• Honam Mathematical Journal
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• v.20 no.1
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• pp.89-95
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• 1998

We show by using some properties of an elliptic integral that certain scalar semilinear elliptic problem has a unique solution.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.21 no.3
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• pp.167-180
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• 2017

According to the fact that the low convergence level of the complete elliptic integral of the first kind for the modulus which having values approach to one. In this paper we propose novelty of the complete elliptic integral which having new infinite series that consists of new modulus introduced as own modulus function. We apply scheme of iteration by substituting the common modulus with own modulus function into the new infinite series. We obtained so many new exact formulas of the complete elliptic integral derived from this method correspond to the number of iterations. On the other hand, it has been also obtained a lot of new transformation functions with the corresponding own modulus functions. The calculation results show that the enhancement of the number of significant figures of the new infinite series of the complete elliptic integral of the first kind corresponds to the level of quadratic convergence.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.4
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• pp.763-769
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• 2014

In this paper, we illustrate a counter example for the converse of a certain conjecture proposed by De Giorgi. De Giorgi suggested a series of conjectures, in which a certain integral condition for singularity or degeneracy of an elliptic operator is satisfied, the solutions are continuous. We construct some singular elliptic operators and solutions such that the integral condition does not hold, but the solutions are continuous.

• 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 $y^2=x^3+b$.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2001.10a
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• pp.163-169
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• 2001

The solution of two-dimensional deflection of circular wavy reinforcing fiber elastics was obtained for one end clamped boundary under concentrated load condition. The fiber was regarded as a linear elastic material. Wavy shape was described as a combination of half-circular arc smoothly connected each other with constant curvature of all the same magnitude and alternative sign. Also load direction was taken into account. As a result, the solution was expressed in terms of a series of elliptic integrals. These elliptic integrals had two different transformed parameters involved with load value and initial radius of curvature. While we found the exact solutions and expressed them in terms of elliptic integrals, the recursive ignition formulae about the displacement and arc length at each segment of circular section were obtained. Algorithm of determining unknown parameters was established and the profile curve of deflected beam was shown in comparison with initial shape.

• Journal of the Society of Naval Architects of Korea
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• v.41 no.4
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• pp.38-44
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• 2004

The motion response analysis of a submerged elliptic cylinder in waves is presented and the elliptic cylinder is a simplification of the section of submarine in this paper. The method is based on boundary integral method and two-dimensional 3 degree motions are calculated in regular harmonic waves. The fully nonlinear free surface boundary condition is assumed in an numerical domain and this solution is matched along an assumed boundary as a linear solution composed of transient Green function, The large amplitude motions of an elliptic cylinder are directly simulated and effects of wave frequency, wave amplitude and the distance from buoyancy center to gravity center are discussed.

• Journal of electromagnetic engineering and science
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• v.4 no.3
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• pp.102-106
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• 2004

A novel Genetic Algorithm(GA)-based method is suggested to transform a coupling matrix to another, without the procedure of Matrix Rotation. This can remove tedious work like pivoting and deciding rotation angles needed for each of the iterations. The error function for the GA is simply formed and used as part of error minimization for obtaining the solution. An 8th order dual-mode elliptic integral function response filter is taken as an example to validate the present method.

• Communications of the Korean Mathematical Society
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• v.27 no.3
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• pp.497-503
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• 2012

In this paper, we study elliptic curves E over $\mathbb{Q}$ such that the 3-torsion subgroup E[3] is split as ${\mu}_3{\oplus}\mathbb{Z}/3{\mathbb{Z}}$. For a non-zero intege $m$, let $C_m$ denote the curve $x^3+y^3=m$. We consider the relation between the set of integral points of $C_m$ and the elliptic curves E with $E[3]{\simeq}{\mu}_3{\oplus}\mathbb{Z}/3{\mathbb{Z}}$.

• Journal for History of Mathematics
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• v.28 no.2
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• pp.85-102
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• 2015

Elliptic curves are a common theme among various fields of mathematics, such as number theory, algebraic geometry, complex analysis, cryptography, and mathematical physics. In the history of elliptic curves, we can find number theoretic problems on the one hand, and complex function theoretic ones on the other. The elliptic curve theory is a synthesis of those two indeed. As an overview of the history of elliptic curves, we survey the Diophantine equations of 3rd degree and the congruent number problem as some of number theoretic trails of elliptic curves. We discuss elliptic integrals and elliptic functions, from which we get a glimpse of idea where the name 'elliptic curve' came from. We explain how the solution of Diophantine equations of 3rd degree and elliptic functions are related. Finally we outline the BSD conjecture, one of the 7 millennium problems proposed by the Clay Math Institute, as an important problem concerning elliptic curves.

• Kyungpook Mathematical Journal
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• v.46 no.1
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• pp.65-77
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• 2006

By using general means, some oscillation criteria for second order nonlinear elliptic differential equation with damping $$\sum_{i,j=1}^{N}D_i[a_{ij}(x)D_iy]+\sum_{i=1}^{N}b_i(x)D_iy+p(x)f(y)=0$$ are obtained. These criteria are of a high degree of generality and extend the oscillation theorems for second order linear ordinary differential equations due to Kamenev, Philos and Wong.