• 대한수학회보
• /
• 제48권2호
• /
• pp.377-386
• /
• 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).

• 대한수학회지
• /
• 제48권6호
• /
• pp.1171-1187
• /
• 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= $max_{\iota=1},{\ldots},k(r(f_l))$.

• 한국수학교육학회지시리즈A:수학교육
• /
• 제50권1호
• /
• pp.61-67
• /
• 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.

• 호남수학학술지
• /
• 제41권2호
• /
• pp.421-433
• /
• 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.

• 한국수학교육학회지시리즈A:수학교육
• /
• 제39권2호
• /
• pp.145-150
• /
• 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.

• 대한수학교육학회지:학교수학
• /
• 제3권2호
• /
• pp.267-279
• /
• 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.

• 한국학교수학회논문집
• /
• 제11권2호
• /
• pp.285-298
• /
• 2008

제 7 차 중학교 교육과정에서는 무리수를 순환하지 않는 무한소수로 도입하기 위해 유리수를 소수와 관련하여 재해석하도록 하도 있다. 여러 선행연구는 중학교 과정에서 유리수와 소수의 관계를 살핌에 있어 실제 나누어 보는 전략이 주요한 교수학적 도구가 됨을 지적하였다. 이 연구에서는 나눗셈 알고리즘을 통한 산술적 조작 활동의 관점에 비추어 정수와 유한소수를 9 또는 0이 순환하는 소수로 다루는 접근 방안의 적절성을 분석하였다. 또한 무리수를 무한소수로 도입하는데 '무리수=비순환소수', '유리수=순환소수'와 같은 대응이 필수적인가에 대해서도 음미해보았다. 나아가 무리수 도입을 위한 대안적인 방안에 대해서도 간접적으로 살펴보았다.

• 호남수학학술지
• /
• 제20권1호
• /
• pp.21-29
• /
• 1998

• East Asian mathematical journal
• /
• 제28권2호
• /
• pp.159-172
• /
• 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.

• 한국통신학회:학술대회논문집
• /
• 한국통신학회 1984년도 추계학술발표회논문집
• /
• pp.82-87
• /
• 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.