• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.11 no.2
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• pp.15-29
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• 2007

In this paper, we explore some interesting models of the quasi-negative-binomial distribution based on difference differential equations applicable to theory of microorganisms and the situations like that. Some characterizations based on conditional distributions and damage process have been obtained. Further, the distribution of number of accidents as the quasi-negative-binomial distribution in the light of Irwin's theory of ";proneness-liability"; model has been derived. Finally, the proposed model (QNBD) has been applied to study the Shunting accidents, home injuries, and strikes in industries.

• Structural Engineering and Mechanics
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• v.45 no.2
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• pp.201-209
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• 2013

A new dynamic reliability analysis of structure under repeated random loads is proposed in this paper. The proposed method is developed based on the idea that the probability density of several times random loads can be derived from the probability density of single-time random load. The reliability prediction models of structure based on time responses under several times random loads with and without strength degradation are obtained by using the stress-strength interference theory and probability density evolution method. The resulting differential equations in the prediction models can be solved by using the forward finite difference method. Then, the probability density functions of strength redundancy of the structures can be obtained. Finally, the structural dynamic reliability can be calculated using integral method. The efficiency of the proposed method is demonstrated numerically through a speed reducer. The results have shown that the proposed method is practicable, feasible and gives reasonably accurate prediction.

• 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.

• Proceedings of the Korean Geotechical Society Conference
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• 2009.09a
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• pp.1090-1094
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• 2009

Many problems in geotechnical engineering such as slop failure, debris flow, ground heaving due to embankment, and lateral flow caused by liquefaction are related to large deformation rather than small deformation. Traditional numerical methods such as finite element and finite difference methods have a difficulty to solve such large deformations because they use grids. A particle method was developed for fluid dynamics. The particle method can solve large deformation problems because it uses particles to discretize differential equations. It can also include soil constitutive model and thus solve soil behavior on various boundary conditions. In this study, a particle method, which is based on particles rather than grids, is introduced and used to simulate large deformation including soil failure. The developed method can be applied for various large deformation problems in geotechnical engineering because it incorporates soil constitutive models.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2002.07b
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• pp.939-944
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• 2002

PD phenomena can be regarded as a deterministic dynamical process where PD should be occurred if the local electric field be reached to be sufficiently high. And thus, its mathematical model can be described by either difference equations or differential equations using several state variables obtained from the time sequential measured data of PD signals. These variables can provide rich and complex behavior of detectable time series, for which Chaos theory can be employed. In this respect, a new PD pattern recognition method is proposed and named as 'Chaotic Analysis of Partial Discharges (CAPD)' for this work. For this purpose, six types of specimen are designed and made as the models of the possible defects that may cause sudden failures of the underground power transmission cables under service, and partial discharge signals, generated from those samples, are detected and then analyzed by means of CAPD. Throughout the work, qualitative and quantitative properties related to the PD signals from different defects are analyzed by use of attractor in phase space, information dimensions ($D_0$ and D2), Lyapunov exponents and K-S entropy as well. Based on these results, it could be pointed out that the nature of defect seems to be identified more distinctively when the CAPD is combined with traditional statistical method such as PRPDA. Furthermore, the relationship between PD magnitude and the occurrence timing is investigated with a view to simulating PD phenomena.

• Journal of Korean Society of Forest Science
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• v.88 no.3
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• pp.320-326
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• 1999

In this study, 15 survival functions in integral and difference forms for forest plantation were derived based on assumptions for the number of surviving trees and the differential forms of the mortality rate model. Then, performance of the models was evaluated by fitting to remeasurement data of unthinned white pine(Pinus strobes) forest plantation. As a result, three equations associated with a power function of age, $t^{\beta}$, are somewhat more suitable for describing the effect of self-thinning over time. On the other hand, a general survival function for Japanese larch(Larix leptolepts) forest plantation was derived in order to exam the effect of site quality on self-thinning procedures. The results indicate that the $N_{min}$ is negatively correlated with site index and, even though the same initial stand density was assumed, the survival function curves differ in shapes associated with site index values.