• 대한수학회지
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• 제35권3호
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• pp.637-658
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• 1998

One-dimensional diffusion processes are characterized by Feller's data of canonical scales and speed measures and, if we apply the theory of spectral functions of strings developed by M. G. Krein, Feller's data are determined by paris of spectral characteristic functions so that theses pairs may be considered as invariants of diffusions under the homeomorphic change of state spaces. We show by examples how these invariants are useful in the study of one-dimensional diffusion processes.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2007년도 추계학술대회논문집
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• pp.979-982
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• 2007

The effect of a scattering wall surfaces on sound diffusion can be assessed by determining the scattering and diffusion coefficients in the laboratory. However, the sound field in a concert hall including scattered reflections is different from the laboratory measurement condition. Therefore, there is a need for objective investigation of diffusion in real sound fields. In this paper, possible acoustical parameters of in-situ measurements are discussed.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제16권4호
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• pp.249-256
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• 2012

In this work, we analyze the spatial patterns of a predator-prey system with cross diffusion. First we get the critical lines of Hopf and Turing bifurcations in a spatial domain by using mathematical theory. More specifically, the exact Turing region is given in a two parameter space. Our results reveal that cross diffusion can induce stationary patterns which may be useful in understanding the dynamics of the real ecosystems better.

• Bulletin of the Korean Chemical Society
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• 제7권3호
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• pp.224-228
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• 1986

A nonlinear theory is presented for the fluctuations of intermediates in the Brusselator near the critical point caused by diffusion. The method used is the two time scaling method different from the conventional method in the sense that a slight nonlinear effect is included in the initial time region where the linear approximation is conventionally valid. The result obtained by the nonlinear theory shows that fluctuations close to the critical point approach the value of a stable steady state or deviate infinitely from an unstable steady state, as time goes to infinity, while the linear theory gives approximately time-independent fluctuations. A brief discussion is given for the correlation at a time between fluctuating intermediates when the system approaches a stable steady state.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제28권1호
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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.

• 디지털산업정보학회논문지
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• 제6권1호
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• pp.197-209
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• 2010

Supply Chain Management have been introduced and used as strategic weapon for many companies. Large investments in the SCM was made, but many companies are not fully getting the performance from the systems. The purpose of this study is to find the determinants of SCM difussion and performance in the perspective of Innovation and Information technology Acceptance. In developing the research model, The model consists of eight independent variables(Management support, Decision Making concentration, IS strategy, training education, relative advantage, technological compatibility, task compatibility, SCM cost), two moderator variables(interorganizational and intraorganizational diffusion), three dependant variables(efficiency, effectiveness, strategic advantage).

• 한국전산유체공학회지
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• 제3권1호
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• pp.63-72
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• 1998

The numerical simulations of flowfield and pollutant dispersion over two-dimensional hills of various shapes are described. The Reynolds-averaged Wavier-Stokes equations and concentration diffusion equation based on the gradient diffusion theory have been applied to the atmospheric shear flow over the bell-shaped hills which are basic components of the complex terrain. The flow characteristics such as velocity profiles of the geophysical boundary layer, speed-up phenomena, mean pollutant concentration profiles are compared with experimental data to validate the present numerical procedure and it has been found that the present numerical results agree well with experiments and other numerical data. It has been also found that the distributions of ground level concentration are strongly influenced by the source location and height.

• Structural Engineering and Mechanics
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• 제75권2호
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• pp.133-144
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• 2020

This investigation is to study the effect of gravitational field and diffusion on a microstretch thermoelastic medium heating by a non-Gaussian laser beam. The problem was studied in the context of the dual-phase-lag model. The normal mode analysis is used to solve the problem to obtain the exact expressions for the non-dimensional displacement components, the micro-rotation, the stresses, and the temperature distribution. The effect of time parameter, heat flux parameter and gravity response of three theories of thermoelasticity i.e. dual-phase-lag model (DPL), Lord and Shulman theory (L-S) and coupled theory (CT) on these quantities have been depicted graphically for a particular model.

• 대한수학회보
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• 제57권3호
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• pp.677-690
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• 2020

In this article, we study a reaction-diffusion system with homogeneous Dirichlet boundary conditions, which describing a three-species food chain model. Under some conditions, the predator-prey subsystem (u₁ ≡ 0) has a unique positive solution (${\bar{u_2}}$, ${\bar{u_3}}$). By using the birth rate of the prey r1 as a bifurcation parameter, a connected set of positive solutions of our system bifurcating from semi-trivial solution set (r₁, (0, ${\bar{u_2}}$, ${\bar{u_3}}$)) is obtained. Results are obtained by the use of degree theory in cones and sub and super solution techniques.

• 한국시스템다이내믹스연구
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• 제14권4호
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• pp.5-35
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• 2013

The study examines the play theory based internet rumor process by using simulating tools, Vensim, which offer a new theoretical basis from which to explore complex adaptive social system. Internet rumor is not a simple linear diffusion process, but a complex interaction behavior between the actors of production and diffusion. Rumor actors consist of two type of diffusion, which is rumor mongers and playful mongers. These two type of mongers make the internet rumor as collective system. Playful mongers play strategically to maximize playfulness. Internet rumor as play is consequence of collective framing constituted by dynamic interaction and playfulness. The networking space spreading internet rumor function as a playground which mobilize play rule, ignoring fact based framing. Rumor as paly, even though it turns out to be a false and loses the public attentions rumor sustains the game play function which makes the rumor without natural extinction. The study proves that playful mongers is a main actors in rumor play ground.