• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1035-1054
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• 2010

We consider a mixed type singularly perturbed one dimensional elliptic problem with discontinuous source term. The domain under consideration is partitioned into two subdomains. A convection-diffusion and a reaction-diffusion type equations are posed on the first and second subdomains respectively. Two hybrid difference schemes on Shishkin mesh are constructed and we prove that the schemes are almost second order convergence in the maximum norm independent of the diffusion parameter. Error bounds for the numerical solution and its numerical derivative are established. Numerical results are presented which support the theoretical results.

• Ocean and Polar Research
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• v.26 no.1
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• pp.43-50
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• 2004

The diffusion model, which considers diffusion and sorption, is proposed. The FEM program developed on the basis of the diffusion model provides the estimation of chloride concentration according to cyclic humidity and sorption. After the humidity diffusion analysis is carried out, the chloride ion diffusion and sorption analysis are conducted on the basis of the preestimated humidity data in each element. Each element has different analysis variables at different ages and locations. At early ages, the difference between inner and outer relative humidity causes the chloride ion penetration by sorption. As the humidity diffusion reduces the difference with age, the effect of sorption on the chloride ion penetration decreases. By the way, the cyclic humidity increases the effect of sorption on the chloride ion penetration at early ages, and the quantity of chloride ion around steel at later ages. Therefore, the in situ analysis of chloride ion penetration for marine concrete structures must be performed considering the cyclic humidity condition and the long term sorption.

• Journal of the Korean Operations Research and Management Science Society
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• v.42 no.1
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• pp.29-41
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• 2017

Korea is expected to become a super-aged society by 2050. Given an aging population and the increasing pressure for the early retirement, a sufficient social safety net for elderly population becomes important. The Korean government introduced public reverse mortgage program in 2007, which is a product for aging seniors and the elderly, The number of reverse mortgage subscribers has also steadily grown. The demand continues to grow, but the reverse mortgage over a long period of time is a highly uncertain and risky product in the position of guarantee or lending institution. Thus, suitable demand prediction of the reverse mortgage subscribers is necessary for stable and sustainable operation. This study uses a Bass diffusion model to forecast the long-term demand for reverse mortgage and provides insight into reverse mortgage by forecasting demand for stability and substantiality of the loan product. We represent the projections of new subscribers on the basis of the data obtained from Korea Housing Finance Corporation. Results show that potential market size of Korean reverse mortgage reaches approximately 760,000-1,160,000 households by 2020. We validate the results by comparing the estimate of the cumulative number of subscribers with that found in literature.

• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.1057-1069
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• 2008

We consider singularly perturbed Boundary Value Problems (BVPs) for third and fourth order Ordinary Differential Equations(ODEs) of convection-diffusion type with discontinuous source term and a small positive parameter multiplying the highest derivative. Because of the type of Boundary Conditions(BCs) imposed on these equations these problems can be transformed into weakly coupled systems. In this system, the first equation does not have the small parameter but the second contains it. In this paper a computational method named as 'An asymptotic finite element method' for solving these systems is presented. In this method we first find an zero order asymptotic approximation to the solution and then the system is decoupled by replacing the first component of the solution by this approximation in the second equation. Then the second equation is independently solved by a fitted mesh Finite Element Method (FEM). Numerical experiments support our theoritical results.

• Health Policy and Management
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• v.18 no.4
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• pp.85-110
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• 2008

In this study, we explore the long-term demand forecasting of high-price medical equipments based on logistic and Bass diffusion model. We analyze the specific pattern of each equipment's diffusion curve by interpreting the parameter estimates of Bass diffusion model. Our findings are as follows. First, ultrasonic imaging system, CT are in the stage of maturity and so, the future demands of them are not too large. Second, medical image processing unit is between growth stage and maturity stage and so, the demand is expected to increase considerably for two or three years. Third, MRI is in the stage of take-off and Mammmography X-ray system is in the stage of maturity but, estimates of the potential number of adopters based on logistic model is considerably different to that based on Bass diffusion model. It means that additional data for these two equipments should be collected and analyzed to obtain the reliable estimates of their demands. Fourth, medical image processing unit have the largest q value. It means that the word-of-mouth effect is important in the diffusion of this equipment. Fifth, for MRI and Ultrasonic system, q/p values have the relatively large value. It means that collective power has an important role in adopting these two equipments.

• Journal of Korea Technical Association of The Pulp and Paper Industry
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• v.34 no.3
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• pp.17-24
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• 2002

An unsteady-state moisture diffusion through cellulosic fibers in paper was characterized from the moisture sorption experiment and the mathematical modeling. The sorption experiment was conducted by exposing thin dry paper specimens to a constant temperature-humidity environment. Oven dried blotting papers and filter papers were used as test samples and the gains of their weights were constantly monitored and recorded as a function of sorption time. For a mathematical approach, the moisture transport was assumed to be an one-dimensional diffusion in thickness direction through the geometrically symmetric structure of paper. The model was asymptotically simplified with a short-term approximation. It gave us a new insight into the moisture uptake phenomena as a function of square root of sorption time. The fiber-phase moisture diffusivities(FPMD) of paper samples were then determined by correlating the experimental data with the unsteady-state diffusion model obtained. Their values were found to be on the order of magnitude of $10^{-6}-10^{-7}cm^2$/min., which were equivalent to the hypothetical effective diffusion coefficients at the limit of zero porosity. The moisture sorption curve predicted from the model fairly agreed with that obtained from the experiment at some limited initial stages of the moisture uptake process. The FPMD value of paper significantly varied depending upon the current moisture content of paper. The mean FPMD was about 0.7-0.8 times as large as the short-term approximated FPMD.

• Communications for Statistical Applications and Methods
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• v.14 no.1
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• pp.241-254
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• 2007

This paper propose a new short-term interest rate model having a different nonlinear drift function and the same diffusion coefficient with Chan et al. (1992) model. The fractional polynomial power of the drift function in our model is linked to the local volatility elasticity of the diffusion coefficient. While the nonlinear drift function estimated by $A\"{\i}t$-Sahalia (1996a) and others has a feature that higher interest rates tend to revert downward and low rates upward, the drift function estimated by our nonlinear model shows that higher interest rate mean-reverts strongly, but, medium rates has almost zero drift and low rates has a very small drift. This characteristic coincides the empirical result based on the nonparametric methodology by Stanton (1997) and the implication by the scatter plot of the short rate data.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2001.05c
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• pp.174-177
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• 2001

The electron transport coefficients, the electron drift velocity W, the longitudinal diffusion coefficient $ND_L$ and $D_L/{\mu}$, in pure Xe were calculated over the wide E/N range from 0.01 to 500 Td at 1 Torr by two-term approximation of the Boltzmann equation for determination of electron collision cross sections set and for quantitative characteristic analysis of Xe molecular gas.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2001.05c
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• pp.182-185
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• 2001

The electron transport coefficients, the electron drift velocity W, the longitudinal diffusion coefficient $ND_L$ and $D_L/{\mu}$, in pure Ne were calculated over the wide E/N range from 0.01 to 300 Td at 1 Torr by two-term approximation of the Boltzmann equation for determination of electron collision cross sections set and for quantitative characteristic analysis of Ne molecular gas.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2001.05c
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• pp.29-32
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• 2001

We measured the electron transport coefficients(the electron drift velocity, W, and the longitudinal diffusion coefficient, $D_L$) in pure $CF_4$ over the E/N range from 0.04 Td to 250 Td by the double shutter drift tube. And these electron transport coefficients in pure $CF_4$ were calculated over the E/N range from 0.01 to 250 Td at 1 Torr by using the two-term approximation of the Boltzmann equation.