• Nuclear Engineering and Technology
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• v.55 no.6
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• pp.2305-2314
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• 2023

The governing equations of atmospheric dispersion most often taking the form of a second-order partial differential equation (PDE). Currently, typical computational codes for predicting atmospheric dispersion use the Gaussian plume model that is an analytic solution. A Gaussian model is simple and enables rapid simulations, but it can be difficult to apply to situations with complex model parameters. Recently, a method of solving PDEs using artificial neural networks called physics-informed neural network (PINN) has been proposed. The PINN assumes the latent (hidden) solution of a PDE as an arbitrary neural network model and approximates the solution by optimizing the model. Unlike a Gaussian model, the PINN is intuitive in that it does not require special assumptions and uses the original equation without modifications. In this paper, we describe an approach to atmospheric dispersion modeling using the PINN and show its applicability through simple case studies. The results are compared with analytic and fundamental numerical methods to assess the accuracy and other features. The proposed PINN approximates the solution with reasonable accuracy. Considering that its procedure is divided into training and prediction steps, the PINN also offers the advantage of rapid simulations once the training is over.

• Journal of Institute of Control, Robotics and Systems
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• v.19 no.6
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• pp.563-568
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• 2013

The purpose of this study is to find the analytic solution for determining the optimal capacity (lot-size) of a batch-storage network to meet the finished product demand under infrequent shutdowns. Batch processes are bound to experience random but infrequent operating time losses. Two common remedies for these failures are duplicating another process or increasing the process and storage capacity, both of which are very costly in modern manufacturing systems. An optimization model minimizing the total cost composed of setup and inventory holding costs as well as the capital costs of constructing processes and storage units is pursued with the framework of a batch-storage network of which flows are susceptible to infrequent shutdowns. The superstructure of the plant consists of a network of serially and/or parallel interlinked batch processes and storage units. The processes transform a set of feedstock materials into another set of products with constant conversion factors.A novel production and inventory analysis method, the PSW (Periodic Square Wave) model, is applied. The advantage of the PSW model stems from the fact it provides a set of simple analytic solutions in spite of a realistic description of the material flow between processes and storage units. The resulting simple analytic solution can greatly enhance a proper and quick investment decision at the early plant design stagewhen confronted with diverse economic situations.

• Bulletin of the Korean Mathematical Society
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• v.55 no.1
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• pp.319-330
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• 2018

This paper is concerned with the global asymptotic stability of strong solutions for a class of semilinear evolution equations with nonlocal initial conditions on infinite interval. The discussion is based on analytic semigroups theory and the gradually regularization method. The results obtained in this paper improve and extend some related conclusions on this topic.

• Proceedings of the Korea Air Pollution Research Association Conference
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• 2001.11a
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• pp.389-390
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• 2001

Deposition of polydisperse aerosols by Brownian diffusion was studied analytically using the penetration efficiency of monodisperse aerosols combined with the correlations among the moments of lognormal distribution functions. The analytic solutions so obtained were validated using the exact solution were applied to recalculate the filtration efficiencies of the existing experimental data for various filtration conditions. (omitted)

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.22 no.4
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• pp.289-294
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• 2018

In this work, a recently developed semi-analytic technique, so called the residual power series method, is generalized to process higher-dimensional linear and nonlinear partial differential equations. The solutions obtained takes a form of an infinite power series which can, in turn, be expressed in a closed exact form. The results reveal that the proposed generalization is very effective, convenient and simple. This is achieved by handling the (m+1)-dimensional Burgers equation.

• Korean Journal of Mathematics
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• v.31 no.4
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• pp.433-444
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• 2023

Given a function f analytic in open disk centred at origin of radius unity and satisfying the condition |f(z)/g(z) - 1| < 1 for a analytic function g with certain prescribed conditions in the unit disk, radii constants R are determined for the values of Rzf'(Rz)/f(Rz) to lie inside the domain enclosed by the curve |w² - 1| = 1 (lemniscate of Bernoulli). This, in turn, provides a partial solution to the conjectures and problems for determination of sharp bounds R for such functions f.

• Journal of the Institute of Electronics and Information Engineers
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• v.51 no.1
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• pp.225-232
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• 2014

Optical parametric amplification has been analyzed for the Cerenkov-idler configuration in planar waveguides. The coupled-mode theory is employed for the analysis. The coupled-mode equations are derived and the approximate analytic solution is obtained for no pump depletion. From the analytic solution, it is shown that the signal power gain can be enhanced as the Cerenkov radiation angle of the idler approaches to zero. The numerical example is also shown for the effect of the Cerenkov radiation angle approaching zero.

• Journal of the Korean Mathematical Society
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• v.37 no.6
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• pp.1071-1084
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• 2000

We show that a weak solution of the Cauchy problem for he nonlinear Schrodinger equation, {i∂(sub)t u + ∂$^2$(sub)x u = f(u,u), t∈(-T,T), x∈R, u(0,x) = ø(x).} in the negative solbolev space H(sup)s has a smoothing effect up to real analyticity if the initial data only have a single point singularity such as the Dirac delta measure. It is shown that for H(sup)s (R)(s>-3/4) data satisfying the condition (※Equations, See Full-text) the solution is analytic in both space and time variable. The argument is based on the recent progress on the well-posedness result by Bourgain [2] and Kenig-Ponce-Vega [18] and previous work by Kato-Ogawa [12]. We give an improved new argument in the regularity argument.

• Journal of Korean Society for Atmospheric Environment
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• v.18 no.5
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• pp.345-353
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• 2002

A study of polydispersed aerosol dynamics by Electrostatic Precipitator (ESP) was carried out. The log-normal particle size distribution was assumed and moment method was considered. In order to apply moment method in Deutsch-Anderson equation, Cunningham slip correction factor and Cochet's charge equation were simplified for certain range of particle size. The three parameters, which explain the particle size distribution, such as total number concentration, geometric mean diameter, and geometric standard deviation were considered to derive the analytic solution. The obtained solution was compared with available numerical results (Bai et al., 1995). The comparison of the numerical and analytic results showed a good agreement.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.14 no.3
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• pp.254-260
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• 2002

There have been many studies for the flow through internally finned tube, since the heat exchangers with fin device derive much attention in heat transfer enhance cent. In this study, analysis of laminar flow through the circular tube with longitudinal fins are investigated. The height and the number of fins are arbitrary. The flow field is assumed to be laminar and conformal mapping is used to obtain analytic solution. From the analytic solution, equi-velocity lines are shown, and the flow rate through the finned tube is calculated for various fin heights and numbers of fins. Darcy friction factor for this finned tube and shear stress distributions on the wall and fin are also considered.