• 2017

The performance of spatial downscaling models depends on the quality of input coarse scale products. Thus, the impact of intrinsic errors contained in coarse scale satellite products on predictive performance should be properly assessed in parallel with the development of advanced downscaling models. Such an assessment is the main objective of this paper. Based on a synthetic satellite precipitation product at a coarse scale generated from rain gauge data, two synthetic precipitation products with different amounts of error were generated and used as inputs for spatial downscaling. Geographically weighted regression, which typically has very high explanatory power, was selected as the trend component estimation model, and area-to-point kriging was applied for residual correction in the spatial downscaling experiment. When errors in the coarse scale product were greater, the trend component estimates were much more susceptible to errors. But residual correction could reduce the impact of the erroneous trend component estimates, which improved the predictive performance. However, residual correction could not improve predictive performance significantly when substantial errors were contained in the input coarse scale data. Therefore, the development of advanced spatial downscaling models should be focused on correction of intrinsic errors in the coarse scale satellite product if a priori error information could be available, rather than on the application of advanced regression models with high explanatory power.

• Journal of Institute of Control, Robotics and Systems
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• v.6 no.11
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• pp.963-967
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• 2000

This paper deals with a sliding mode control with uncertainty adaptation for the robust stabilization of input-delay systems with unknown uncertainties. A sliding surface including a state predictor is employed to compensate for the effect of the input delay. The proposed method does not need a priori knowledge of upper bounds on the norm of uncertainties, but estimates those upper bounds by adaptation laws based on the sliding surface. Then, a robust control law with the uncertainty adaptation is derived to ensure the existence of the sliding mode. A numerical example is given to illustrate the design procedure.

• Journal of the Korean Mathematical Society
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• v.59 no.1
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• pp.13-33
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• 2022

The quaternionic Calabi conjecture was introduced by Alesker-Verbitsky, analogous to the Kähler case which was raised by Calabi. On a compact connected hypercomplex manifold, when there exists a flat hyperKähler metric which is compatible with the underlying hypercomplex structure, we will consider the parabolic quaternionic Monge-Ampère equation. Our goal is to prove the long time existence and C^∞ convergence for normalized solutions as t → ∞. As a consequence, we show that the limit function is exactly the solution of quaternionic Monge-Ampère equation, this gives a parabolic proof for the quaternionic Calabi conjecture in this special setting.