• Journal of the Chungcheong Mathematical Society
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• v.33 no.2
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• pp.205-217
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• 2020

We will introduce a new type of quartic functional equation and then investigate the stability for a quartic functional equation in a convex modular space.

• 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.

• The Pure and Applied Mathematics
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• v.28 no.1
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• pp.15-26
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• 2021

The purpose of this paper is to introduce a new type of a cubic functional equation and then investigate its stability problems in a convex modular space with a generalized ∆a-condition.

• The Pure and Applied Mathematics
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• v.26 no.1
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• pp.49-58
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• 2019

In this paper, I prove the stability problem for a quadratic-cubic functional equation $$f(x+ky)-k^2f(x+y)-k^2f(x-y)+f(x-ky)+f(kx)-{\frac{k^3-3k^2+4}{2}}f(x)+{\frac{k^3-k^2}{2}}f(-x)=0$$ in modular spaces by applying the direct method.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.3
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• pp.529-531
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• 2011

We show that for all $N{\geq}1$, the modular function field $K(X_0^+(N))$ is generated by j(z)j(Nz) and j(z) + j(Nz) over ${\mathbb{C}}$, where j(z) is the modular invariant. Moreover we derive the defining equation of the the modular function field $K(X_0^+(N))$ from the classical modular polynomial ${\Phi}_N(X, Y )$.

• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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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).

• Journal of Korean Association for Spatial Structures
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• v.21 no.4
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• pp.65-72
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• 2021

The Precast concrete(PC) modular structures are a method of assembling pre-fabricated unit modules in the construction site. The essential aim of modular structures is to introduce a connection method that can ensure splicing performance and effectively resist shear strength. This study proposed PC module using a connecting plate that can replace splice sleeves and shear keys used in the conventional PC modular structures. To evaluate the splicing performance and shear capacity of the proposed method, the shear test was conducted by fabricating one monolithic reinforced concrete(RC) beam and two PC modular beams with a shear span-to-depth ratio as variables. The experimental results showed that the shear capacity of the PC modular beam was about 89% compared to that of the RC beam, and showed a failure of the RC beam according to the shear span-to-depth ratio. Therefore, it was considered that the connecting plate effectively transferred the stress between each PC module through the joint and ensure integrity. In addition, the applicability of shear strength equation of ACI 318-19 and Zsutty's equation to PC modular beams were evaluated. Results demonstrated that the improved shear strength equations are needed to consider reduction of shear strength in PC modules.

• Journal of applied mathematics & informatics
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• v.38 no.5_6
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• pp.415-426
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• 2020

In this paper, we will prove some uniqueness theorems that can be applied to the generalized Hyers-Ulam stability of some additive-quadratic-cubic functional equation in complete modular spaces without Δ₂-conditions.

• Bulletin of the Korean Mathematical Society
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• v.58 no.1
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• pp.163-170
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• 2021

We present a concise proof of the conjecture of Mazur-Rubin-Stein on the distribution of modular symbols.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.2
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• pp.321-330
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• 2015

In this paper, we prove the generalized Hyers-Ulam stability for the following additive-quadratic functional equation f(2x + y) + f(2x - y) = f(x + y) + f(x - y) + 4f(x) + 2f(-x) in modular spaces by using a fixed point theorem for modular spaces.