• 대한수학회지
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• 제42권2호
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• pp.203-222
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• 2005

Thompson series is a Hauptmodul for a genus zero group which lies between $\Gamma$o(N) and its normalizer in PSL2(R) ([1]). We construct explicit ring class fields over an imaginary quadratic field K from the Thompson series $T_g$($\alpha$) (Theorem 4), which would be an extension of [3], Theorem 3.7.5 (2) by using the Shimura theory and the standard results of complex multiplication. Also we construct various class fields over K, over a CM-field K (${\zeta}N + {\zeta}_N^{-1}$), and over a field K (${\zeta}N$). Furthermore, we find an explicit formula for the conjugates of Tg ($\alpha$) to calculate its minimal polynomial where $\alpha$ (${\in}{\eta}$) is the quotient of a basis of an integral ideal in K.

• 대한수학회보
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• 제44권1호
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• pp.47-59
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• 2007

We find the uniformizers of modular curves $X_{1}(N)\;(N=2,3)$ and explore the relationship with Thompson series and number theoretic property.

• 대한수학회지
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• 제36권4호
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• pp.707-723
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• 1999

Since the modular curve $X(4)=\Gamma(4)/{\mathfrak{}}^*$ has genus 0, we have a field isomorphism K(X(4)){\approx}\mathcal{C}(j_{4})$ where $j_{4}(z)={\theta}_{3}(\frac{z}{2})/{\theta}_{4}(\frac{z}{2})$ is a quotient of Jacobi theta series ([9]). We derive recursion formulas for the Fourier coefficients of $j_4$ and $N(j_{4})$ (=the normalized generator), respectively. And we apply these modular functions to Thompson series and the construction of class fields.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2004년도 학술발표논문집
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• pp.155-160
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• 2004

불균등 확률 계통추출에서는 모집단 총합에 대한 Horvitz-Thompson 추정량의 대안적 분산 추정량들을 사용하게 된다. 이와 같은 모총합에 관한 분산 추정량들의 설계와 관련한 일반적인 방법은 균등 확률 계통추출에 대한 분산 추정량들에서 시작하고 비율 $y_i,/P_i$에 의한 추정량의 정의에서 $y_i$를 재배치하게 한다. 비선형 조사 통계학에서 추정량들 중의 하나로 테일러 급수 공식을 적용한다. 불균등 확률 계통추출에서의 분산은 8가지 방법으로 추정이 가능하므로 이를 이용한 분산추정량을 구해보고, 비복원 불균등 확률에서의 jackknife방법을 살펴보고자 한다. 또한 이들 분산추정량들에 대한 비교를 몇 가지 방법을 이용하여 알아보도록 한다.

• 충청수학회지
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• 제26권3호
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• pp.641-645
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• 2013

In this article, we show that the modular equation ${\Phi}_p^{T_q}(X,Y)$ of Thompson series $T_q$ corresponding to ${\Gamma}_0(q)+q$ gives an affine model of a modular curve $X_0(pq)+q$.

• 대한수학회보
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• 제45권4호
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• pp.709-715
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• 2008

We construct certain ring class fields over an imaginary quadratic field by making use of Shimura's canonical models and extend the result of Chen-Yui ([1] Theorem 3.7.5(2)) to the case where (a, b, N) $\neq$ N or (a/N, N) $\neq$ 1 for a positive integer N > 1.

• 대한수학회지
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• 제44권2호
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• pp.343-371
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• 2007

We find the super-replication formulae which would be a generalization of replication formulae. And we apply the formulae to derive periodically vanishing property in the Fourier coefficients of the Hauptmodul $\aleph(j_{1,N})$ as a super-replicable function.

• Journal of Biosystems Engineering
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• 제21권1호
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• pp.72-83
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• 1996

This study was performed to find out drying characteristics and develop drying model for the design of an efficient dryer or drying system of garlic. The basic model which describes drying phenomenon of garlic was first established. A series of drying test were conducted with two varieties of garlic(Uiseong, Namdo) at 9-different drying conditions (drying temperatures ; $40^{\circ}C$, $50^{\circ}C$, $60^{\circ}C$, relative humidities ; 20%, 35%, 50%) and statistical analysis was made to fit the data with exponential equation, approximated diffusion equation, page equation, thompson equation and wang equation, respectively. In this test, the effects of drying air temperature and relative humidity on the drying rate were undertaken. Finally, new drying model based on these experimental results was developed to describe the drying characteristics of garlic. Also, the volatile components of garlic extracts were investigated. For experiment both Uisoeng and Namdo garlic were dried by heated-air-drying, followed by ether extraction. The extracts were analysed by Gas chromatography/Mass spectrometer.

• 대한수학회보
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• 제44권2호
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• pp.379-383
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• 2007

We show that the modular equation ${\phi}^{T_n}_m$ (X, Y) for the Thompson series $T_n$ corresponding to ${\Gamma}_0$(n) gives an affine model of the modular curve $X_0$(mn) which has better properties than the one derived from the modular j invariant. Here, m and n are relative prime. As an application, we construct a ring class field over an imaginary quadratic field K by singular values of $T_n(z)\;and\;T_n$(mz).

• Applied Microscopy
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• 제33권2호
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• pp.93-104
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• 2003

본고에서는 유리의 확대력 발견으로부터 현재까지 이르는 전자현미경과 관련된 중요한 이론 및 개발 과정들을 시대별로 검토하였다. Jansen에 의한 최초의 광학현미경 제작으로부터, 분해능의 한계를 해결하려는 노력들, 짧은 광원을 찾는 노력, 그리고 보다 양질의 해상력과 확대력을 얻으려는 여러 과학자들의 부단한 노력들을 특히 전자현미경 원리 및 TEM과 SEM의 초기 개발과정에 초점을 맞추어 생명과학적 측면에서 고찰하고, 아울러 우리나라의 전자현미경 도입 과정을 살펴보았다.