• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.1 no.1
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• pp.83-104
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• 1997

This paper studies parameter estimation for a first-order hyperbolic integro-differential equation modelling one-sex population dynamics. A second-order finite difference scheme is used to estimate parameters such as the age-specific death-rate and the age-specific fertility from fully discrete observations on the population. The function space parameter estimation convergence of this scheme is proved. Also, numerical simulations are performed.

• Journal of Korean Society on Water Environment
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• v.23 no.5
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• pp.683-688
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• 2007

Water flow into unsaturated soils is most often modeled by Richards equation consisting of the mass conservation law and Darcy's law. Three standard forms of Richards equation are presented as the head (${\Psi}$)-based form, the moisture content (${\theta}$) based form, and the mixed form. Numerical solutions of these partial differential equations with highly nonlinear terms can cause poor results along with significant mass balance errors. The numerical solution based on the mixed form of Richards equation is known that the mass is perfectly conserved without any additional computational efforts. The aim of this study is to develop fully implicit numerical scheme of Richards equation for one-dimensional vertical unsaturated flow in homogeneous soils using the finite difference approximation, and then to perform sensitivity analysis of infiltration to the variations in the unsaturated soil properties and to different soil types.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.10 no.4
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• pp.8-15
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• 2011

In this paper, the influence of a crack on the natural frequency of cracked cantilever L-shaped beam with coupled bending and torsional vibrations by analytically and experimentally is analyzed. The L-shaped beam with a crack is modeled by Hamilton's principle with consideration of bending and torsional energy. The two coupled governing differential equations are reduced to one sixth-order ordinary differential equation in terms of the flexural displacement. The crack is assumed to be in the first, second and third mode of fracture and to be always opened during the vibrations. The theoretical results are validated by a comparison with experimental measurements. The maximal difference between the theoretical results and experimental measurements of the natural frequency is less than 7.5% in the second vibration mode.

• East Asian mathematical journal
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• v.36 no.1
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• pp.81-90
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• 2020

Many compartment models assume a kinetically homogeneous amount of materials that have well-stirred compartments. However, based on observations from such processes, they have been heuristically fitted by exponential or gamma distributions even though biological media are inhomogeneous in real environments. Fractional differential equations using a specific kernel in Pharmacokinetic/Pharmacodynamic (PKPD) model are recently introduced to account for abnormal drug disposition. We discuss a tumor growth inhibition (TGI) model using fractional-order derivative from it. This represents a tumor growth delay by cytotoxic agents and additionally show variations in the equilibrium points by the change of fractional order. The result indicates that the equilibrium depends on the tumor size as well as a change of the fractional order. We find that the smaller the fractional order, the smaller the equilibrium value. However, a difference of them is the number of concavities and this indicates that TGI over time profile for fitting or prediction should be determined properly either fractional order or tumor sizes according to the number of concavities shown in experimental data.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.3 no.2
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• pp.166-172
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• 2003

The dynamics of the DDWMR depends on the velocity difference of the two driving wheels. And which is known as a type of non-holonomic equation. By this reason, the treatment of DDWMR had become difficult and conservative. In this paper, the differential-driving wheeled mobile robot is considered. The Takaki-Surgeno fuzzy model and a control method for DDWMR is presented. The suggested controller has three control elements. The first element is fuzzy state feedback designed for eliminating the dependence of time-varying parameter. The second element is weighting controller which is designed for good frequency response. The third controller is PI-controller which is designed for good command following and robustness with un-modeled dynamics. In order for achieving the performance objective, the design of controller is based on the loop-shaping algorithm.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.10a
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• pp.109-116
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• 1998

The method of vibration analysis used is the one developed by the senior author. He developed and reported, in 1974, a simple but exact method of calculating the natural frequency of beam and tower structures with irregular cross-sections and attached mass/masses. Since 1989, this method has been extended to two-dimensional problems with several types of given conditions and has been reported at several international conferences. This method uses the deflection influence surfaces. The finite difference method is used for this purpose, in this paper. In order to reduce the pivotal points required, the three simultaneous partial differential equations of equilibrium with three dependent variables, w, M$_{x}$, and $M_{y}$, are used instead of the one forth order partial differential equation. By neglecting the M$_{x}$ terms, the size of the matrices needed to solve the resulting linear equations are reduced to two thirds of the "non-modified" equations.tions.

• Journal of the Korean Chemical Society
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• v.14 no.1
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• pp.127-131
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• 1970

The variational approach for the direct evaluation of the energy difference ${\Delta}$E is studied. The method is based on the differential equation corresponding to the integral Hellmann-Feynman formula. The ${\Delta}$E is given by the expectation value of the Hermitian operator which does not involve the 1/$r_{ij}$ term. Because of its variational nature of the method, the coupling problem of the differential equations which are encountered in perturbation treatment does not occur. The method is applied to the evaluation of the electric polarizabilities of the Helium isoelectronic series atoms. The result is in good agreement with the experiment. The method is compared with the recent works of Karplus et al.

• Structural Engineering and Mechanics
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• v.4 no.6
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• pp.589-600
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• 1996

An explicit 4th order time integration scheme for solving the convection-diffusion equation is discussed in this paper. A system of ordinary differential equations are derived first by discretizing the spatial derivatives of the relevant PDE using the finite difference method. The integration of the ODEs is then carried out using a 4th order scheme and a self-adaptive technique based on the spatial grid spacing. For a non-uniform spatial grid, different time step sizes are used for the integration of the ODEs defined at different spatial points, which improves the computational efficiency significantly. A numerical example is also discussed in the paper to demonstrate the implementation and effectiveness of the method.

• Food Science and Biotechnology
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• v.17 no.6
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• pp.1352-1356
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• 2008

Bootstrap method, a computer-intensive statistical technique to estimate the distribution of a statistic was applied to deal with uncertainty and variability of the experimental data in stochastic prediction modeling of microbial growth on a chill-stored food. Three different bootstrapping methods for the curve-fitting to the microbial count data were compared in determining the parameters of Baranyi and Roberts growth model: nonlinear regression to static version function with resampling residuals onto all the experimental microbial count data; static version regression onto mean counts at sampling times; dynamic version fitting of differential equations onto the bootstrapped mean counts. All the methods outputted almost same mean values of the parameters with difference in their distribution. Parameter search according to the dynamic form of differential equations resulted in the largest distribution of the model parameters but produced the confidence interval of the predicted microbial count close to those of nonlinear regression of static equation.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.25 no.4
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• pp.224-261
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• 2021

The interest in implicit-explicit (IMEX) integration methods has emerged as an alternative for dealing in a computationally cost-effective way with stiff ordinary differential equations arising from practical modeling problems. In this paper, we introduce implicit-explicit second derivative linear multi-step methods (IMEX SDLMM) with error control. The proposed IMEX SDLMM is based on second derivative backward differentiation formulas (SDBDF) and recursive SDBDF. The IMEX second derivative schemes are constructed with order p ranging from p = 1 to 8. The methods are numerically validated on well-known stiff equations.