• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.199-209
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• 2003

When a sampling theorem holds in wavelet subspaces, sampling expansions can be a good approximation to projection expansions. Even when the sampling theorem does not hold, the scaling function series with the usual coefficients replaced by sampled function values may also be a good approximation to the projection. We refer to such series as hybrid sampling series. For this series, we shall investigate the local convergence and analyze Gibbs phenomenon.

• Communications of the Korean Mathematical Society
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• v.13 no.1
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• pp.181-193
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• 1998

The Shannon sampling series is the prototype of an interpolating series or sampling series. Also the Shannon wavelet is one of the protypes of wavelets. But the coefficients of the Shannon sampling series are different function values at the point of discontinuity, we analyze the Gibbs phenomenon for the Shannon sampling series. We also find a way to go around this overshoot effect.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.719-736
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• 2005

An understanding of Fourier series and their generalization is important for physics and engineering students, as much for mathematical and physical insight as for applications. Students are usually confused by the so-called Gibbs' phenomenon, an overshoot between a discontinuous function and its approximation by a Fourier series as the number of terms in the series becomes indefinitely large. In this paper we give short story of Gibbs phenomenon in chronological order.

• International Journal of Reliability and Applications
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• v.11 no.1
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• pp.17-22
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• 2010

It is desired to estimate the reliability of a system that has two subsystems connected in series where each subsystem has two components connected in parallel. A batch sequential sampling scheme is introduced. It is shown that the batch sequential sampling scheme is asymptotically optimal as the total number of units goes to infinity. Numerical comparisons indicate that the batch sequential sampling scheme performs better than the balanced sampling scheme and is nearly optimal.

• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.267-275
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• 2004

While the convergence of the classical Fourier series has been well known, the rate of its convergence is not well acknowledged. The results regarding the rate of convergence of the Fourier series and wavelet expansions can be found in the book of Walter[5]. In this paper, we give the rate of convergence of hybrid sampling series associated with orthogonal wavelets.

• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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• pp.351-358
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• 2007

For an entire function f whose Fourier transform has a compact support confined to $[-{\pi},\;{\pi}]$ and restriction to ${\mathbb{R}}$ belongs to $L^2{\mathbb{R}}$, we derive a nonuniform sampling theorem of Lagrange interpolation type with sampling points ${\lambda}_n{\in}{\mathbb{R}},\;n{\in}{\mathbb{Z}}$, under the condition that $$\frac{lim\;sup}{n{\rightarrow}{\infty}}|{\lambda}_n-n|<\frac {1}{4}$.

• Communications for Statistical Applications and Methods
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• v.22 no.3
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• pp.209-222
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• 2015

Time series are used in many studies for model building and analysis. We must be very careful to understand the kind of time series data used in the analysis. In this review article, we will begin with some issues related to the use of aggregate and systematic sampling time series. Since several time series are often used in a study of the relationship of variables, we will also consider vector time series modeling and analysis. Although the basic procedures of model building between univariate time series and vector time series are the same, there are some important phenomena which are unique to vector time series. Therefore, we will also discuss some issues related to vector time models. Understanding these issues is important when we use time series data in modeling and analysis, regardless of whether it is a univariate or multivariate time series.

• International Journal of Reliability and Applications
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• v.14 no.2
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• pp.71-78
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• 2013

The problem of designing an experiment to estimate the reliability of a system that has N subsystems connected in series where each subsystem n has n $T_n$ components connected in parallel is investigated both theoretically and by simulation. An accelerated sampling sheme is introduced. It is shown that the accelerated sampling scheme is asymptotically optimal as the total number of units goes to infinity. Numerical comparisons for a system that has two subsystems connected in series where each subsystem has two components connected in parallel are also given. They indicate that the accelerated sampling scheme performs better than the batch sequential sampling scheme and is nearly optimal.

• Korean Journal of Hydrosciences
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• v.4
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• pp.51-63
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• 1993

This study is to verify the applicability of statistical models in predicting flood frequency at the stage gaging stations of which the flow is under natural condition in the Han River basin. The results of the study show that the statistical flood frequency models were proven to be fairly reasonable to apply in practice, and also were compared with sampling variance to calibrate the statistical efficiency of the estimators of the T year floods Q(T) by two different flood frequency models. As a result, it was showed that for return periods greater than about T = 10 years the annual exceedance series estimators of Q(T) has smaller sampling variance than the annual maximum series estimators. It was showed that for the range of return periods the partial duration series estimators of !(T) has smaller sampling variance than the annual maximum series estimate only if the POT model contains at least 2N(N : record length) items or more in order to estimate Q(T) more efficiently than the ANNMAX model.

• Communications of the Korean Mathematical Society
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• v.29 no.2
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• pp.379-385
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• 2014

For a bandlimited function with polynomial growth on the real line, we derive a nonuniform sampling expansion using a special bandlimited function which has polynomial decay on the real line. The series converges uniformly on any compact subsets of the real line.