• Kyungpook Mathematical Journal
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• v.48 no.3
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• pp.395-410
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• 2008

A one site chemotherapy agent-diffusion model is proposed which accounts for diffusion of chemotherapy agent, normal and cancer cells. It is shown that, by controlling the initial conditions, consequently an initial dose of the chemotherapy agent, the system is guaranteed to evolute towards a target equilibrium state. Or, growth of the normal cells occurs against decay of the cancer cells. Effects of diffusion of chemotherapy-agent and cells are investigated through numerical computations of the concentrations in square and triangular cancer sites.

• ETRI Journal
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• v.34 no.2
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• pp.245-255
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• 2012

Among emerging devices propelling the growth of mobile devices, smartphones and tablet-PCs are among the most recognizable. In this study, a research model is designed for exploring acceptance-diffusion strategies for tablet-PCs from the viewpoint of consumer perception, which is verified through a survey. The results of this study show that tablet-PCs have great potential to be versatile, multifunctional devices, even though they are currently considered mostly as entertainment-oriented rather than fulfilling the essential needs of everyday life. An analysis of the acceptance model for tablet-PCs revealed that playability, cost level, functionality, and complexity significantly affect user acceptance. An analysis of the diffusion model, on the other hand, showed that playability and user interface have a significant influence on satisfaction, trust, and positive behavioral intention. We also found that cost level is not a major hindrance in the market diffusion of tablet-PCs. The results of this study can be used to establish effective acceptance and diffusion strategies for tablet-PCs and other emerging devices.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.17 no.7
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• pp.708-712
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• 2004

Shallow $p^+-n$ junctions were formed by ion implantation and dual-step annealing processes. The dopant implantation was performed into the crystalline substrates using BF$_2$ ions. The annealing was performed with a rapid thermal processor and a furnace. FA+RTA annealing sequence exhibited better junction characteristics than RTA+FA thermal cycle from the viewpoint of junction depth and sheet resistance. A new simulator is designed to model boron diffusion in silicon. The model which is used in this simulator takes into account nonequilibrium diffusion, reactions of point defects, and defect-dopant pairs considering their charge states, and the dopant inactivation by introducing a boron clustering reaction. Using initial conditions and boundary conditions, coupled diffusion equations are solved successfully. The simulator reproduced experimental data successfully.

• Computers and Concrete
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• v.7 no.5
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• pp.421-435
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• 2010

This paper utilizes the modified Davis model and the mode coupling theory, as parts of the electrolyte solution theory, to investigate the diffusivity of the ion in concrete. Firstly, a computational model of the ion diffusion coefficient, which is associated with ion species, pore solution concentration, concrete mix parameters including water-cement ratio and cement volume fraction, and microstructure parameters such as the porosity and tortuosity, is proposed in the saturated concrete. Secondly, the experiments, on which the chloride diffusion coefficient is measured by the rapid chloride penetration test, have been carried out to investigate the validity of the proposed model. The results indicate that the chloride diffusion coefficient obtained by the proposed model is in agreement with the experimental result. Finally, numerical simulation has been completed to investigate the effects of the porosity, tortuosity, water-cement ratio, cement volume fraction and ion concentration in the pore solution on the ion diffusion coefficients. The results show that the ion diffusion coefficient in concrete increases with the porosity, water-cement ratio and cement volume fraction, while we see a decrease with the increasing of tortuosity. Meanwhile, the ion concentration produces more obvious effects on the diffusivity itself, but has almost no effects on the other ions.

• Fisheries and Aquatic Sciences
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• v.7 no.2
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• pp.90-95
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• 2004

An analytical model for predicting the convection-diffusion of solute dumped in a homogeneous open sea of constant water depth has been developed in a time-integral form. The model incorporates spatially uniform, uni-directional, mean and oscillatory currents for horizontal convection, the settling velocity for the vertical convection, and the anisotropic turbulent diffusion. Two transformations were introduced to reduce the convection-diffusion equation to the Fickian type diffusion equation, and then the Galerkin method was then applied via the expansion of eigenfunctions over the water column derived from the Sturm-Liouville problem. A series of calculations has been performed to demonstrate the applicability of the model.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.1003-1008
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• 2010

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 define $T_tf\;=\;E_{p_0}^{p^*}\;[f((P(t))]$ for $t\;{\geq}\;0$ for using a new diffusion operator $L^*$ and we show the diffusion relations between $T_t$ and diffusion operator $L^*$.

• 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 Pharmaceutical Investigation
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• v.20 no.2
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• pp.79-88
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• 1990

A numerical model for diffusion and dissolution controlled transport from dispersed matrix is presented. The rate controlling process for transport is considered to be diffusion of drug through a concentration gradient coupled with time-dependent surface change and/or disappearance of the dispersed drug in response to the dissolution. The transport behavior of drug was explained in terms of ${\nu}$ parameter: ${\nu}$ value means a ratio of diffusion time constant and dissolution time constant. This general model has wide range of application from where release is controlled by the diffusion rate to where release is governed by the dissolution rate. Based on this model, theoretical drug concentration, particle size distributions in the polymer matrix system and the resulting release rate were also investigated.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.28 no.1
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• pp.1-21
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• 2024

This review comprehensively explores the evolution, theoretical underpinnings, variations, and applications of diffusion models. Originating as a generative framework, diffusion models have rapidly ascended to the forefront of machine learning research, owing to their exceptional capability, stability, and versatility. We dissect the core principles driving diffusion processes, elucidating their mathematical foundations and the mechanisms by which they iteratively refine noise into structured data. We highlight pivotal advancements and the integration of auxiliary techniques that have significantly enhanced their efficiency and stability. Variants such as bridges that broaden the applicability of diffusion models to wider domains are introduced. We put special emphasis on the ability of diffusion models as a crucial foundation model, with modalities ranging from image, 3D assets, and video. The role of diffusion models as a general foundation model leads to its versatility in many of the downstream tasks such as solving inverse problems and image editing. Through this review, we aim to provide a thorough and accessible compendium for both newcomers and seasoned researchers in the field.

• Journal of Digital Convergence
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• v.6 no.2
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• pp.55-64
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• 2008

The Internet possesses not only features of mass media but also features of word of mouth communication. Communication channel is considered as one of most important variables in diffusion process. In this paper, we examined functionality of technology diffusion on the Internet through the use of meta tags. We have measured the coefficients of the Bass diffusion model which has been well-established in new product diffusion. This research shows that the Bass model is appropriate for describing technology diffusion on the Internet. The external influence as represented by the coefficient of innovation was found to be much smaller while the internal influence dominates in all meta tag diffusion. In meta tag diffusion, the internal influence as represented by the coefficient of imitation was increased at least twice bigger than that of consumer durables and information technology. Collecting necessary data in social sciences research can be a burden. This research shows that it can be alleviated through the use of software agents over the Internet. The research made use of software agents for collecting longitudinal data from publicly accessible archive such as Archive.org.