• Bulletin of the Korean Mathematical Society
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• v.48 no.2
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• pp.377-386
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• 2011

For a smooth algebraic curve C of genus g $\geq$ 4, let $SU_C$(r, d) be the moduli space of semistable bundles of rank r $\geq$ 2 over C with fixed determinant of degree d. When (r,d) = 1, it is known that $SU_C$(r, d) is a smooth Fano variety of Picard number 1, whose rational curves passing through a general point have degree $\geq$ r with respect to the ampl generator of Pic($SU_C$(r, d)). In this paper, we study the locus swept out by the rational curves on $SU_C$(r, d) of degree < r. As a by-product, we present another proof of Torelli theorem on $SU_C$(r, d).

• Journal of the Korean Mathematical Society
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• v.48 no.6
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• pp.1171-1187
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• 2011

Silverman [14] proved a height inequality for a jointly regular family of rational maps and the author [10] improved it for a jointly regular pair. In this paper, we provide the same improvement for a jointly regular family: let h : ${\mathbb{P}}_{\mathbb{Q}}^n{\rightarrow}{{\mathbb{R}}$ be the logarithmic absolute height on the projective space, let r(f) be the D-ratio of a rational map f which is de ned in [10] and let {$f_1,{\ldots},f_k|f_l:\mathbb{A}^n{\rightarrow}\mathbb{A}^n$} bbe finite set of polynomial maps which is defined over a number field K. If the intersection of the indeterminacy loci of $f_1,{\ldots},f_k$ is empty, then there is a constant C such that $ \sum\limits_{l=1}^k\frac{1}{def\;f_\iota}h(f_\iota(P))>(1+\frac{1}{r})f(P)-C$ for all $P{\in}\mathbb{A}^n$ where r= $max_{\iota=1},{\ldots},k(r(f_l))$.

• The Mathematical Education
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• v.50 no.1
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• pp.61-67
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• 2011

There may be two methods defining the rational exponent $a^{\frac{m}{n}}$ for any positive real number a. The one which is used in all korean highschool mathematics textbooks is to define it as $\sqrt[n]{a^m}$, that is $(a^m)^{\frac{1}{n}}$. The other is to define it as $(\sqrt[n]a)^m}$, that is $(a^{\frac{1}{n}})^m$. In this paper, we insist that the latter is more appropriate and universal, and that the contents of current textbooks on the definition of the rational exponent should be corrected.

• Honam Mathematical Journal
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• v.41 no.2
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• pp.421-433
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• 2019

Let n denote an integer greater than 2 and let c denote a nonzero complex number. In this paper, we introduce a family of elements of the rational Cherednik algebra $H^{sl_n}(c)$ of type $sl_n$, which are analogous to the Dunkl-Cherednik elements of the rational Cherednik algebra $H^{gl_n}(c)$ of type $gl_n$. We also introduce the raising and lowering element of $H^{sl_n}(c)$ which are useful in the representation theory of the algebra $H^{sl_n}(c)$, and provide simple results related to these elements.

• The Mathematical Education
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• v.39 no.2
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• pp.145-150
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• 2000

In this paper, we study the subject-matter knowledge related to the problem about rational exponent with negative bases. From the school mathematics point of view, we first investigate the meaning of the extensions of the number systems. We analyze the intrinsic meaning involved in the (-8)$^{1}$ 3) through the natural interpretation of rational exponent with negative bases by the complex number. we explain why it is important for a teacher to have the subject-matter knowledge in order to detect and correct student\`s mistake and misunderstanding.

• School Mathematics
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• v.3 no.2
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• pp.267-279
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• 2001

The aim of this study is to examine the number concept of middle school student at grade 9. The research problems of this study are "Can the students classify the various number correctly\ulcorner", "How do the students understand the proposition related to the number concept\ulcorner", and "How do the students know the definition of rational number, irrational number, and real number\ulcorner". In order to examine these problems, we analyze the students' responses about the questions related to the number concept. The result of this examination is that the number concept of students is very insufficient and lacking.

• Journal of the Korean School Mathematics Society
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• v.11 no.2
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• pp.285-298
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• 2008

According to the 7th curriculum, irrational numbers should be introduced using infinite decimals in 9th grade. To do so, the relation between rational numbers and decimals should be explained in 8th grade. Preceding studies remarked that middle school students could understand the relation between rational numbers and decimals through the division appropriately. From the point of view with the arithmetic handling activity, I analyzed that the integers and terminating decimals was explained as decimals with repeating 0s or 9s. And, I reviewed the equivalent relations between irrational numbers and non-repeating decimals, rational numbers and repeating decimals. Furthermore, I suggested an alternative method of introducing irrational numbers.

• Honam Mathematical Journal
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• v.20 no.1
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• pp.21-29
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• 1998

• East Asian mathematical journal
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• v.28 no.2
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• pp.159-172
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• 2012

In all Mathematics I Textbooks(Kim, S. H., 2010; Kim, H. K., 2010; Yang, S. K., 2010; Woo, M. H., 2010; Woo, J. H., 2010; You, H. C., 2010; Youn, J. H., 2010; Lee, K. S., 2010; Lee, D. W., 2010; Lee, M. K., 2010; Lee, J. Y., 2010; Jung, S. K., 2010; Choi, Y. J., 2010; Huang, S. K., 2010; Huang, S. W., 2010) in high schools in Korea these days, it is written and taught that for a positive real number $a$, $a^{\frac{m}{n}}$ is defined as $a^{\frac{m}{n}}={^n}\sqrt{a^m}$, where $m{\in}\mathbb{Z}$ and $n{\in}\mathbb{N}$ have common prime factors. For that situation, the author shows his opinion that the definition is not well-defined and $a^{\frac{m}{n}}$ must be defined as $a^{\frac{m}{n}}=({^n}\sqrt{a})^m$, whenever $^n\sqrt{a}$ is defined, based on the field axiom of the real number system including rational number system and natural number system. And he shows that the following laws of exponents for reals: $$\{a^{r+s}=a^r{\cdot}a^s\\(a^r)^s=a^{rs}\\(ab)^r=a^rb^r$$ for $a$, $b$>0 and $s{\in}\mathbb{R}$ hold by the completeness axiom of the real number system and the laws of exponents for natural numbers, integers, rational numbers and real numbers are logically equivalent.

• Proceedings of the Korean Institute of Communication Sciences Conference
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• 1984.10a
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• pp.82-87
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• 1984

A 2-D digital filter with rational frequency response can be expanded into an infinite sequence of filterins operations. Each filtering operation can be implemented by convolution with a Low-order 20D finite-extent impulse response. If a convergence constraint is satisfied, the sequence of estimates will approach the desired output signal. In practice, as the number of iterations is finite, the frequency response implemented by iterative computations is an approximation to the desired rational frequency response.