• Journal of Industrial Technology
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• v.22 no.B
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• pp.231-240
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• 2002

The rational method of estimating peak flow is used largely for the simplicity. But the accuracy of rational method is not easy to estimate, because the rational method is analyzed by the deterministic point or view and the runoff coefficients of the rational method are proposed from other countries. In this study the rational method is analyzed by the probabilistic way to be a more reliable method. The runoff coefficient is regarded to parameter that changes the probabilistic rainfall to the peak flow. The runoff coeffient for each return period is analyzed to be a reliable index which is used to estimate the peak flow of ungauged natural catchments.

• Wind and Structures
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• v.16 no.6
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• pp.561-577
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• 2013

Rational Functions are used to express the self-excited aerodynamic forces acting on a flexible structure for use in time-domain flutter analysis. The Rational Function Approximation (RFA) approach involves obtaining of these Rational Functions from the frequency-dependent flutter derivatives by using an approximation. In the past, an algorithm was developed to directly extract these Rational Functions from wind tunnel section model tests in free vibration. In this paper, an algorithm is presented for direct extraction of these Rational Functions from section model tests in forced vibration. The motivation for using forced-vibration method came from the potential use of these Rational Functions to predict aerodynamic loads and response of flexible structures at high wind speeds and in turbulent wind environment. Numerical tests were performed to verify the robustness and performance of the algorithm under different noise levels that are expected in wind tunnel data. Wind tunnel tests in one degree-of-freedom (vertical/torsional) forced vibration were performed on a streamlined bridge deck section model whose Rational Functions were compared with those obtained by free vibration for the same model.

• Bulletin of the Korean Mathematical Society
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• v.44 no.1
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• pp.13-29
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• 2007

In this paper, we first present a method for finding the implicit equation of the curve given by rational parametric equations. The method is based on the computation of $Gr\"{o}bner$ bases. Then, another method for implicitization of curve and surface is given. In the case of rational curves, the method proceeds via giving the implicit polynomial f with indeterminate coefficients, substituting the rational expressions for the given curve and surface into the implicit polynomial to yield a rational expression $\frac{g}{h}$ in the parameters. Equating coefficients of g in terms of parameters to 0 to get a system of linear equations in the indeterminate coefficients of polynomial f, and finally solving the linear system, we get all the coefficients of f, and thus we obtain the corresponding implicit equation. In the case of polynomial surfaces, we can similarly as in the case of rational curves obtain its implicit equation. This method is based on characteristic set theory. Some examples will show that our methods are efficient.

• Journal of Institute of Control, Robotics and Systems
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• v.17 no.8
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• pp.768-776
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• 2011

This paper considers a data fitting problem for rational function models using the LM (Levenberg-Marquardt) optimization method. Rational function models have various merits on representing a wide range of shapes and modeling complicated structures by polynomials of low degrees in both the numerator and denominator. However, rational functions are nonlinear in the parameter vector, thereby requiring nonlinear optimization methods to solve the fitting problem. In this paper, we propose a data fitting method for rational function models based on the LM algorithm which is renowned as an effective nonlinear optimization technique. Simulations show that the fitting results are robust against the measurement noises and uncertainties. The effectiveness of the proposed method is further demonstrated by the real application to a 3D depth camera calibration problem.

• Journal of Korea Society of Digital Industry and Information Management
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• v.7 no.4
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• pp.133-139
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• 2011

In this paper, we propose a hybrid filter for noise reduction. The proposed method adjusts rational filtering direction according to an edge in the image using median filtered data. Rational filter modulates the coefficients of a linear lowpass filter to limit its action in presence of image details. By the ratio of polynomials in the input variables, rational filter reduces noise adaptively. Median filter is widely used to reduce impulse noise, but removes some details for highly corrupted images. Also, desirable details are removed when the window size is large. Our proposed algorithm combines rational filter and median filter. Thus, proposed method not only preserves edge, but also reduces noise in uniform region. Experimental results show that our proposed method has better quality than those by existing median and rational filtering methods.

• Journal of Korea Society of Digital Industry and Information Management
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• v.8 no.3
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• pp.41-48
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• 2012

In this paper, we propose a method of edge detection for noisy image. The proposed method uses a progressive filter for noise reduction and a Sobel operator for edge detection. The progressive filter combines a median filter and a modified rational filter. The proposed method for noise reduction adjusts rational filter direction according to an edge in the image which is obtained by median filtering. Our method effectively attenuates the noise while preserving the image details. Edge detection is performed by a Sobel operator. This operator can be implemented by integer operation and is therefore relatively fast. Our proposed method not only preserves edge, but also reduces noise in uniform region. Thus, edge detection is well performed. Our proposed method could improve results using further developed Sobel operator. Experimental results show that our proposed method has better edge detection with correct positions than those by existing median and rational filtering methods for noisy image.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.241-251
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• 2005

In this paper, we introduce a new algebraic method to characterize rational PH plane curves. And using this method, we study the algebraic characterization of generic strongly regular rational plane PH curves expressed in the complex formalism which is introduced by R.T. Farouki. We prove that generic strongly semi-regular rational PH plane curves are completely characterized by solving a simple functional equation H(f, g) = $h^2$ where h is a complex polynomial and H is a bi-linear operator defined by H(f, g) = f'g - fg' for complex polynomials f,g.

• Kyungpook Mathematical Journal
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• v.52 no.3
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• pp.347-357
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• 2012

When Newton's method, or Halley's method is used to approximate the pth root of 1-z, a sequence of rational functions is obtained. In this paper, a beautiful formula for these rational functions is proved in the square root case, using an interesting link to Chebyshev's polynomials. It allows the determination of the sign of the coefficients of the power series expansion of these rational functions. This answers positively the square root case of a proposed conjecture by Guo(2010).

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.159-169
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• 2005

An algorithmic approach to degree reduction of rational Bezier curves is presented. The algorithms are based on the degree reduction of polynomial Bezier curves. The method is introduced with the following steps: (a) convert the rational Bezier curve to polynomial Bezier curve by using homogenous coordinates, (b) reduce the degree of polynomial Bezier curve, (c) determine weights of degree reduced curve, (d) convert the Bezier curve obtained through step (b) to rational Bezier curve with weights in step (c).

• The Pure and Applied Mathematics
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• v.30 no.4
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• pp.347-355
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• 2023

For numerical evaluation of Cauchy principal value integrals, we present a simple rational function with a parameter satisfying some reasonable conditions. The proposed rational function is employed in coordinate transformation for accelerating the accuracy of the Gauss quadrature rule. The efficiency of the proposed rational transformation method is demonstrated by the numerical result of a selected test example.