• Proceedings of the KIEE Conference
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• 1998.07b
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• pp.641-643
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• 1998

This paper deals with the stability of discrete time linear systems with time - varying delays in state. In this paper, the magnitude of time - varying delays is assumed to be upper-bounded. The stability of discrete time linear systems with time - varying delays in state is related with the stability of discrete time linear systems with constant time delay in state. To show this, a new Lyapunov function is proposed. Using this Lyapunov function, a sufficient condition for the asymptotic stability is derived.

• Journal of the Korean Institute of Telematics and Electronics S
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• v.35S no.7
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• pp.29-36
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• 1998

In this paper we propose a control law using a Lyapunov-like function that makes stable the systems which have mis-matched uncertainties. The existing control law using a Lyapunov-like function, which gives global saymptotic stability, is designed under the assumption of a targetsystem to be stable locally. But we broaden here the class of target systems by designing the control law which can give uniform ultimate boundedness to even the systems not satisfing the locally asymptotic stability. And we also show that the control law giving global asymptotic stability can be designed more systematically through using the uniform ultimate boundedness.

• Journal of the Korean Mathematical Society
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• v.56 no.6
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• pp.1599-1611
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• 2019

Let $m,n{\in}{\mathbb{N}}$. We represent the additive subgroups of the ring ${\mathbb{Z}}_m{\times}{\mathbb{Z}}_n$, which are also (unital) subrings, and deduce explicit formulas for $N^{(s)}(m,n)$ and $N^{(us)}(m,n)$, denoting the number of subrings of the ring ${\mathbb{Z}}_m{\times}{\mathbb{Z}}_n$ and its unital subrings, respectively. We show that the functions $(m,n){\mapsto}N^{u,s}(m,n)$ and $(m,n){\mapsto}N^{(us)}(m,n)$ are multiplicative, viewed as functions of two variables, and their Dirichlet series can be expressed in terms of the Riemann zeta function. We also establish an asymptotic formula for the sum $\sum_{m,n{\leq}x}N^{(s)}(m,n)$, the error term of which is closely related to the Dirichlet divisor problem.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.20 no.4
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• pp.66-72
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• 2021

Since the behavior of an autonomous underwater vehicle (AUV) is influenced by disturbances and moments that are not accurately known, the depth control law of AUVs must have the ability to track the input signal and to reject disturbances simultaneously. Here, we proposed robust tracking control for controlling the depth of an AUV. An augmented closed-loop system is represented by an error dynamic equation, and we can easily show the asymptotic stability of the overall system by using a Lyapunov function. The robust tracking controller is consisted of the internal model of the command signal and a state feedback controller, and it has the ability to track the input signal and reject disturbances. The closed-loop control system is robust to parameter uncertainties. Simulation results showed the control performance of the robust tracking controller to be better than that of a P + PD controller.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.23 no.6
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• pp.1454-1460
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• 1998

In this ppaer, we propose a new detector based on the median-shift sign, and then investigate its asymptotic and finite sample-size performance. We call it the median-shift sign (MSS) detector, which is an extension of the classical sign detector. First, we consider the asymptotic opti$$\mu$ median shift values and their characteristics. Next, we consider the asymptotic relative efficiency of the MSS detectors. we then consider the problem of detecting known signals in noise of known probability density function, and the problem of detecting known signals when only partial information is available on the noise.

• Journal of the Korean Data and Information Science Society
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• v.13 no.1
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• pp.47-53
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• 2002

A new redescending M-estimating function is introduced. The estimators by this new redescending function attain the same level of robustness as the existing redescending M-estimators, but have less asymptotic variances than others except few cases. We have focused on estimating a location parameter, but the method can be extended for a scale estimation.

• Journal of the Korean Statistical Society
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• v.36 no.3
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• pp.387-395
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• 2007

We propose a doubly robustified estimating function for the estimation of parameters in the context of ARCH models. We investigate asymptotic properties of estimators obtained as solutions of robust estimating equations. A simulation study shows that robust estimator from specified doubly robustified estimating equation provides better performance than conventional robust estimators especially under heavy-tailed distributions of innovation errors.

• Journal of the Korean Mathematical Society
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• v.49 no.1
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• pp.49-67
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• 2012

In this paper we give asymptotic formulas for the number of ${\ell}$-cyclic extensions of the rational function field $k=\mathbb{F}_q(T)$ with prescribe ${\ell}$-class numbers inside some cyclotomic function fields, and density results for ${\ell}$-cyclic extensions of k with certain properties on the ideal class groups.

• Journal of the Korean Data and Information Science Society
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• v.17 no.3
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• pp.707-716
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• 2006

When the regression function is discontinuous at a point, the variance function is usually discontinuous at the point. In this case, we had better propose a test for the existence of a discontinuity point with the regression function rather than the variance function. In this paper we consider that the variance function only has a discontinuity point. We propose a nonparametric test for the existence of a discontinuity point with the second moment function since the variance function and the second moment function have the same location and jump size of the discontinuity point. The proposed method is based on the asymptotic distribution of the estimated jump size.

• International Journal of Naval Architecture and Ocean Engineering
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• v.13 no.1
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• pp.50-56
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• 2021

An accurate evaluation of three-dimensional (3D) Time-Domain Green Function (TDGF) in infinite water depth is essential for ship's hydrodynamic analysis. Various numerical algorithms based on the TDGF properties are considered, including the ascending series expansion at small time parameter, the asymptotic expansion at large time parameter and the Taylor series expansion combines with ordinary differential equation for the time domain analysis. An efficient method (referred as "Present Method") for a better accuracy evaluation of TDGF has been proposed. The numerical results generated from precise integration method and analytical solution of Shan et al. (2019) revealed that the "Present method" provides a better solution in the computational domain. The comparison of the heave hydrodynamic coefficients in solving the radiation problem of a hemisphere at zero speed between the "Present method" and the analytical solutions proposed by Hulme (1982) showed that the difference of result is small, less than 3%.