• Proceedings of the Safety Management and Science Conference
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• 2010.11a
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• pp.35-39
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• 2010

The research classifies three types of asymptotic tail distributions such as long(heavy, thick) tailed distribution, medium tailed distribution and short(light, thin) tailed distribution. The extreme value distributions(EVD) classified in this paper can be used in SPC(Statistical Process Control) control chart and reliability engineering.

• Journal of the Korean Mathematical Society
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• v.46 no.3
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• pp.493-511
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• 2009

Let $q\;{\geq}\;3$ be an odd integer and a be an integer coprime to q. Denote by N(a, q) the number of pairs of integers b, c with $bc\;{\equiv}\;a$ (mod q), $1\;{\leq}\;b$, $c\;{\leq}\;{\frac{q-1}{2}}$ and with b, c having different parity. The main purpose of this paper is to study the sum ${\sum}^{'q}_{a=1}\;\(N(a,\;q)\;-\;\frac{{\phi}(q)}{8}\)^2$ and obtain a sharp asymptotic formula.

• Journal of applied mathematics & informatics
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• v.35 no.3_4
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• pp.371-385
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• 2017

Jain and Saraswat (2012) introduced new generalized f-information divergence measure, by which we obtained many well known and new information divergences. In this work, we introduce new information inequalities in absolute form on this new generalized divergence by considering convex normalized functions. Further, we apply these inequalities for getting new relations among well known divergences, together with numerical verification. Application to the Mutual information is also presented. Asymptotic approximation in terms of Chi- square divergence is done as well.

• Journal of the Korean Mathematical Society
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• v.47 no.5
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• pp.947-965
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• 2010

The main purpose of this paper is using estimates for character sums and analytic methods to study the mean value involving the incomplete character sums, 2-th power mean of the inversion of Dirichlet L-function and general Kloosterman sums, and give four interesting asymptotic formulae for it.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1996.10a
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• pp.275-281
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• 1996

In order to examine the validity of an asymptotic solution obtained from the method of multiple scales, we investigate a third-order subharmonic resonance response of a bar constrained by a nonlinear spring to a harmonic excitation. The motion of the bar is governed by a linear partial differential equation with a nonlinear boundary condition. The nonlinear boundary value problem is solved by using the finite difference method. The numerical solution is compared with the asymptotic solution.

• Journal of the Korea institute for structural maintenance and inspection
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• v.13 no.2 s.54
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• pp.231-242
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• 2009

The baseline distribution of a structure represents the statistical distribution of dynamic response feature from the healthy state of the structure. Generally, damage-sensitive dynamic response feature of a structure manifest themselves near the tail of a baseline statistical distribution. In this regard, some researchers have paid attention to extreme value distribution for modeling the tail of a baseline distribution. However, few researches have been conducted to theoretically understand the extreme value distribution from a perspective of statistical damage assessment. This study investigates the asymptotic convergence of domain of attraction in extreme value distribution through parameter estimation, which is needed for reliable statistical damage assessment. In particular, the asymptotic convergence of a domain of attraction is quantified with respect to the sample size out of which each extreme value is extracted. The effect of the sample size on false positive alarms in statistical damage assessment is quantitatively investigated as well. The validity of the proposed method is demonstrated through numerically simulated acceleration data on a two span continuous truss bridge.

• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.485-502
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• 2015

A computational method for solving singularly perturbed boundary value problem of differential equation with shift arguments of mixed type is presented. When shift arguments are sufficiently small (o(ε)), most of the existing method in the literature used Taylor's expansion to approximate the shift term. This procedure may lead to a bad approximation when the delay argument is of O(ε). The main idea for this work is to deal with constant shift arguments, which are independent of ε. In the present method, we construct the formally asymptotic solution of the problem using the method of composite expansion. The reduced problem is solved numerically by using operator compact implicit method, and the second problem is solved analytically. Error estimate is derived by using the maximum norm. Numerical examples are provided to support the theoretical results and to show the efficiency of the proposed method.

• Journal of the Korean Mathematical Society
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• v.47 no.6
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• pp.1107-1122
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• 2010

In this paper, we shall use analytic methods to study the hybrid mean value involving the mixed two-term exponential sums C(m, n, r, $\chi$; q), and give several sharp asymptotic formulae.

• Journal of Institute of Control, Robotics and Systems
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• v.10 no.1
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• pp.15-21
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• 2004

This paper deals with asymptotic stabilization problems for linear systems with time-varying input disturbances. In order to eliminate the influence of a disturbance on the system, a disturbance observer is designed and the time-varying disturbance can be rejected using its estimated value. Since the disturbance observer is kind of low-pass filter, it has inevitably estimation errors. To eliminate the inflences on the performance due to these errors, the additional control is designed based on these estimation errors using a well-known min-max control method. It is shown that the asymptotic stability of the closed-loop system is guaranteed. In general, the min-max control method requires the switching of control inputs and the switching magnitude of the control input is determined by the disturbance estimation error bounds. As the error bounds can be made arbitrarily small by choosing the high gain for the disturbance observer, the control method suggested in this paper can reduce the chattering phenomena as small as possible. Therefore, it has superior performance to the existing ones.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2003.05d
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• pp.96-99
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• 2003

In this paper, it presents a method to calculate the escape frequency factor$(\nu)$ and its verification from TSC(Thermally Stimulated Current) equation and their simulation curves. To apply calculation method of $\nu$ using asymptotic estimation, it utilized TSC data with 1K interval. This method enables one to get the exact value of $\nu$ and activation energy at the same time by using computer programming. So, it regards their calculation method as a useful process to obtain the value of physical behavior.