• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제11권2호
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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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• 제45권2호
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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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• 제36권1호
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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.

• 한국지반공학회:학술대회논문집
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• 한국지반공학회 2009년도 세계 도시지반공학 심포지엄
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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.

• 한국전기전자재료학회:학술대회논문집
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• 한국전기전자재료학회 2002년도 하계학술대회 논문집 Vol.3 No.2
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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.

• 한국산림과학회지
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• 제88권3호
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• pp.320-326
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• 1999

연구에서는 잔존목의 본수에 대한 수식형태 및 고사율 추정 미분함수형태를 가정하여 인공림에 대한 잔존목을 추정하기 위한 15개의 함수들을 적분 및 지수함수형태로 유도하였다. 또한 이 모델들을 간벌이 되지 않은 스트로부스 잣나무 인공림의 반복측정 자료를 이용하여 모델의 적용성을 검토하였다. 그 결과 $t^{\beta}$와 같이 임령의 지수형태를 포함하는 3개의 함수들이 시간에 따른 자연 간벌효과를 설명하는데 상대적으로 유효한 것으로 나타났다. 한편 지위가 자연 간벌에 미치는 효과를 분석하기 위하여 낙엽송 임분의 잔존목 추정을 위한 함수를 유도하였다. 그 결과 $N_{min}$이 지위지수와 부의 상관관계를 가지는 것으로 나타났고, 초기 임분밀도를 같은 값으로 가정한 경우에도 잔존목 추정함수의 곡선이 지위지수별로 달라짐을 알 수 있었다.