• Journal of the Korean Statistical Society
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• v.33 no.3
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• pp.313-321
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• 2004

We consider the problem of testing cell probabilities in sparse multinomial data. Aerts et al. (2000) presented T=${{\Sigma}_{i=1}}^{k}{[{p_i}^{*}-E{(p_{i}}^{*})]^2$ as a test statistic with the local least square polynomial estimator ${{p}_{i}}^{*}$, and derived its asymptotic distribution. The local least square estimator may produce negative estimates for cell probabilities. The local maximum likelihood polynomial estimator ${{\hat{p}}_{i}}$, however, guarantees positive estimates for cell probabilities and has the same asymptotic performance as the local least square estimator (Baek and Park, 2003). When there are cell probabilities with relatively much different sizes, the same contribution of the difference between the estimator and the hypothetical probability at each cell in their test statistic would not be proper to measure the total goodness-of-fit. We consider a Pearson type of goodness-of-fit test statistic, $T_1={{\Sigma}_{i=1}}^{k}{[{p_i}^{*}-E{(p_{i}}^{*})]^2/p_{i}$ instead, and show it follows an asymptotic normal distribution. Also we investigate the asymptotic normality of $T_2={{\Sigma}_{i=1}}^{k}{[{p_i}^{*}-E{(p_{i}}^{*})]^2/p_{i}$ where the minimum expected cell frequency is very small.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.33 no.8
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• pp.75-83
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• 2005

A steady transonic dilute premixed combustion in a diverging channel is investigated by using asymptotic analysis. This model explores the nonlinear interactions between the near-sonic speed of the flow, the small changes in geometry from a straight channel, and the small heat release due to the one-step first-order Arrhenius chemical reaction. The reactive flow is described by a nonhomogeneous transonic small-disturbance (TSD) equation coupled with an ordinary differential equation for the calculation of the reactant mass fraction in the combustible gas. Also the asymptotic analysis reveals the similarity parameters that govern the reacting flow problem. The results show the complicated nonlinear interaction between the convection, reaction, and geometry effects and its effect on the flow behavior.

• 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.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.40 no.7
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• pp.1217-1233
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• 2015

The paper studies characteristics of the minimum mean-square error symmetric scalar quantizers for the generalized gamma, Bucklew-Gallagher and Hui-Neuhoff probability density functions. Toward this goal, asymptotic formulas for the inner- and outermost thresholds, and distortion are derived herein for nonuniform quantizers for the Bucklew-Gallagher and Hui-Neuhoff densities, parallelling the previous studies for the generalized gamma density, and optimal uniform and nonuniform quantizers are designed numerically and their characteristics tabulated for integer rates up to 20 and 16 bits, respectively, except for the Hui-Neuhoff density. The assessed asymptotic formulas are found consistently more accurate as the rate increases, essentially making their asymptotic convergence to true values numerically acceptable at the studied bit range, except for the Hui-Neuhoff density, in which case they are still consistent and suggestive of convergence. Also investigated is the uniqueness problem of the differentiation method for finding optimal step sizes of uniform quantizers: it is observed that, for the commonly studied densities, the distortion has a unique local minimizer, hence showing that the differentiation method yields the optimal step size, but also observed that it leads to multiple solutions to numerous generalized gamma densities.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.46 no.1
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• pp.78-85
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• 2018

As a numerical analysis technique to predict the radar cross section of an aircraft, a full wave method or an asymptotic method is mainly used. The full-wave method is expected to be relatively accurate compared with the asymptotic method. The asymptotic method is numerically efficient, and it is more widely used in the RCS analysis. However, the error that occurs when estimating the RCS using the asymptotic method is difficult to predict easily. In this paper, we analyze the allowable limits of physical optics by constructing a wedge-cylinder model and comparing the RCS prediction results between the method of moment and physical optics while changing the edge shape. Finally, this study proposes a criterion for allowable limit of physical optics in the RCS estimation.

• International Journal of Control, Automation, and Systems
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• v.3 no.2
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• pp.244-251
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• 2005

In this paper, we study the problem of stabilizing a general nonlinear control system by means of gradient descent control method which is a dynamic feedback control law. In this method, the general nonlinear control system can be considered as an affine nonlinear control systems. Then by using Sontag's formula we investigate the stability (asymptotic) of the general nonlinear control system.

• Journal of Mechanical Science and Technology
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• v.14 no.1
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• pp.48-56
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• 2000

The bifurcation problem of thin walled structures in contact with rigid surfaces is formulated by adopting the multiple scales asymptotic technique. The general theory developed in this paper is very useful for the bifurcation analysis of waviness instabilities in the sheet metal forming. The formulation is presented in a full Lagrangian formulation. Through this general formulation, the bifurcation functional is derived within an error of O($(E^4)$) (E: shell's thickness parameter). This functional can be used in numerical solutions to sheet metal forming instability problem.

• Journal of Mechanical Science and Technology
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• v.16 no.8
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• pp.1117-1126
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• 2002

A conducting crack in an electrostrictive ceramic under combined electric and mechanical loading is investigated. Analysis based on linear dielectric model predicts that the surfaces of the crack are not open completely but they are contact near the crack tip. The complete solution for the crack with a contact zone in a linear electrostrictive ceramic under combined electric and mechanical loading is obtained by using the complex variable formula. The asymptotic problems for a semi-infinite crack with a partial opening zone as well as for a fully open semi-infinite crack in a nonlinear electrostrictive ceramic are analyzed in order to investigate the effect of the electrical nonlinearity on the stress intensity factor under small scale nonlinear conditions. Particular attention is devoted to a finite crack in the nonlinear electrostrictive ceramic subjected to combined electric and mechanical loading. The stress intensity factor for the finite crack under small scale nonlinear conditions is obtained from the asymptotic analysis.

• Proceedings of the Korean Society for Quality Management Conference
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• 1998.11a
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• pp.259-268
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• 1998

A family of test statistics is proposed for testing whether or not the mean residual life(MRL) changes its trend. We do not assume that the turning point or the proportion before the turning point is known. This family includes the test statistic proposed by Aly (1990) and Hawkins, Kochar and Leader (1992) for complete samples. We establish the asymptotic null distribution of test statistics and obtain asymptotic critical values of the asymptotic null distribution using Durbin's approximation. We study Monte Carlo simulation to compare the proposed tests with previously known tests.

• Proceedings of the IEEK Conference
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• 2002.07a
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• pp.70-73
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• 2002

High frequency digital LSI circuits are usually composed of many sub-circuits coupled with interconnects. They sometimes causes serious problems of the fault switching by time-delays, crosstalks, reflections of signals and so on. Therefore, it is very important to develop a user-friendly simulator for solving these problems. Although a moment matching method is widely used as the reduction technique of interconnects, it may happen to arise erroneous results for evaluating the poles far from the origin. In this paper, we show an asymptotic method in the complex frequency-domain, where we calculate the exact poles and residues giving large effect to the transient responses. Then, the interconnects are replaced by the asymptotic equivalent circuits using the poles and residues. Thus, we can develop a users-friendly simulator using the equivalent circuits.