• Bulletin of the Korean Mathematical Society
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• v.47 no.6
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• pp.1225-1234
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• 2010

Numerical solutions for the fractional differential dispersion equations with nonlinear forcing terms are considered. The backward Euler finite difference scheme is applied in order to obtain numerical solutions for the equation. Existence and stability of the approximate solutions are carried out by using the right shifted Grunwald formula for the fractional derivative term in the spatial direction. Error estimate of order $O({\Delta}x+{\Delta}t)$ is obtained in the discrete $L_2$ norm. The method is applied to a linear fractional dispersion equations in order to see the theoretical order of convergence. Numerical results for a nonlinear problem show that the numerical solution approach the solution of classical diffusion equation as fractional order approaches 2.

• Journal of the Korean Society for Precision Engineering
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• v.15 no.4
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• pp.134-140
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• 1998

The authors have shown that the performance of discrete-time observer-based monitoring systems can be represented by the performance index k$_2$(P) (condition number of the eigensystem P of the observer matrix in terms of L$_2$ norm). The observers with the minimized performance index can be defined as robust observers in the sense that the observer performance can be guaranteed in harsh environments. In this paper, based on the performance index, a design methodology for the robust discrete-time observer is developed. Similar to the continuous-time case, the methodology determines the structure and eigenvalues of the observer matrix simultaneously. A complete design procedure is given for single-output case and is illustrated with a spindle-driver example. The simulation results demonstrate the improved performance compared with a traditional pole-placement observer technique.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.24 no.2
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• pp.143-159
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• 2020

We propose a consistent numerical method for elliptic interface problems with nonhomogeneous jumps. We modify the discontinuous bubble immersed finite element method (DB-IFEM) introduced in (Chang et al. 2011), by adding a consistency term to the bilinear form. We prove optimal error estimates in L² and energy like norm for this new scheme. One of the important technique in this proof is the Bramble-Hilbert type of interpolation error estimate for discontinuous functions. We believe this is a first time to deal with interpolation error estimate for discontinuous functions. Numerical examples with various interfaces are provided. We observe optimal convergence rates for all the examples, while the performance of early DB-IFEM deteriorates for some examples. Thus, the modification of the bilinear form is meaningful to enhance the performance.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.32 no.2
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• pp.43-49
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• 1983

In this study, model simplification problem using singular perturbation technique is considered. The correctness and errors of simplified model which is obtained by the use of this technique, depends upon the order and the time scaling factor of the simplified model But, unfortunately, there is no explicit criteria for selections of these parameters. In this paper, error equations are derived and expanded by using the useful properties of $L_2$-norm. Then, new criteria for selecting the order of the simplified model and time scaling factor with respect to error bound are suggested. Since these criteria, newly proposed in this study, have strong concern about error bound, it can be used to choose the minimum order of the simplified model and time scaling factor with respect to given error bound. Conversely, if the order of the simplified model and time scaling factor are given, the error induced by the simplification can also be computed easily.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.39 no.1
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• pp.32-39
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• 2002

Vector quantization for image compression needs expensive encoding time to find the closest codeword to the input vector. This paper proposes a search algorithm for fast vector quantization encoding. Firstly, we derive a robust condition based on the efficient topological structure of the codebook to dramatically eliminate unnecessary matching operations from the search procedure. Then, we Propose a fast search algorithm using the elimination condition. Simulation results show that with little preprocessing and memory cost, the encoding time of the proposed algorithm is reduced significantly while the encoding quality remains the same with respect to the full search algorithm. It is also found that the Proposed algorithm outperforms the existing search algorithms.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.40 no.2
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• pp.10-18
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• 2003

This paper presents a method for designing guaranteed cost fuzzy filter with a desired H$_{\infty}$ disturbance rejection constraint of delayed fuzzy dynamic systems. This method not only guarantees an induced L$_2$ norm bound constraint on disturbance attenuation, but also minimizes an upper bound on a linear quadratic performance measure. A sufficient condition for the existence of guaranteed cost fuzzy filter with H$_{\infty}$ constraint is then presented in terms of linear matrix inequalities(LMIs). A simulation example is given to illustrate the design procedures and performances of the proposed methods.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.30 no.12C
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• pp.1231-1238
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• 2005

This paper presents a new fast encoding algorithm for image vector quantization that incorporates the partial distances of multiple features with a multidimensional look-up table (LUT). Although the methods which were proposed earlier use the multiple features, they handles the multiple features step by step in terms of searching order and calculating process. On the other hand, the proposed algorithm utilizes these features simultaneously with the LUT. This paper completely describes how to build the LUT with considering the boundary effect for feasible memory cost and how to terminate the current search by utilizing partial distances of the LUT Simulation results confirm the effectiveness of the proposed algorithm. When the codebook size is 256, the computational complexity of the proposed algorithm can be reduced by up to the $70\%$ of the operations required by the recently proposed alternatives such as the ordered Hadamard transform partial distance search (OHTPDS), the modified $L_2-norm$ pyramid ($M-L_2NP$), etc. With feasible preprocessing time and memory cost, the proposed algorithm reduces the computational complexity to below the $2.2\%$ of those required for the exhaustive full search (EFS) algorithm while preserving the same encoding quality as that of the EFS algorithm.

• Journal of Soil and Groundwater Environment
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• v.18 no.3
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• pp.82-92
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• 2013

This study has investigated naturally occurring radioactive materials (N.O.R.M; $^{238}U$, $^{222}Rn$) for 353 drinking groundwater wells in metamorphic rock areas in Korea. Uranium concentrations ranged from N.D (not detected) to 563.56 ${\mu}g/L$ (median value, 0.68 ${\mu}g/L$) and radon concentrations ranged from 108 to 11,612 pCi/L (median value, 1,400 pCi/L). Uranium and radon concentrations in the groundwater generally are similar to USA with similar geological setting. Uranium concentrations in 9 wells (2.6%) exceeded 30 ${\mu}g/L$, which is the maximum contaminant level (MCL) by the US environmental protection agency (EPA), radon concentrations in 46 wells (13%) exceeded 4,000 pCi/L, which is the Alternative MCL (AMCL) by the US.EPA. The log-log correlation coefficient between uranium and radon was 0.32. The correlation coefficient between uranium and pH was 0.12 and the correlation coefficient between radon and temperature was -0.01. The correlation coefficient between uranium and $HCO_3$ was 0.09 and the correlation coefficient between uranium and Ca was 0.11. The median value of uranium was high Chung-Buk (1.78 ${\mu}g/L$), Gyeong-Buk (1.37 ${\mu}g/L$), In-Cheon (1.06 ${\mu}g/L$) for each province. On the other hand, the median value of radon was high In-Cheon (2,962 pCi/L), Chung-Buk (2,339 pCi/L), Jeon-Buk (2,165 pCi/L) for each province. Jeon-Buk for log-log correlation coefficient is the highest (0.63) among provinces.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 2001.10a
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• pp.313-318
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• 2001

In this paper, the well-conditioned observer is designed to be insensitive to the ill-conditioning factors in transient and steady-state observer performance. A condition number based on $L_2-norm$ of the eigenvector matrix of the observer matrix has been proposed on a principal index in the observer performance. For the well-conditioned observer design, the non-normality measure and the observability condition of the observer matrix are utilized. The two constraints are specified into observer gain boundary region that guarantees a small condition number and a stable observer. The observer gain selected in this region guarantees a well-conditioned and observable property. In this study, this method is applied to the Luenberger observer and Kalman filters. In designing Kalman filters for small order systems, the ratio of the process noise covariance to the measurement noise covariance is a design parameter and its effect on the condition number is investigated.

• Proceedings of the KIEE Conference
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• 1999.11c
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• pp.494-496
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• 1999

In this paper, we consider the design of a state feedback $H_{\infty}$ controller for uncertain linear systems with saturating actuators. We consider a general saturating actuator and employ the additive decomposition to deal with it effectively. And the considered uncertainty is the unstructured uncertainty which is only known its norm bound. Based on Linear Matrix Inequality(LMI) techniques, we present a condition on designing a controller that guarantees the $L_2$ gain, from the noise to the output, is not greater than a given value. A controller is obtained by checking the feasibility of three LMI's, and this can be easily done by well-known control package. Finally, we show the usefulness of our result by a numerical example.