• Communications for Statistical Applications and Methods
• /
• v.7 no.1
• /
• pp.55-64
• /
• 2000

We propose a criterion for testing homogeneity of matrix intraclass covariance matrices of K multivariate normal populations, It is based on a variable transformation intended to propose and develop a likelihood ratio criterion that makes use of properties of eigen structures of the matrix intraclass covariance matrices. The criterion then leads to a simple test that uses an asymptotic distribution obtained from Box's (1949) theorem for the general asymptotic expansion of random variables.

• Communications for Statistical Applications and Methods
• /
• v.15 no.3
• /
• pp.465-481
• /
• 2008

Item response theory(IRT) estimates latent ability of a subject based on the property of item and item parameters using item characteristics curve(ICC) of each item case. The initial value and another problems occurs when we try to estimate item parameters of IRT(e.g. the maximum likelihood estimate). Thus, we propose the asymptotic approximation method(AAM) to solve the above mentioned problems. We notice that the proposed method can be thought as an alternative to estimate item parameters when we have small size of data or need to estimate items with local fluctuations. We developed 'Any Assess' and tested reliability of the system result by simulating a practical use possibility.

• Korean Journal of Mathematics
• /
• v.26 no.3
• /
• pp.467-481
• /
• 2018

In this paper we present a postprocessing scheme for the Raviart-Thomas mixed finite element approximation of the second order elliptic eigenvalue problem. This scheme is carried out by solving a primal source problem on a higher order space, and thereby can improve the convergence rate of the eigenfunction and eigenvalue approximations. It is also used to compute a posteriori error estimates which are asymptotically exact for the $L^2$ errors of the eigenfunctions. Some numerical results are provided to confirm the theoretical results.

• Communications of the Korean Mathematical Society
• /
• v.29 no.4
• /
• pp.505-518
• /
• 2014

Considered here is the first initial boundary value problem for the two-dimensional g-Navier-Stokes equations in bounded domains. We first study the long-time behavior of strong solutions to the problem in term of the existence of a global attractor and global stability of a unique stationary solution. Then we study the long-time finite dimensional approximation of the strong solutions.

• Proceedings of the Korean Magnestics Society Conference
• /
• 2000.09a
• /
• pp.191-199
• /
• 2000

The reflection-amplitude approximation is used to calculate the interlayer exchange coupling in (001) Co/Cu/Co multilayers. The dependence of the phase factor of the reflection amplitude on the energy and wave vector is included. The contribution of each period is calculated and the results are compared with those from the asymptotic behavior. It is shown that the energy and wave-vector dependence of the phase factor may affect the interlayer exchange coupling significantly.

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

• Kyungpook Mathematical Journal
• /
• v.59 no.4
• /
• pp.735-769
• /
• 2019

In this paper, we consider the Robin-Dirichlet problem for a nonlinear wave equation of Kirchhoff-Carrier type with a viscoelastic term. Using the Faedo-Galerkin method and the linearization method for nonlinear terms, the existence and uniqueness of a weak solution are proved. An asymptotic expansion of high order in a small parameter of a weak solution is also discussed.

• Journal of applied mathematics & informatics
• /
• v.33 no.5_6
• /
• pp.485-502
• /
• 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 Statistical Society
• /
• v.26 no.4
• /
• pp.543-554
• /
• 1997

A family of some capability indices { $C_{p}$(.alpha.,.beta.); .alpha..geq.0, .beta..geq.0}, containing the indices $C_{p}$, $C_{{pk}}$, $C_{{pm}}$, and $C_{{pmk}}$, has been defined by Vannman(1993) for the case of two-sided specification interval. By varying the parameters of the family various capability indices with suitable properties are obtained. We derive tha asymptotic distribution of the family { $C_{p}$(.alpha.,.beta.); .alpha..geq.0,.beta..geq.0} under general proper conditions. It is also shown that the bootstrap approximation to the distribution of the estimator $C_{p}$(.alpha., .beta.) is vaild for almost all sample sequences. These asymptotic distributions would be used in constructing some bootstrap confidence intervals.tervals.

• Journal of the Korean Society of Manufacturing Process Engineers
• /
• v.20 no.2
• /
• pp.72-79
• /
• 2021

The present paper aims to set forth a two-dimensional theory for the dynamics of plates that is valid over a large range of excitation. To construct a dynamic plate theory within the long-wavelength approximation, two dimensional-reduction procedures must be used for analyzing the low- and high-frequency behaviors under the dynamic variational-asymptotic method. Moreover, a separate and logically independent step for the short-wavelength regime is introduced into the present approach to avoid violation of the positive definiteness of the derived energy functional and to facilitate qualitative description of the three-dimensional dispersion curve in the short-wavelength regime. Two examples are presented to demonstrate the capabilities and accuracy of all of the formulas derived herein by using various dispersion curves through comparison with the three-dimensional finite element method.