• 충청수학회지
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• 제24권2호
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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.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2005년도 추계학술대회논문집
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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.

• 한국수자원학회논문집
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• 제52권6호
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• pp.411-420
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• 2019

본 연구의 목적은 합리식 기반의 하수관거 설계모델 Makesw와 도시유출해석모델 SWMM을 활용한 국내 하수관거 설계 방법의 적정성 평가를 수행하는 것이다. 대상유역으로는 군자배수구역을 선정하였으며, 강수량, 유량, 토지피복도, 토양도, 불투수도, 수치지형도의 자료를 수집하여 홍수량 산정에 활용하였다. 적정성 평가는 SWMM 기반 홍수량을 기초로 Makesw 기반 홍수량과 비교하여 수행하였다. 홍수량 비교분석은 설계강우와 실제 침수강우사상 기반의 Makesw와 SWMM의 홍수량에 대하여 수행하였다. 설계강우 기반 홍수량 비교 결과 유역의 간선에서는 합리식 설계홍수량이 SWMM 설계홍수량보다 과대모의 하였으나, 유역 내 지선에서는 합리식 설계홍수량이 과소모의되는 관거가 다수 나타났다. 또한 실제 침수사상 적용 결과, 간선 및 지선에서 합리식 모델의 홍수량이 SWMM의 홍수량보다 과소모의되는 관거가 다수 발견되었다. 특히, 유역 중심에 위치하는 간선, 1차 2차지선에서 유량 차이가 큰 관거가 집중되었다. 따라서 합리식 설계방법은 보수적인 설계방법이라고 말하기 어려우며, 하수관거 설계시 정상류해석 방법인 합리식과 부정류 해석방법인 SWMM을 활용한 설계를 병행하고 안정적인 해석결과를 활용하여 설계를 할 필요가 있다.

• Journal of electromagnetic engineering and science
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• 제6권3호
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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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• 제15권3호
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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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• 제28권2호
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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.

• 한국측량학회지
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• 제31권6_2호
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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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• 제51권6호
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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.

• 한국전산유체공학회지
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• 제12권3호
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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.

• 한국방재학회 논문집
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• 제7권4호
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• pp.67-74
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• 2007

합리식은 구조가 간단하고 사용하기 편리하기 때문에 소배수유역의 우수관거 설계에 가장 많이 사용되고 있다. 합리식을 이용한 유출해석에서 가장 중요한 요소인 유출계수 값은 강우강도, 재현기간, 강우의 지속시간, 지표특성 등에 따라 달라지지만 토지이용도에 따라 제시된 일정한 값을 그대로 사용하고 있다. 그러므로 실무자들이 합리식을 이용하여 우수관거 설계를 위한 적정 설계홍수량 산정을 위해서는 유출계수에 영향을 미치는 중요한 인자들을 고려한 통합유출계수의 산정이 필수적이다. 따라서 본 연구에서는 합리식에 대한 기본이론을 검토하고 유출계수에 영향을 미치는 주요인자와 유출과의 관계를 연구하여 합리식에서의 유출계수(C)와 강우지속시간, 재현기간(T) 및 NRCS(Natural Resources Conservation Service)방법에서 CN(유출곡선지수)와의 관계를 연구하여 보다 합리적으로 유출계수를 산정할 수 있도록 하였다.