• 대한수학회지
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• 제50권4호
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• pp.847-864
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• 2013

By a change of variables we obtain new $y$-coordinates of elliptic curves. Utilizing these $y$-coordinates as meromorphic modular functions, together with the elliptic modular function, we generate the fields of meromorphic modular functions. Furthermore, by means of the special values of the $y$-coordinates, we construct the ray class fields over imaginary quadratic fields as well as normal bases of these ray class fields.

• 대한수학회보
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• 제52권1호
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• pp.263-273
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• 2015

We derive modular equations of degree 2 to establish explicit relations for the parameterizations for the theta functions ${\varphi}$ and ${\psi}$. We then find specific values of the parameterizations to evaluate some new values of the modular j-invariant in terms of $J_n$.

• 대한수학회지
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• 제53권6호
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• pp.1445-1457
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• 2016

For a positive integer N divisible by 4, let ${\mathcal{O}}^1_N({\mathbb{Q}})$ be the ring of weakly holomorphic modular functions for the congruence subgroup ${\Gamma}^1(N)$ with rational Fourier coefficients. We present explicit generators of the ring ${\mathcal{O}}^1_N({\mathbb{Q}})$ over ${\mathbb{Q}}$ in terms of both Fricke functions and Siegel functions, from which we are able to classify all Fricke families of such level N.

• 대한수학회지
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• 제35권4호
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• pp.903-931
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• 1998

Since the modular curves X(N) = $\Gamma$(N)\(equation omitted)＊ (N =1,2,3) have genus 0, we have field isomorphisms K(X(l))(equation omitted)C(J), K(X(2))(equation omitted)(λ) and K(X(3))(equation omitted)( $j_3$) where J, λ are the classical modular functions of level 1 and 2, and $j_3$ can be represented as the quotient of reduced Eisenstein series. When N = 4, we see from the genus formula that the curve X(4) is of genus 0 too. Thus the field K(X(4)) is a rational function field over C. We find such a field generator $j_4$(z) = x(z)/y(z) (x(z) = $\theta$$_3$((equation omitted)), y(z) = $\theta$$_4$((equation omitted)) Jacobi theta functions). We also investigate the structures of the spaces $M_{k}$($\Gamma$(4)), $S_{k}$($\Gamma$(4)), M(equation omitted)((equation omitted)(4)) and S(equation omitted)((equation omitted)(4)) in terms of x(z) and y(z). As its application, we apply the above results to quadratic forms.rms.

• Kyungpook Mathematical Journal
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• 제56권3호
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• pp.715-726
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• 2016

In this paper, we establish some new P-Q type modular equations, by using the modular equations given by Srinivasa Ramanujan.

• 대한수학회보
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• 제50권4호
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• pp.1315-1328
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• 2013

We first derive several modular equations of degree 5 and present their concise proofs based on algebraic computations. We then establish explicit relations and formulas for some parameterizations for the theta functions ${\varphi}$ and ${\psi}$ by using the derived modular equations. In addition, we find specific values of the parameterizations and evaluate some numerical values of the Rogers-Ramanujan continued fraction.

• 대한수학회보
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• 제50권4호
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• pp.1221-1233
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• 2013

We first derive some modular equations of degrees 3 and 9 and present their concise proofs based on algebraic computations. We then use these modular equations to establish explicit relations and formulas for the parameterizations for the theta functions ${\varphi}$ and ${\psi}$ In addition, we find specific values of the parameterizations to evaluate some numerical values of the cubic continued fraction.

• Kyungpook Mathematical Journal
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• 제45권2호
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• pp.211-220
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• 2005

In this paper we obtain the transformations of the Ramanujan's tenth order mock theta functions under the modular group generators ${\tau}\;{\rightarrow}\;{\tau}\;+\;1\;and\;{\tau}\;{\rightarrow}\;-1/ {\tau}\;where\;q\;=\;e^{{\pi}it}$.

• 한국정보통신학회:학술대회논문집
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• 한국정보통신학회 2019년도 춘계학술대회
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• pp.398-399
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• 2019

본 논문에서는 최근에 디지털논리시스템의 회로 구현시에 적용되기 시작한 분할설계기법의 한가지 방법을 제안하였다. 기존의 디지털논리회로설계기법은 적용되는 개별소자를 어떻게 효과적이며 효율적으로 이용하느냐 하는 것이 큰 목적이었으나, 최근의 전자공학의 발달과 회로의 집적도가 높아짐에 따라서 디지털논리설계기법은 각각의 모듈을 구성하고 있는 소자들의 개별소자를 사용하는 것보다는 복잡하더라도 좀 더 경제적이고 다기능의 분할설계기법이 요구되고 있다. 이러한 내용을 근간으로 본 논문에서는 효과적인 분할기법을 이용한 스위칭함수구성의 한가지 방법을 제안하였다.

• 한국정밀공학회지
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• 제23권5호
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• pp.119-127
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• 2006

Design structure of a mobile phone has been changed to a converged style, which has so many functions. However, the converged mobile phone could not satisfy the users who want to use only specific functions, so with Axiomatic Design, we have studied for making a proposal to set up the new concept. The goal of this study is to derive a general solution with Axiomatic Design to verify the Independence. By enhancing the existing design model and differentiating the function of mobile phone, user will be able to choose desirable products, which have only specific functions and/or specific parts. First of all, we checked the Independence about the existing design model. Then, we developed the new design model with the idea that base mobile phone should have basic functions and additional functions can be separated, surely be connected when users want.