• Journal of Technology Innovation
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• v.13 no.1
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• pp.113-139
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• 2005

The purpose of this study is to analyse the diffusion process of personal computer (PC) in Korea during the 1990's. To achieve the goal, five research steps have been done such as the literature survey of diffusion theory, set-up of theoretic equilibrium model of supply and demand, derivation of an equilibrium path using Hamiltonian, and empirical analysis. The empirical analysis has been performed based on that equilibrium path. The results can be summarized as follows : First, technological attribute of diffusing product influences the diffusion speed of Product. It has been proven that the size of the network has a significant effect on the diffusion of PC in empirical study Second, supply factors have an important role in the diffusion process. According to the empirical analysis, decreasing cost of production as a result of technological advance promotes the speed of diffusion. This point seems to be manifest theoretically, but existing empirical models have not included supply factors explicitly, Third, it has been found out that expectation of decreasing cost would influence the speed of diffusion negatively as expected ex ante. Theoretically this result is supported by arbitrage condition of purchasing timing.

• Journal of Ocean Engineering and Technology
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• v.16 no.5
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• pp.41-48
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• 2002

Numerical experiments are conducted using a three-dimensional baroclinic equation model and a Lagrangian method for clarifying the effect of th settling velocity on the suspended solids diffusion caused by the dredging and the reclamination works. Diffusion characteristics of the neutral particles and the weighting particles is experimented by the Lagrangian particles trajectory model, The results show that the diffusion characteristics of the suspended solids is effected by the settling velocity classified by the particles size in the density layered semi-closed bay. To estimate exactly the diffusion characteristics of the suspended solids and the contaminant with weight the three-dimensional baroclinic equation model and the three-dimensional Lagrangian particles trajectory model considering the settling velocity of the particle in the density layered semi-closed bay must be used.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.455-460
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• 2007

In allelic model $X=(x_1,\;x_2,\;{\cdots},\;x_d)$, $$M_f(t)=f(p(t))-{\int}_0^t\;Lf(p(t))ds$$ is a P-martingale for diffusion operator L under the certain conditions. In this note, we try to apply diffusion processes for countable-allelic model in population genetic model and we can define a new diffusion operator $L^*$. Since the martingale problem for this operator $L^*$ is related to diffusion processes, we can define a integral which is combined with operator $L^*$ and a bilinar form $<{\cdot},{\cdot}>$. We can find properties for this integral using maximum principle.

• Journal of Korean Institute of Industrial Engineers
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• v.13 no.1
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• pp.25-29
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• 1987

When the historical data are available, the diffusion model, which describes the time pattern of the adoption process of a new product or technology or service, has been used as a reasonable predictor in the telecommunication demand forecasting area. This paper shows that the diffusion model is applicable when the historical data are not available. The model used is in the form of a "logistic" function. The parameters of the function are estimated using the questionnaire and the historical data of reference products. From the questionnaire, an initial and an upper limit long run value of the market share are estimated, and the diffusion time to the upper limit value is determined by the relation between the investment and the utility.

• Proceedings of the Korea Information Processing Society Conference
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• 2023.05a
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• pp.633-635
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• 2023

센서 데이터를 예측 또는 분석하여 시스템을 제어하거나 모니터링할 수 있다. 센서 데이터를 이용한 예측의 신뢰성을 확보하기 위해서는 데이터의 적절한 빈도수가 중요하다. 이를 위해 본 논문에서는 Diffusion Model을 사용한 센서 데이터 주파수 보간을 통해 행동을 예측하는 방법을 제시하고자 한다. 주파수 보간은 반려동물 행동별 25hz 센서 데이터로 학습된 Diffusion Model을 사용한다. 학습된 Diffusion Model에 1hz 센서 데이터와 가우시안 노이즈를 결합한 데이터를 입력으로 사용해 센서데이터를 보간한다. 제안한 방법은 CNN-LSTM 모델 학습 후 예측 성능 비교를 통해 검증한다.

• Communications of the Korean Mathematical Society
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• v.10 no.3
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• pp.715-733
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• 1995

We present a transient queue size distribution for $M/G/m/N$ queue with state dependent arrival rates, using the diffusion process with piecewise constant diffusion parameters, with state space [0, N] and elementary return boundaries at x = 0 and x = N. The model considered here contains not only many basic model but the practical models such as as two-node cyclic queue, repairmen model and overload control in communication system with finite storage buffer. For the accuracy check, we compare the approximation results with the exact and simulation results.

• Bulletin of the Korean Mathematical Society
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• v.47 no.2
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• pp.251-261
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• 2010

This paper deals with a predator-prey model with Holling type III response function and cross-diffusion subject to the homogeneous Neumann boundary condition. We first give a priori estimates (positive upper and lower bounds) of positive steady states. Then the non-existence and existence results of non-constant positive steady states are given as the cross-diffusion coefficient is varied, which means that stationary patterns arise from cross-diffusion.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.1043-1048
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• 2011

W. Choi([1]) identified and characterized the limiting diffusion of this diploid model by defining discrete generator for the rescaled Markov chain. We denote by F the homozygosity and by S the average selection intensity. In this note, we define the Fleming-Viot process with generator of limiting diffusion and provide exact result for the relations of F and S.

• Journal of the Korean Mathematical Society
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• v.57 no.1
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• pp.249-281
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• 2020

A reaction-diffusion model with spatiotemporal delay modeling the dynamical behavior of a single species is investigated. The parameter regions for the local stability, global stability and instability of the unique positive constant steady state solution are derived. The conditions of the occurrence of Turing (diffusion-driven) instability are obtained. The existence of time-periodic solutions, the existence and nonexistence of nonconstant positive steady state solutions are proved by bifurcation method and energy method. Numerical simulations are presented to verify and illustrate the theoretical results.

• Journal of Korean Society for Atmospheric Environment
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• v.12 no.1
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• pp.29-41
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• 1996

The two-stage numerical model was used to study the relation between three-dimensional local wind model, advection/diffusion model of random walk method and second moment method on Pusan coastal area. The first stage is three dimensional time-dependent local wind model which gives the wind field and vertical dirrusion coefficient. The second stage is advection/diffusion model which uses the results of the first stage as input data. First, wind fields on Pusan coastal area for none synoptic scale wind showed typical land and sea breeze circulation, and convergence zone occured at 1200LST in northern of domain, in succession, moved northward of domain. Emissions from Sinpyeong industrial district were trasnported toward the inland by sea breeze during daytime, and reached the end part of domain about 1800LST. During nighttime, emissions return to sea by land breeze and vertical diffusion also contributes to upward transport. In order to use this model for forecast of air pollution concentration on the Pusan coastal area, it is necessary that computed value must be compared with measured value and wind fields model must also be dealt in detail.