• 대한수학회보
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• 제52권3호
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• pp.895-906
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• 2015

Recently, Li [12] gave an asymptotic formula for the ultimate ruin probability in a delayed-claim risk model with constant force of interest and pairwise quasi-asymptotically independent and extended-regularly-varying-tailed claims. This paper extends Li's result to the case in which the risk model is perturbed by diffusion, the claims are consistently-varying-tailed and the main-claim interarrival times are widely lower orthant dependent.

• 한국막학회:학술대회논문집
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• 한국막학회 1995년도 추계 총회 및 학술발표회
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• pp.43-44
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• 1995

The diffusion behavior of liquid into polymer has been described by Fick's law, but the departure from Fickian diffusion is frequently found. In this study, 'noble' expressions for the rates of relaxation and sorption are introduced to eliminate these limitations. The ralaxation-sorption coupled mechanism model are based on the possibility of contacting liquid molecule and the active site which has the numerical concept of free volume. The concept has an analogy of reaction rate expressed by the possibility of collision with molecules and used in adsorption and reactive extraction etc. The new model simulated by Rungc-Kutta method for initial-value problem and Fickian diffusion is caompared with experimental data. The results show that the ralaxation-sorption coupled mechanism is able to account well for Fickian and non-Fickian sorption behavior including sigmoid and two-stage. In addition, this model has a chance of expansion to multi-component sorption with ease.

• 전기학회논문지
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• 제65권2호
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• pp.253-256
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• 2016

In this paper, the power system with electric vehicles is analyzed considering the mobility and diffusion rate of electric vehicles in the smart grid environment. In the previous studies, load modeling and load composition rates have been researched and the results are applied to develop a new load model to explain the mobility of electric vehicles which could affect on the power system status such as power flow and stability. The results would be utilized to research and develop power system analysis methods considering movable charging characteristics of electric vehicles including movable discharging characteristics which could be affected by the diffusion progress of electric vehicles.

• 호남수학학술지
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• 제44권3호
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• pp.402-418
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• 2022

Noise is a fundamental factor to increased validity and regularity of spike propagation and neuronal firing in the nervous system. In this paper, we examine the stochastic version of the Izhikevich-FitzHugh neuron dynamical model. This approach is based on techniques presented by Luo and Guo, which provide a general framework for the bifurcation and stability analysis of two dimensional stochastic dynamical system as an Itô averaging diffusion system. By using largest lyapunov exponent, local and global stability of the stochastic system at the equilibrium point are investigated. We focus on the two kinds of stochastic bifurcations: the P-bifurcation and the D-bifurcations. By use of polar coordinate, Taylor expansion and stochastic averaging method, it is shown that there exists choices of diffusion and drift parameters such that these bifurcations occurs. Finally, numerical simulations in various viewpoints, including phase portrait, evolution in time and probability density, are presented to show the effects of the diffusion and drift coefficients that illustrate our theoretical results.

• 한국지리정보학회지
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• 제12권3호
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• pp.88-100
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• 2009

본 연구에서는 GIS와 연계한 2차원 확산파 침수해석 모형을 개발하여 2002년 8월 집중호우로 인하여 침수피해가 발생했던 낙동강의 지류인 화포천유역에 대하여 하천제방의 월류 및 붕괴에 따른 침수해석을 실시하였다. 당시의 침수흔적도 및 FLUMEN 모형의 침수해석 결과와 시간별 침수심 및 최대 침수면적의 비교를 통해 모형의 적용성을 평가해 보았다. 침수흔적도와의 비교를 통해 침수면적에 대한 적합도를 분석한 결과 88.61%의 적합도를 갖는 것으로 확인되었으며, FLUMEN 모형과의 비교를 통하여 최대 침수면적 및 침수지역의 공간적 분포가 상당부분 일치하는 것으로 확인되었다. 따라서 2차원 확산파 침수해석 모형의 적용으로 계산된 시간별 침수구역 및 최대 침수면적 등은 홍수에 대비한 위험지역의 파악 및 재난저감 대책을 수립하기 위한 판단자료로 활용될 수 있을 것으로 기대된다.

• Journal of applied mathematics & informatics
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• 제16권1_2호
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• pp.69-78
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• 2004

This paper treats the conditions for the existence of rotating wave solutions of a system modelling the behavior of students in graduate programs at neighbouring universities near each other which is a modified form of the model proposed by Scheurle and Seydel. We assume that both types of individuals are continuously distributed throughout a bounded two-dimension spatial domain of two types (circle and annulus), across whose boundaries there is no migration, and which simultaneously undergo simple (Fickian) diffusion. We will show that at a critical value of a system-parameter bifurcation takes place: a rotating wave solution arises.

• Journal of applied mathematics & informatics
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• 제30권3_4호
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• pp.677-683
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• 2012

W.Choi([1]) obtains a complete description of ergodic property and several property by making use of the semigroup method. In this note, we shall consider separately the martingale problems for two operators A and B as a detail decomposition of operator L. A key point is that the (K, L, $p$)-martingale problem in population genetics model is related to diffusion processes, so we begin with some a priori estimates and we shall show existence of contraction semigroup {$T_t$} associated with decomposition operator A.

• 해양환경안전학회지
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• 제20권5호
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• pp.511-525
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• 2014

본 연구는 반폐쇄성 해역인 마산만을 대상으로 eco-hydrodynamic model을 이용하여 해역의 물리적 구조를 분석하여, 물리적 안정도를 나타내는 수직확산계수를 산정하고, 생태계 모델에 적용하여 그 타당성을 평가하는 것이다. 해역의 물리적 구조는 EFDC모델을 사용하여 구하였으며, 수직 확산계수는 수층간의 밀도차이가 커질수록 감소하도록 산정하였다. 산정된 수직 확산계수를 Stella프로그램을 이용하여 구축한 생태계모델에 적용하여, 용존산소 재현성으로 그 타당성을 평가하였다. 수직확산계수 변화를 추정하여 적용한 모델의 결과는 2008년의 $R^2$값은 0.529~0.700으로 나타났으며, 2009년 $R^2$값은 0.542~0.791로 나타났다. 계산값은 관측값과 유사한 경향을 나타내었으며, 만 내측의 빈산소수괴를 잘 재현하였다. 본 연구에서 적용된 수직확산계수는 해역의 밀도성층과 물리적 안정도를 의미하는데, 향후 폐쇄성 내만해역의 빈산소수괴 발생 예측에 유용하게 활용될 것으로 판단된다.

• 대한산업공학회지
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• 제23권3호
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• pp.545-557
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• 1997

This paper deals with dynamic optimal pricing for new products by a firm which maximizes the discounted profit stream of it's own in a duopoly. The problem is constructed as differential games and dynamic optimization theory. Cost is assumed to decline as time goes on. A modified customer's choice model is formulated as a diffusion model and we solve a dynamic optimization problem by adopting the diffusion model. Since this paper focus on deriving real prices not showing a time trend, we formulate recursive form equations of costate variables(shadow price) and a simultaneous equation of price. Hence we derive a dynamic optimal pricing model for using in real market. In particular, we construct a dynamic optimal pricing model in the case that there are benefits from not only new subscribers but also previous subscribers. We analyze instant camera market in U.S.A(1976-1985) by utilizing the above model.

• Journal of applied mathematics & informatics
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• 제27권1_2호
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• pp.385-400
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• 2009

The adverse effect of harmful plankton on the marine ecosystem is a topic of deep concern. To investigate the role of such phytoplankton, a mathematical model containing distinct dynamical equations for toxic and non-toxic phytoplankton is analyzed. Stability analysis of the resulting three equation model is carried out. A continuous time variation in toxin liberation process is incorporated into the model and a stability analysis of the resulting delay model is performed. The distributed delay model is then extended to include the spatial distribution of plankton and the delay-diffusion model is analyzed with spatial and spatiotemporal kernels. Conditions for diffusion-driven instability in both the cases are derived and compared to explore the significance of these kernels. Numerical studies are performed to justify analytical findings.