• Journal of the Korean Mathematical Society
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• v.42 no.2
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• pp.335-351
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• 2005

This paper concerns the relation between the degree and the projective dimension of linear systems on curves. We generalize Clifford's theorem and its improvement by Coppens and G. Martens and classify the special curves for our problem, and estimate their gonality.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.4 no.1
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• pp.23-28
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• 2000

We compute the order of jacobian groups of hyperelliptic curves on a finite field of characteristic 3 and we determine which curves are secure against known attacks.

• Korean Journal of Mathematics
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• v.21 no.3
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• pp.305-309
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• 2013

In this paper, we give a new method to get defining equations of modular curves $X_1(2N)$ which show the moduli problems.

• Bulletin of the Korean Mathematical Society
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• v.32 no.2
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• pp.349-357
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• 1995

In the theory of elliptic curves over a complete field with bad reduction (i.e. with nonintegral j-invariant) Tate elliptic curves play an important role. Likewise, in the theory of Drinfeld modules, Tate-Drinfeld modules replace Tate elliptic curves.

• The Pure and Applied Mathematics
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• v.14 no.4
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• pp.231-253
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• 2007

The purpose of this paper is to study the geometry of null curves in a semi-Riemannian manifold (M, g) of index 2. We show that it is possible to construct new Frenet equations of two types of null curves in M.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.3
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• pp.299-307
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• 2009

We count the isomorphism classes of elliptic curves over finite fields $\mathbb{F}_{3^{n}}$ and list a representative of each isomorphism class. Also we give the number of rational points for each supersingular elliptic curve over $\mathbb{F}_{3^{n}}$.

• Journal of the Korean Mathematical Society
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• v.45 no.2
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• pp.393-404
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• 2008

Biharmonic Legendre curves in a Sasakian space form are studied. A non-existence result in a 7-dimensional 3-Sasakian manifold is obtained. Explicit formulas for some biharmonic Legendre curves in the 7-sphere are given.

• Journal of Integrative Natural Science
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• v.4 no.4
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• pp.289-293
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• 2011

In this paper we obtain some Sobolev estimates for the integral operator over singular curves (t, $t^m$) on $\mathbb{R}^2$ for $m{\geq}2$.

• The Pure and Applied Mathematics
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• v.12 no.3 s.29
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• pp.211-221
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• 2005

The purpose of this paper is to study the geometry of null curves in a Lorentzian manifold (M, g). We show that it is possible to construct new type of Frenet equations of null curves in M, supported by two examples.

• Bulletin of the Korean Mathematical Society
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• v.35 no.1
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• pp.149-156
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• 1998

We relate the existence of rational curves with the existence of rigid bundles of any even rank on Enriques surfaces and compare with the case of K3 surfaces.