• Nonlinear Functional Analysis and Applications
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• 제28권4호
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• pp.887-902
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• 2023

In this article, we investigate an approximate quadratic Lie *-derivation of a quadratic functional equation f(ax + by) + abf(x - y) = (a + b)(af(x) + bf(y)), where ab ≠ 0, a, b ∈ ℕ, associated with the identity f([x, y]) = [f(x), y²] + [x², f(y)] on a 𝜌-complete convex modular *-algebra χ_𝜌 by using ∆₂-condition via convex modular 𝜌.

• Kyungpook Mathematical Journal
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• 제55권2호
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• pp.313-326
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• 2015

In this paper, we present a fixed point method to prove generalized Hyers-Ulam stability of the systems of quadratic-cubic functional equations with constant coefficients in modular spaces.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제23권3호
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• pp.223-236
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• 2016

We show how to evaluate the cubic continued fraction $G(e^{-{\pi}\sqrt{n}})$ and $G(-e^{-{\pi}\sqrt{n}})$ for n = 4^m, 4^−m, 2 · 4^m, and 2⁻¹ · 4^−m for some nonnegative integer m by using modular equations of degree 9. We then find some explicit values of them.

• 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 $X_0(pq)+q$.

• 대한수학회지
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• 제38권3호
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• pp.595-611
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• 2001

Let Q(n,1) be the set of even unimodular positive definite integral quadratic forms in n-variables. Then n is divisible by 8. For A[X] in Q(n,1), the theta series $\theta$(sub)A(z) = ∑(sub)X∈Z(sup)n e(sup)$\pi$izA[X] (Z∈h (※Equations, See Full-text) the complex upper half plane) is a modular form of weight n/2 for the congruence group Γ$_1$(8) = {$\delta$∈SL$_2$(Z)│$\delta$≡()mod 8} (※Equation, See Full-text). If n$\geq$24 and A[X], B{X} are tow quadratic forms in Q(n,1), the quotient $\theta$(sub)A(z)/$\theta$(sub)B(z) is a modular function for Γ$_1$(8). Since we identify the field of modular functions for Γ$_1$(8) with the function field K(X$_1$(8)) of the modular curve X$_1$(8) = Γ$_1$(8)＼h(sup)* (h(sup)* the extended plane of h) with genus 0, we can express it as a rational function of j(sub) 1,8 over C which is a field generator of K(X$_1$(8)) and defined by j(sub)1,8(z) = $\theta$$_3$(2z)/$\theta$$_3$(4z). Here, $\theta$$_3$ is the classical Jacobi theta series.

• 전력전자학회논문지
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• 제21권4호
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• pp.328-334
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• 2016

This paper examines the reliability of a VSC-HVDC valve based on a modular multilevel converter (MMC) HVDC system. The main objective of this paper is to determine the redundancy of the MMC valve. Several prediction methods are introduced, but the binomial failure method is selected to be used. To determine the availability and reliability prediction of MMC valve, which comprises a DC/DC converter, a gate driver, a capacitor, and an IGBT, the failure data of the MMC module are used as the tracking data according to the experimental result. This method uses a simplified equation to find the valve redundancy by transforming the binomial function to De Moivre's formula. This method is the first to be used to find the valve margin.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2007년도 추계학술대회논문집
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• pp.471-475
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• 2007

Design equations of coupling plates, which connects floor beam of the upper modular unit and overhead beam of the lower one in order to improve serviceability in vibration, are proposed. End conditions of the coupled beams is semi-rigid and the optimal location of the coupling plates are assumed. Rotational constraints for both ends of the coupling plate modeled with beam elements are released and flexibility method is applied to obtain deflection equations of the coupled beam. Proposed equations are defined using the flexibility of the coupling plate, of which size can be determined inversely. Based on numerical analysis, coefficients of the design equations are calibrated and the revised equations are verified to be useful in the design of the coupled beam.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제25권1호
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• pp.17-29
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• 2018

We find modular equations of degree 3 to evaluate some new values of the cubic continued fraction $G(e^{-{\pi}\sqrt{n}})$ and $G(-e^{-{\pi}\sqrt{n}})$ for $n={\frac{2{\cdot}4^m}{3}}$, ${\frac{1}{3{\cdot}4^m}}$, and ${\frac{2}{3{\cdot}4^m}}$, where m = 1, 2, 3, or 4.

• 한국도로학회논문집
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• 제17권6호
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• pp.37-45
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• 2015

PURPOSES : The purpose of this study is to validate the design criteria of the concrete modular road system, which is a new semi-bridge-type concept road, through a comparison of numerical analysis results and actual loading test results under static axial loads. METHODS : To design the semi-bridge-type modular road, both the bridge design code and the concrete structural design code were adopted. The standard truck load (KL-510) was applied as the major traffic vehicle for the design loading condition. The dimension of the modular slab was designed in consideration of self-weight, axial load, environmental load, and combined loads, with ultimate limit state coefficients. The ANSYS APDL (2010) program was used for case studies of center and edge loading, and the analysis results were compared with the actual mock-up test results. RESULTS : A full-scale mock-up test was successfully conducted. The maximum longitudinal steel strains were measured as about 35 and 83.5 micro-strain (within elastic range) at center and edge loading locations, respectively, under a 100 kN dual-wheel loading condition by accelerating pavement tester. CONCLUSIONS : Based on the results of the comparison between the numerical analysis and the full-scale test, the maximum converted stress range at the edge location is 32~51% of the required standard flexural strength under the two times over-weight loading condition. In the case of edge loading, the maximum converted stresses from the Westergaard equation, the ANSYS APDL analysis, and the mock-up test are 1.95, 1.7, and 2.3 times of that of the center loading case, respectively. The primary reason for this difference is related to the assumption of the boundary conditions of the vertical connection between the slab module and the crossbeam module. Even though more research is required to fully define the boundary conditions, the proposed design criteria for the concrete modular road finally seems to be reasonable.

• 한국강구조학회 논문집
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• 제20권4호
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• pp.539-548
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• 2008

본 연구는 기존에 발표한 T형 모듈단면 프로파일보의 적용가능성을 확인하기 위해 실험체를 제작하고 전단보강 유무에 따른 휨 및 전단거동을 측정하여 그 결과를 소성이론식과 비교 분석하였다. 모듈단면 프로파일보는 프로파일이 거푸집기능에 추가하여 휨 및 전단저항성능에 기여하고 모듈개념을 통해 성형성능을 향상시킨다. 실험결과 전단보강을 실시한 TS계열 실험체가 전단보강이 없는 T계열 실험체에 비해 우수한 휨저항 능력을 나타내 사용된 전단보강재는 적절하게 전단력을 분담하고 있는 것으로 파악되었으나 T1-1실험체를 제외한 모든 실험체에서 볼트의 전단파괴에 의한 모듈간 슬립현상이 발생되어 휨저항 성능이 충분히 발휘되지 못한 것으로 판단된다. 추후 전단연결재를 변수로 한 T형 모듈단면 프로파일보에 관한 연구를 통해 적절한 모듈간 접합방법이 연구 되어져야 할 것으로 판단된다.