• Journal of the Chungcheong Mathematical Society
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• v.24 no.2
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• pp.359-370
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• 2011

In this work, we obtain new solitary wave solutions for some nonlinear partial differential equations. The Jacobi elliptic function rational expansion method is used to establish new solitary wave solutions for the combined KdV-mKdV and Klein-Gordon equations. The results reveal that Jacobi elliptic function rational expansion method is very effective and powerful tool for solving nonlinear evolution equations arising in mathematical physics.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.11a
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• pp.287-292
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• 2005

This paper presents a rational polynomial approximation method to estimate modal parameters of wind excited structures using incomplete noisy measurements of structural responses and partial measurements of wind velocities only. A stochastic model of the excitation wind force acting on the structure is estimated from partial measurements of wind velocities. Then the transfer functions of the structure are approximated as rational polynomial functions. From the poles and zeros of the estimated rational polynomial functions, the modal parameters, such as natural frequencies, damping ratios, and mode shapes are extracted. Since the frequency characteristics of wind forces acting on structures can be assumed as a smooth Gaussian process especially around the natural frequencies of the structures according to the central limit theorem (Brillinger, 1969; Yaglom, 1987), the estimated modal parameters are robust and reliable with respect to the assumed stochastic input models. To verify the proposed method, the modal parameters of a TV transmission tower excited by gust wind are estimated. Comparison study with the results of other researchers shows the efficacy of the suggested method.

• Journal of Korea Water Resources Association
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• v.52 no.6
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• pp.411-420
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• 2019

The objective of this study is to evaluate the appropriateness of methodology for designing urban sewer system using a rational method-based model, Makesw and an urban runoff model, SWMM. The Gunja basin was selected as a study area and precipitation, runoff, vegetation, soil, imperviousness data were used to estimate floods. The appropriateness of methodology was evaluated based on comparison analysis between floods estimated from Makesw and SWMM. The comparison analysis was conducted between floods estimated from Makesw and SWMM, which were simulated using design rainfall and measured rainfall from past inundation events. The comparison results showed that in the case of design rainfall, the rational method-based floods were larger than that based on SWMM in all main lines. However in several branch lines, the rational method-based floods were smaller than thoes based on SWMM. In addition, for the case of measured rainfall from past inundation events, it was easily to find the main and branch lines where the rational method-based floods were smaller than SWMM based ones. Especially, the lines where rational method-based floods were underestimated, were mostly main, $1^{st}$, $2^{nd}$ lines. It was concluded that the rational method-based results were not conservative. Based on rational method (steady flow analysis) and SWMM (unsteady flow analysis), the more conservative results the method provides, the more highly it is recommended to use in designing an urban sewer system.

• Journal of electromagnetic engineering and science
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• v.6 no.3
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• pp.155-159
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• 2006

An efficient method is presented to design filters without the similarity transform of their coupling coefficient matrix as circuit parameters, which is very tedious due to pivoting and deciding rotation angles needed during the iterations. The transfer function of a filter is directly used for the design and its desired form is derived by the optimized rational-function fitting technique. A 3rd order coaxial lowpass filter is taken as an example to validate the proposed method.

• Korea-Australia Rheology Journal
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• v.15 no.3
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• pp.131-150
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• 2003

A new numerical algorithm of finite element methods is presented to solve high Deborah number flow problems with geometric singularities. The steady inertialess planar 4 : 1 contraction flow is chosen for its test. As a viscoelastic constitutive equation, we have applied the globally stable (dissipative and Hadamard stable) Leonov model that can also properly accommodate important nonlinear viscoelastic phenomena. The streamline upwinding method with discrete elastic-viscous stress splitting is incorporated. New interpolation functions classified as rational interpolation, an alternative formalism to enhance numerical convergence at high Deborah number, are implemented not for the whole set of finite elements but for a few elements attached to the entrance comer, where stress singularity seems to exist. The rational interpolation scheme contains one arbitrary parameter b that controls the singular behavior of the rational functions, and its value is specified to yield the best stabilization effect. The new interpolation method raises the limit of Deborah number by 2∼5 times. Therefore on average, we can obtain convergent solution up to the Deborah number of 200 for which the comer vortex size reaches 1.6 times of the half width of the upstream reservoir. Examining spatial violation of the positive definiteness of the elastic strain tensor, we conjecture that the stabilization effect results from the peculiar behavior of rational functions identified as steep gradient on one domain boundary and linear slope on the other. Whereas the rational interpolation of both elastic strain and velocity distorts solutions significantly, it is shown that the variation of solutions incurred by rational interpolation only of the elastic strain is almost negligible. It is also verified that the rational interpolation deteriorates speed of convergence with respect to mesh refinement.

• East Asian mathematical journal
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• v.28 no.2
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• pp.135-158
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• 2012

The ideals of the rings of integers are used to induce rational number system as operators(=group homomorphisms). We modify this inducing method to be effective in teaching rational numbers in secondary school. Indeed, this modification provides a nice model for explaining the equality property to define addition and multiplication of rational numbers. Also this will give some explicit ideas for students to understand the concept of 'field' efficiently comparing with the integer number system.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.31 no.6_2
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• pp.577-583
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• 2013

Recently, massive archives of ground information imagery from new sensors have become available. To establish a functional relationship between the image and the ground space, sensor models are required. The rational functional model (RFM), which is used as an alternative to the rigorous sensor model, is an attractive option owing to its generality and simplicity. To determine the rational polynomial coefficients (RPC) in RFM, however, we encounter the problem of obtaining a stable solution. The design matrix for solutions is usually ill-conditioned in the experiments. To solve this unstable solution problem, regularization techniques are generally used. In this paper, we describe the effective determination of the optimal regularization parameter in the regularization technique during RPC derivation. A brief mathematical background of RFM is presented, followed by numerical approaches for effective determination of the optimal regularization parameter using the Euler Method. Experiments are performed assuming that a tilted aerial image is taken with a known rigorous sensor. To show the effectiveness, calculation time and RMSE between L-curve method and proposed method is compared.

• Structural Engineering and Mechanics
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• v.51 no.6
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• pp.923-937
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• 2014

The rational finite element method is different from the standard finite element method, which is constructed using basic solutions of the governing differential equations as interpolation functions in the elements. Therefore, it is superior to the isoparametric approach because of its obvious physical meaning and accuracy; it has successfully been applied to the isotropic elasticity problem. In this paper, the formulation of rational finite elements for plane orthotropic elasticity problems is deduced. This method is formulated directly in the physical domain with full consideration of the requirements of the patch test. Based on the number of element nodes and the interpolation functions, different approaches are applied with complete polynomial interpolation functions. Then, two special stiffness matrixes of elements with four and five nodes are deduced as a representative application. In addition, some typical numerical examples are considered to evaluate the performance of the elements. The numerical results demonstrate that the present method has a high level of accuracy and is an effective technique for solving plane orthotropic elasticity problems.

• Journal of computational fluids engineering
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• v.12 no.3
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• pp.20-28
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• 2007

A fast and robust method of grid generation to multiple functions has been developed for flow analysis in three dimensional space. It is based on the Non-Uniform Rational B-Spline(NURBS) of an approximation method. Many of NURBS intrinsic properties are introduced and much more easily understood. The grid generation method, details of numerical implementation. examples of application, and potential extensions of the current method are illustrated in this paper. The object of this study is to develop the surface grid generation and the grid cluster techniques capable of resolving complex flows with shock waves, expansion waves, shear layers. The knot insert method of Non-Uniform Rational B-Spline seems well worked. In addition, NURBS has been widely utilized to generate grids in the computational fluid dynamics community. Computational examples associated with practical configurations have shown the utilization of the algorithm.

• Journal of the Korean Society of Hazard Mitigation
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• v.7 no.4
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• pp.67-74
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• 2007

Rational method has been widely used to calculate peak runoff drainage design or small watershed because of simplicity and convenience. Runoff coefficient(C) is the most important parameter in the rational method which varies according to rainfall intensity, return period, rainfall duration time and soil characteristics. In practice, constant which is value of C in rational formula has been used from the table, originally based on ASCE. These table value does not consider the upper conditions of the depending factors, hence peak runoff calculation could be in correct. Therefore to calculate C in this paper we have devised an improved formula, considering relationship with rainfall duration, return period and CN of NRCS method. This formula is considered to be more reliable and helpful to the hydrologists and engineers to predict correct peak runoff.