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Vol.12 No.3

Lee, Jun-Ik pp.161-167
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Abstract

In this note we consider the projective property <TEX>$\sigma(Re(T))\;=\;Re\;(\sigma$(T))$</TEX> of p-hyponormal operators and log-hyponormal operators.

NAM HEE-SEOK pp.169-178
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Abstract

In this paper we study the existence and local asymptotic limit of the topological Chern-Simons vortices of the CP(1) model in <TEX>$\mathbb{R}^2$</TEX>. After reducing to semilinear elliptic partial differential equations, we show the existence of topological solutions using iteration and variational arguments & prove that there is a sequence of topological solutions which converges locally uniformly to a constant as the Chern­Simons coupling constant goes to zero and the convergence is exponentially fast.

CHOE KWANGSEOK ; NAM HEE-SEOK pp.179-191
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Abstract

In this paper we consider a Dirichlet problem in the unit disk. We show that the equation has a unique or multiple solutions according to the range of the parameter. Moreover, we prove that the equation admits a nonradial bifurcation at each branch of radial solutions.

Hur, Kul ; Jang, Su-Youn ; Kang, Hee-Won pp.193-209
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Abstract

We introduce the notions of intuitionistic fuzzy prime ideals, intuitionistic fuzzy completely prime ideals and intuitionistic fuzzy weakly completely prime ideals. And we give a characterization of intuitionistic fuzzy ideals and establish relationships between intuitionistic fuzzy completely prime ideals and intuitionistic fuzzy weakly completely prime ideals.

JIN, Dae-Ho pp.211-221
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Abstract

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.

CHOI JUNESANG ; HARSH HARSHVARDHAN ; RATHIE ARJUN K. pp.223-228
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Abstract

In 2001, Choi, Harsh & Rathie [Some summation formulas for the Appell's function <TEX>$F_1$</TEX>. East Asian Math. J. 17 (2001), 233-237] have obtained 11 results for the Appell's function <TEX>$F_1$</TEX> with the help of Gauss's summation theorem and generalized Kummer's summation theorem. We aim at presenting 22 more results for <TEX>$F_1$</TEX> with the help of the generalized Gauss's second summation theorem and generalized Bailey's theorem obtained by Lavoie, Grondin & Rathie [Generalizations of Whipple's theorem on the sum of a <TEX>$_3F_2$</TEX>. J. Comput. Appl. Math. 72 (1996), 293-300]. Two interesting (presumably) new special cases of our results for <TEX>$F_1$</TEX> are also explicitly pointed out.

KIM SEONG-A pp.229-235
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Abstract

The notions of spherically concave functions defined on a subregion of the Riemann sphere P are introduced in different ways in Kim & Minda [The hyperbolic metric and spherically convex regions. J. Math. Kyoto Univ. 41 (2001), 297-314] and Kim & Sugawa [Charaterizations of hyperbolically convex regions. J. Math. Anal. Appl. 309 (2005), 37-51]. We show continuity of the concave function defined in the latter and show that the two notions of the concavity are equivalent for a function of class <TEX>$C^2$</TEX>. Moreover, we find more characterizations for spherically concave functions.

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics