• International Journal of Fuzzy Logic and Intelligent Systems
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• v.3 no.1
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• pp.13-17
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• 2003

A continuous solution of the Dirichlet boundary value problem for the heat equation $u_t$＝$a2u_{xx}$ using a fuzzy system is described. We first apply the Crank-Nicolson method to obtain a discrete solution at the grid points for the heat equation. Then we find a continuous function to represent approximately the discrete values at the grid points in the form of a bicubic spline function (equation omitted) that can in turn be represented exactly by a fuzzy system. We show that the computed values at non-grid points using the bicubic spline function is much smaller than the ones obtained by linear interpolations of the values at the grid points. We also show that the fuzzy rule table in the fuzzy system representation of the bicubic spline function can be viewed as a gray scale image. Hence, the fuzzy rules provide a visual representation of the functions of two variables where the contours of different levels for the function are shown in different gray scale levels

• Journal of the Society of Naval Architects of Korea
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• v.28 no.1
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• pp.53-59
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• 1991

By employing multiple-scale expansion techniques, the diffraction of sinusoidally-modulated nonlinear Stokes waves by a stationary thin wedge has been studied within the framework of potential theory. It is found that the evolution of diffracted waves can be described by the Zakharov equation to the leading order and it can be replaced by the cubic $Schr\ddot{o}dinger$ equation with an additional linear term for stable modulations. Computations are made for the cubic $Schr\ddot{o}dinger$ equation with different values of nonlinear and dispersion parameters. Numerical results well reflect the experimental findings in the amplitude and width of generated stem waves. It is numerically confirmed that the nonlinearity dominates the wave field, while the dispersion hardly affects the wave evolution, and stem waves are likely to be formed for steep incident waves in the case of stable sinusoidal modulations.

• Transactions of the Korean Society of Automotive Engineers
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• v.9 no.1
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• pp.171-180
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• 2001

Collision accident reconstruction algorithm are developed based on the deformation shape and severity of a car body. At first, the body stiffness equation representing the force-deformation relationship is derived using finite element analysis for head on collision of two cars. The database of deformation shapes and energies is constructed for five different collision configurations; each configuration contains three velocity conditions. Deformation shapes are obtained using a curve fitting method and result in cubic polynomials. Deformation energies are calculated using a stiffness equation and deformation data. Three algorithms are developed to reconstruct collision configuration compared with constructed database. The developed algorithms show reasonably good performance to find collisions conditions for some test problems.

• Journal of computational fluids engineering
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• v.6 no.4
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• pp.1-7
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• 2001

Wind flow perturbations, recirculations and turbulence generated by buildings often dominate air pollutant distributions around buildings. This paper describes dispersion of contaminants in the vicinity of a building by solving the concentration equation based on previously simulated wind flow field. Turbulence closure is achieved by using the standard k-ε two-equation model. The paper shows application of the CIP method for solving a species concentration equation of contaminant gas around a rectangular building for two different sources under conditions of neutral atmospheric stratification. Results have been compared to the experimental data and the previous numerical results by hybrid scheme. The computational results of concentration profiles by the CIP method agree well with experimental data.

• Proceedings of the Korean Institute of Navigation and Port Research Conference
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• 2017.11a
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• pp.27-29
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• 2017

Container terminals in Northern Vietnam have recorded an impressive development in recent years. This development, however, also raises a fierce competition among local container terminals to attract customers. Beside the handling charges, the vessels' waiting cost is also an important factor that drive the opinion of users in choosing appropriate terminal. This research plans to estimate the waiting cost in different container terminals in Northern Vietnam by building regression equation that describe the relationship between the rate of throughput/capacity and waiting cost/TEU. Queuing theory with the application of Poisson distibution is used to estimate the waiting time of arrival vessels and uncertainty theory is applied to estimate the vessel's daily expenses. Previous studies suggested two different formation of the equation and according to the research results, cubic equation is more suitable in the given case. The research results are also useful for further research which require calculation of waiting cost per TEU in each container terminal in Northern Vietnam.

• Proceedings of the KSME Conference
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• 2001.11b
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• pp.723-728
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• 2001

Wind flow perturbations, recirculations and turbulence generated by buildings often dominate air pollutant distributions around buildings. This paper describes dispersion of contaminants in the vicinity of a building by solving the concentration equation based on previously simulated wind flow field. Turbulence closure is achieved by using the standard k-e two-equation model. The paper shows application of the CIP method for solving a species concentration equation of contaminant gas around a rectangular building for two different sources under conditions of neutral atmospheric stratification. Results have been compared to the experimental data and the previous numerical results by hybrid scheme. The computational results of concentration profiles by the CIP method agree well with experimental data.

• Structural Engineering and Mechanics
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• v.43 no.2
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• pp.211-223
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• 2012

This paper deals with large deformation post-buckling of a linear-elastic and hygrothermal beam with axially nonmovable pinned-pinned ends and subjected to a significant increase in swelling by an alternative method. Analytical approximate solutions for the geometrically nonlinear problem are presented. The solution for the limiting case of a string is also obtained. By coupling of the well-known Maclaurin series expansion and orthogonal Chebyshev polynomials, the governing differential equation with sinusoidal nonlinearity can be reduced to form a cubic-nonlinear equation, and supplementary condition with cosinoidal nonlinearity can also be simplified to be a polynomial integral equation. Analytical approximations to the resulting boundary condition problem are established by combining the Newton's method with the method of harmonic balance. Two approximate formulae for load along axis, potential strain for free hygrothermal expansion and periodic solution are established for small as well as large angle of rotation at the end of the beam. Illustrative examples are selected and compared to "reference" solution obtained by the shooting method to substantiate the accuracy and correctness of the approximate analytical approach.

• Economic and Environmental Geology
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• v.52 no.4
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• pp.291-297
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• 2019

Fluid flow through rock fractures has been quantified using equations such as Stokes equations, Reynolds equation (or local cubic law), cubic law, etc. derived from the Navier-Stokes equations under the assumption that linear flow prevails. Therefore, these simplified equations are limited to linear flow regime, and cause errors in nonlinear flow regime. In this study, causal mechanism of nonlinear flow and critical Reynolds number were presented by carrying out fluid flow modeling with both the Navier-Stokes equations and the Stokes equations for a three-dimensional rough-walled rock fracture. This study showed that flow regimes changed from linear to nonlinear at the Reynolds number greater than 10. This is because the inertial forces, proportional to the square of the fluid velocity, increased enough to overwhelm the viscous forces. This tendency was also shown for the unmated (slightly sheared) rock fracture. It was found that nonlinear flow was caused by the rapid increase in the inertial forces with increasing fluid velocity, not by the growing eddies that have been ascribed to nonlinear flow.

• East Asian mathematical journal
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• v.34 no.5
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• pp.693-702
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• 2018

In this paper, we consider the generalized Hyers-Ulam stability for the following additive-quadratic functional equation with involution $f(x+2y)-f(2x+y)+f(x+y)+f({\sigma}(x)+y)+f(x)-4f(y)-f({\sigma}(y))=0$ in non-Archimedean spaces.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.2 no.2
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• pp.21-25
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• 1998

An algorithm for a solution of ordinary differential equations using a modified corrector in the Adams predictor-corrector method of order four is described. The Lagrange interpolation used in the corrector of the Adams method is replaced partially by the cubic spline interpolation satisfying the first derivative constraints at the two end points. By exhibiting three examples, we show that the proposed method is more effcient when the solution of a differential equation is highly oscillating.