• Journal of applied mathematics & informatics
• /
• v.24 no.1_2
• /
• pp.191-207
• /
• 2007

Based on a mixed Galerkin approximation, we construct the fully discrete approximations of $U_y$ as well as U to a single-phase quasilinear Stefan problem with a forcing term in non-divergence form. We prove the optimal convergence of approximation to the solution {U, S} and the superconvergence of approximation to $U_y$.

• Journal of the Korean Statistical Society
• /
• v.22 no.1
• /
• pp.133-138
• /
• 1993

We consider two estimators of the infection rate in the simple stochastic epidemic model. It is shown that the maximum likelihood estimator of teh infection rate under the discrete time observation does not have the moment of any positive order. Some properties of the Choi-Severo estimator, an approximation to the maximum likelihood estimator, are also investigated.

• Journal of applied mathematics & informatics
• /
• v.11 no.1_2
• /
• pp.357-364
• /
• 2003

A fully discrete $H^1-mixed$ finite element approximation for the single-phase Stefan problem is introduced and the unique existence of the approximation is established. And some numerical experiments are given.

• Journal of the Korean Statistical Society
• /
• v.36 no.2
• /
• pp.321-333
• /
• 2007

In the proportional hazard model with the beta process prior, the posterior computation with the discrete approximation is considered. The time period of interest is partitioned by small intervals. On each partitioning interval, the likelihood is approximated by that of a binomial experiment and the beta process prior is by a beta distribution. Consequently, the posterior is approximated by that of many independent binomial model with beta priors. The analysis of the leukemia remission data is given as an example. It is illustrated that the length of the partitioning interval affects the posterior and one needs to be careful in choosing it.

• Journal of applied mathematics & informatics
• /
• v.20 no.1_2
• /
• pp.575-584
• /
• 2006

In this paper we introduce a discrete tangent vector of a polygon defined on each vertex by a linear combination of forward difference and backward difference, and show that if the polygon is originated from a smooth curve then direction of the discrete tangent vector is a second order approximation of the direction of the tangent vector of the original curve. Using this discrete tangent vector, we also introduced the geometric cubic Hermite interpolation of a polygon with controlled initial and terminal speed of the curve segments proportional to the edge length. In this case the whole interpolation is $C^1$. Experiments suggest that about $90\%$ of the edge length is the best fit for the initial and terminal speeds.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.12 no.1
• /
• pp.33-39
• /
• 2008

We consider a queueing system fed by a superposition of multiple discrete autoregressive processes of order 1, and propose an approximation method to estimate the overflow probability of the system. Numerical examples are provided to validate the proposed method.

• Kyungpook Mathematical Journal
• /
• v.57 no.3
• /
• pp.493-502
• /
• 2017

We propose an accurate approximation method via discrete Krawtchouk orthogonal polynomials to the distribution of a sum of independent but non-identically distributed binomial random variables. This approximation is a weighted binomial distribution with no need for continuity correction unlike commonly used density approximation methods such as saddlepoint, Gram-Charlier A type(GC), and Gaussian approximation methods. The accuracy obtained from the proposed approximation is compared with saddlepoint approximations applied by Eisinga et al. [4], which are the most accurate method among higher order asymptotic approximation methods. The numerical results show that the proposed approximation in general provide more accurate estimates over the entire range for the target probability mass function including the right-tail probabilities. In addition, the method is mathematically tractable and computationally easy to program.

• Journal of the Korean Chemical Society
• /
• v.51 no.2
• /
• pp.136-140
• /
• 2007

By using the discrete-dipole approximation, we computed the extinction spectrum of a gold-silver alloy nanoparticle. We have examined how the surface plasmon resonance changes with respect to the variation in the composition of the alloy particle. As the fraction of silver increases for a 10nm particle, the peak position of the extinction spectrum blue-shifts linearly. The intensity of the peak however increases exponentially with increasing the silver fraction. These results are in accord with the previous experimental results.

• Journal of Environmental Science International
• /
• v.11 no.12
• /
• pp.1195-1204
• /
• 2002

We calculated dose rate using radiative transfer equations to consider radiative processes distinctly. The dose rate at Pohang(36°02'N, 129°23'E) was calculated using measured ozone and meteorological data and two-stream approximations(quadrature, Eddington, delta Eddington, PIFM(practical improved flux method), discrete ordinate, delta discrete ordinate) are used in solving equation. The purpose of this study is to determine the most compatible radiative transfer approximation for simulating the radiative and photochemical processes of atmosphere through comparision between calculated and measured values. Dose rate of the biologically effective irradiance in the region 0.28-0.32 U m showed the highest value when quadrature and Eddington was used and lower value on condition that delta scaling was applied. Correlation coefficient between dose rate at surface using radiation transfer equation and measured UV-B at Pohang was 0.78, 0.79 and 0.81 when delta Eddington, PIFM and delta discrete ordinate were used. Also, in case of above approximations were used, MBE(Mean Bias Error) was within -0.3MED/30min and RMBE(Relative Mean Bias Error) was below 10% between 1200 LST and 1400 LST Approximations which are compatible in estimating radiative process are delta Eddington, PIFM and delta discrete ordinate. Especially, in case that radiative process is considered more detail, delta discrete ordinate increased the number of stream is proper.

• The Transactions of the Korean Institute of Electrical Engineers
• /
• v.36 no.8
• /
• pp.584-593
• /
• 1987

A new combined approximation method using Routh stability array and mean-square error (MSE) method is proposed for deriving reduced-order z-transter functions for discrete time systems. The Routh stability array is used to obtain the reduced-order denominator polynomial, and the numerator polynomial is obtained by minimizing the mean-square error between the unit step responses of the original system and reduced model. The advantages of the new combined approximation method are that the reduced model is always stable provided the original model is stable and the initial and steady-state characteristics of the original model can be preserved in the reduced model.