• Journal of the Korean Data and Information Science Society
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• v.21 no.1
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• pp.51-59
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• 2010

In the case that the regression function has a discontinuity point in generalized linear model, Huh (2009) estimated the location and jump size using the log-likelihood weighted the one-sided kernel function. In this paper, we consider estimation of the unknown number of the discontinuity points in the regression function. The proposed algorithm is based on testing of the existence of a discontinuity point coming from the asymptotic distribution of the estimated jump size described in Huh (2009). The finite sample performance is illustrated by simulated example.

• 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.

• Journal of the Korean Data and Information Science Society
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• v.23 no.1
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• pp.79-87
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• 2012

In the case that the probability density function has a discontinuity point, Huh (2002) estimated the location and jump size of the discontinuity point based on the difference between the right and left kernel density estimators using the one-sided kernel function. In this paper, we consider the cross-validation, made by the right and left maximum likelihood cross-validations, for the bandwidth selection in order to estimate the location and jump size of the discontinuity point. This method is motivated by the one-sided cross-validation of Hart and Yi (1998). The finite sample performance is illustrated by simulated example.

• Proceedings of the Membrane Society of Korea Conference
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• 1997.10a
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• pp.27-30
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• 1997

1. Introduction : Molecular diffusion of small molecules in polymers plays an important role in many areas where polymers are acting as barriers, and in separation processes, such as selective diffusion. Different applications of polymers have different requirements on their transport properties. Therefore, reliable predictions of diffusion coefficients for small molecules in polymeric materials could be a useful tool to design appropriate materials. For many years, the theories based on free-volume concepts have been widely used to correlate and predict diffusion behavior in polymer/solvent systems. In the theory derived by Vrentas and Duda, the empty space between molecules that is available for molecular transport, referred to as hole free-volume, is being redistributed. Molecular transport will occur only when a free-volume of sufficient size appears adjacent to a molecule and the molecule has enough energy to jump into this void. The diffusive jump is considered complete when the void left behind is closed before the molecule returns to its original position. In this paper, the Vrentas-Duda free-volume theory is presented and the methods to estimate free-volume parameters for predicting polymer/ solvent diffusion coefficients are described in detail.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.05a
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• pp.283-288
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• 2001

The nonlinear vibration of a cantilever beam due to electromagnetic force is studied. The dynamic responses of the beam show various phenomena with the variation of the system parameters, such as jump phenomenon, multiple solutions and the change of the natural frequency. The nonlinear stiffness due to electromagnetic forces which depends on air gap size is measured experimentally. This system was modeled by a single degree of freedom nonlinear dynamic system and solved numerically for the system parameters. The numerical results show good agreements with the experimental observations, which demonstrates the nonlinearity of magnetic force.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.17 no.4
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• pp.267-278
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• 2013

We consider zero range processes with density dependent jump rates g given by $g=g(n,k)=g_1(n)g_2(k/n)$ with $g_1(x)=x^{-\alpha}$ and $$g_2(x)=\{^{x^{-\alpha}\;if\;a&lt;x}_{Mx^{-\alpha}\;if\;x{\leq}a}$$. (0.1) In this case, with 1/2 < a < 1 and ${\alpha}$ > 0, we show that non-complete condensation occurs with maximum cluster size an. More precisely, for any ${\epsilon}$ > 0, there exists $M^*$ > 0 such that, for any 0 < M ${\leq}M^*$, the maximum cluster size is between (a - ${\epsilon}$)n and (a + ${\epsilon}$)n for large n. This provides a simple example of non-complete condensation under perturbation of rates which are deep in the range of perfect condensation (e.g. ${\alpha}$ >> 1) and supports the instability of the condensation transition.

• Journal of applied mathematics & informatics
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• v.4 no.2
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• pp.529-534
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• 1997

Even though the Shannon wavelet is a prototype of wavelets are assumed to have. By providing a sufficient condition to compute the size of Gibbs phe-nomenon for the Shannon wavelet series we can see the overshoot is propotional to the jump at discontinuity. By comparing it with that of the Fourier series we also that these two have exactly the same Gibbs constant.

• Journal of the Korean Statistical Society
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• v.31 no.2
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• pp.261-276
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• 2002

Probability density or its derivatives may have a discontinuity/change point at an unknown location. We propose a method of estimating the location and the jump size of the discontinuity point based on kernel type density or density derivatives estimators with one-sided equivalent kernels. The rates of convergence of the proposed estimators are derived, and the finite-sample performances of the methods are illustrated by simulated examples.

• Journal of the Korean Statistical Society
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• v.35 no.1
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• pp.1-23
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• 2006

In this paper we consider an estimation of the discontinuous variance function in nonparametric heteroscedastic random design regression model. We first propose estimators of the change point in the variance function and then construct an estimator of the entire variance function. We examine the rates of convergence of these estimators and give results for their asymptotics. Numerical work reveals that using the proposed change point analysis in the variance function estimation is quite effective.

• Journal of the Korean Data and Information Science Society
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• v.18 no.3
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• pp.669-678
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• 2007

An algorithm to detect the number of discontinuity points of the variance function in regression model is proposed. The proposed algorithm is based on the left and right one-sided kernel estimators of the second moment function and test statistics of the existence of a discontinuity point coming from the asymptotic distribution of the estimated jump size. The finite sample performance is illustrated by simulated example.