• Journal of the Korean Mathematical Society
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• v.60 no.5
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• pp.987-998
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• 2023

It is shown that every continuum-wise expansive C¹ generic vector field X on a compact connected smooth manifold M satisfies Axiom A and has no cycles, and every continuum-wise expansive homoclinic class of a C¹ generic vector field X on a compact connected smooth manifold M is hyperbolic. Moreover, every continuum-wise expansive C¹ generic divergence-free vector field X on a compact connected smooth manifold M is Anosov.

• Journal of the Korean Mathematical Society
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• v.55 no.2
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• pp.343-372
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• 2018

Let K be an imaginary quadratic field with ring of integers ${\mathcal{O}}_K$. Let E be an elliptic curve with complex multiplication by ${\mathcal{O}}_K$, and let $h_E$ be the Weber function on E. Let $N{\in}\{2,3,4,6\}$. We show that $h_E$ alone when evaluated at a certain N-torsion point on E generates the ray class field of K modulo $N{\mathcal{O}}_K$. This would be a partial answer to the question raised by Hasse and Ramachandra.

• Journal of the Korean Mathematical Society
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• v.52 no.5
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• pp.907-928
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• 2015

We show in many cases that the Siegel-Ramachandra invariants generate the ray class fields over imaginary quadratic fields. As its application we revisit the class number one problem done by Heegner and Stark, and present a new proof by making use of inequality argument together with Shimura's reciprocity law.

• Communications of the Korean Mathematical Society
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• v.12 no.1
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• pp.37-43
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• 1997

Some formulas of the genus numbers and the ambiguous ideal class numbers of function fields are given and these numbers are shown to be the same when the extension is cyclic.

• Korean Journal of Mathematics
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• v.24 no.4
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• pp.601-612
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• 2016

In this paper we obtain average of class numbers of some family of Artin-Schreier extensions of rational function field ${\mathbb{F}}_q(t)$, where q is a power of 3.

• Communications of the Korean Mathematical Society
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• v.22 no.2
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• pp.163-171
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• 2007

In this paper, we determine all subfields of cyclotomic function fields with divisor class number two. We also give the generators of such fields explicitly.

• Communications of the Korean Mathematical Society
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• v.27 no.2
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• pp.223-231
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• 2012

We obtain some density results for the 4-ranks of class groups of quadratic extensions of quadratic function fields analogous to those results of F. Gerth in the classical case.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.1
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• pp.17-23
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• 2009

Let F be a finite real abelian extension of a global function field k with G = Gal(F/k). Assume that F is an extension field of the Hilbert class field $K_e$ of k and is contained in a cyclotomic function field $K_n$. Let $\ell$ be any prime number not dividing $ph_k{\mid}G{\mid}$. In this paper, we show that if $\theta{\in}\mathbb{Z}[G]$ annihilates the Sylow $\ell$-subgroup of ${\mathcal{O}}^{\times}_F/{\mathcal{C}}_F$, then (q-1)$\theta$ annihilates the Sylow $\ell$-subgroup of ${\mathcal{Cl}}_F$.

• Proceedings of the KSME Conference
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• 2001.06d
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• pp.744-750
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• 2001

In now a days, the concern to environment and energy saving problem is increased worldly. So many countries are developing the wind power system as clean energy system. In our country, Cheju local government has the plan of the Cheju Island wind farm and 600kW class 2 wind turbines, 660kW class 2 turbines, 225kW class 1 turbine and 750kW class 2 turbines has been operated at Hangwon. In this paper the field operation data of the wind turbines was analyzed and was compared with the characteristics & performance of each turbines. As the results, we would find the possibility of wind turbine in domestic and suggest the direction of developing technology.

• Honam Mathematical Journal
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• v.26 no.4
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• pp.509-532
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• 2004

Lower dimensional cases of Einstein's connection were already investigated by many authors for n = 2, 3, 4, 5, 6, 7. This paper is the first part of the following series of two papers, in which we obtain a surveyable tensorial representation of 8-dimensional Einstein's connection in terms of the unified field tensor, with main emphasis on the derivation of powerful and useful recurrence relations which hold in 8-dimensional Einstein's unified field theory(i.e., 8-g-UFT): I. The recurrence relations in 8-g-UFT II. The Einstein's connection in 8-g-UFT All considerations in these papers are restricted to the second class only, since the case of the first class are done in [1], [2] and the case of the third class, the simplest case, was already studied by many authors.