• Journal of the Korean Mathematical Society
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• v.50 no.4
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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.

• Bulletin of the Korean Mathematical Society
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• v.52 no.1
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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 $J_n$.

• Journal of the Korean Mathematical Society
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• v.53 no.6
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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.

• Journal of the Korean Mathematical Society
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• v.35 no.4
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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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• v.56 no.3
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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.

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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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.

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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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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• v.45 no.2
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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 ${\tau}\;{\rightarrow}\;{\tau}\;+\;1\;and\;{\tau}\;{\rightarrow}\;-1/ {\tau}\;where\;q\;=\;e^{{\pi}it}$.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2019.05a
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• pp.398-399
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• 2019

This paper presents a method of the circuit design of the multiple-valued digital logic switching functions based on the modular techniques. Fisr of all, we introduce the necessity, background and concepts of the modular design techniques for the digital logic systems. Next, we discuss the definitions that are used in this paper. For the purpose of the circuit design for the multiple-valued digital logic switching functions, we discuss the extraction of the partition functions. Also we describe the construction method of the building block, that is called the modules, based on each partition functions. And we apply the proposed method to the example, we compare the results with the results of the earlier methods. In result, we decrease the control functions, it means that we obtain the effective cost in the digital logic design for any other earlier methods. In the future research, we require the universal module that traet more partition functions and more compact module.

• Journal of the Korean Society for Precision Engineering
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• v.23 no.5 s.182
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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.