• Journal of Environmental Impact Assessment
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• v.16 no.5
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• pp.341-350
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• 2007

Lake Youngrang is a lagoon whose effluent flows into the East Sea. Because two resort towns and two golf courses are situated at the lake basin, many tourists visit this area. Stormwater runoff surveys were carried out for the eight storm events from 2004 to 2005 in the eutrophic lake watershed to give a basic data for the diffuse pollution control of the lake. Dimensionless mass-volume curves indicating the distribution of pollutant mass vs. volume were used to analyze the first flush phenomenon. The mass-volume curves were fitted with a power function and polynomial equation curves. The regression analysis showed that the polynomial equation curves were better than the power function in representing the tendency of the first flush, and second degree polynomial equation curves indicated the strength of the first flush effectively.

• 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.

• Communications of the Korean Mathematical Society
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• v.28 no.2
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• pp.209-224
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• 2013

The problem of finding rational or integral points of an elliptic curve basically boils down to solving a cubic equation. We look closely at the cubic formula of Cardano to find a criterion for a cubic polynomial to have a rational or integral roots. Also we show that existence of a rational root of a cubic polynomial implies existence of a solution for certain Diophantine equation. As an application we find some integral solutions of some special type for $y^2=x^3+b$.

• Honam Mathematical Journal
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• v.44 no.3
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• pp.391-401
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• 2022

In this study, we investigate the explicit characterization of spherical curves using the Flc (Frenet like curve) frame in Euclidean 3-space. Firstly, the axis of curvature and the osculating sphere of a polynomial space curve are calculated using Flc frame invariants. It is then shown that the axis of curvature is on a straight line. The position vector of a spherical curve is expressed with curvatures connected to the Flc frame. Finally, a differential equation is obtained from the third order, which characterizes a spherical curve.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.3
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• pp.529-531
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• 2011

We show that for all $N{\geq}1$, the modular function field $K(X_0^+(N))$ is generated by j(z)j(Nz) and j(z) + j(Nz) over ${\mathbb{C}}$, where j(z) is the modular invariant. Moreover we derive the defining equation of the the modular function field $K(X_0^+(N))$ from the classical modular polynomial ${\Phi}_N(X, Y )$.

• Structural Engineering and Mechanics
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• v.76 no.1
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• pp.129-139
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• 2020

In this piece of work, carbon nanotubes motion equations are framed by Kelvin's method. Employment of the Kelvin's method procedure gives birth to the tube frequency equation. It is also exhibited that the effect of frequencies is investigated by varying the different index of polynomial function. By using volume fraction for power law index, the fundamental natural frequency spectra for two forms of single-walled carbon nanotubes are calculated. The influence of frequencies against length-to-diameter ratios with varying power law index are investigated in detail for these tubes. Throughout the computation, it is observed that the frequency behavior for the boundary conditions follow as; clamped-clamped, simply supported-simply supported and these frequency curves are higher than that of clamped-free curves. Computer software MATLAB is utilized for the frequencies of single-walled carbon nanotubes.

• 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.

• Transactions of the Korean Society of Automotive Engineers
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• v.2 no.4
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• pp.59-71
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• 1994

A multi-polynomial method is proposed to synthesize DRRD cam profiles. A cam lift duration s divided into 10 sections, each of them is expressed by a polynomial equation. 12 design variables are extracted from the cam profile displacement, velocity, and acceleration curves. Because all the design variables have physical meanings which are familiar to most cam designers, it is easy to imagine a profile shape from the design variables. The design envelope of the method is wide enough to be used in DRRD automotive cam designs. Polydyne cams, widely used in automotive engines, are included into the envelope. Unlike Polydyne cams, the method provides capability of wide velocity factor variations, which gives much flexibility in flat-faced tappet design. Area factor of profiles designed by the method can be increased 5-10% compared to those of Polydyne cams without increasing acceleration factor. The method is especially useful for cam profile optimizations.

• IE interfaces
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• v.9 no.2
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• pp.119-128
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• 1996

A procedure is presented for a 3D-contour machining without cutter interferences. The 3D-contouring machining along a spatial curve is often required for manufacturing trimming and flange dies in motor industries. Input data for the machining contour is a spline curve with polynomial vector equation provided by CATIA system. Points are sampled on the contour curve and line segments and helical curves are approximated from the point data. Cutter interference is checked on the approximated spline and all of interference curves are substituted with interference-free helical curves for a tool path generation. The non-machined curve areas are locally machined by tools with smaller diameters. A tool radius offset is considered for generating NC data to be free with tool size.

• Journal of the Korean Mathematical Society
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• v.58 no.5
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• pp.1211-1226
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• 2021

The study of reducible Hilbert curves of conic fibrations over a smooth surface is carried on in this paper and the question of when the main component is itself the Hilbert curve of some ℚ-polarized surface is dealt with. Special attention is paid to the polynomial defining the canonical equation of the Hilbert curve.