• 대한수학회보
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• 제57권2호
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• pp.481-488
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• 2020

In this paper we give an exact formula for the Fourier coefficients of the Jacobi-Eisenstein series of square free discriminant lattice index. For a special case the discriminant of lattice is prime we show that the Jacobi-Eisenstein series corresponds to a well known Eisenstein series of modular forms.

• 충청수학회지
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• 제22권4호
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• pp.799-814
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• 2009

A class invariant is the value of a modular function that generates a ring class field of an imaginary quadratic number field such as the singular moduli of level 1. In this paper, using Shimura Reciprocity Law, we compute the Galois actions of some class invariants from the generalized Weber functions $\mathfrak{g}_0,\mathfrak{g}_1,\mathfrak{g}_2$ and $\mathfrak{g}_3$ over quadratic number fields with discriminant $D{\equiv}1$ (mod 12).

• 충청수학회지
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• 제26권1호
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• pp.213-219
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• 2013

A class invariant is the value of a modular function that generates a ring class field of an imaginary quadratic number field such as the singular moduli of level 1. In this paper, we compute the Galois actions of a class invariant from a generalized Weber function $g_1$ over imaginary quadratic number fields with discriminant $D{\equiv}64(mod72)$.

• 충청수학회지
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• 제24권4호
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• pp.921-925
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• 2011

A class invariant is the value of a modular function that generates a ring class field of an imaginary quadratic number field such as the singular moduli of level 1. In this paper, using Shimura Reciprocity Law, we compute the Galois actions of a class invariant from a generalized Weber function $g_2$ over quadratic number fields with discriminant $D{\equiv}21$ (mod 36).

• 충청수학회지
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• 제23권4호
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• pp.853-860
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• 2010

A class invariant is the value of a modular function that generates a ring class field of an imaginary quadratic number field such as the singular moduli of level 1. In this paper, using Shimura Reciprocity Law, we compute the Galois actions of a class invariant from a generalized Weber function $g_2$ over quadratic number fields with discriminant $D{\equiv}-3$ (mod 36).

• 호남수학학술지
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• 제20권1호
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• pp.57-65
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• 1998

In this paper, we consider properties of Dedekind eta-function, modular discrimiant, thata-series and Weierstrass ${\wp}$-function. We prove the integrablities of ${\Delta}({\tau})$ and ${\eta}({\tau})$. Also, we give explicit formulae about ${\Delta}({\tau})$ and ${\tau}(n)$.

• Korean Journal of Mathematics
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• 제6권1호
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• pp.67-70
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• 1998

Let ${\eta}(\tau)=q^{1/24}\prod_{n=1}^{\infty}(1-q^n)$, where $q=e^{2{\pi}i{\tau}}$ and ${\tau}{\in}\mathbb{C}$. Then the transformation $$g(\tau)={\rho}\frac{\{\eta(\frac{\tau+1}{2})\eta(\frac{\tau+2}{2})\}^{16}}{\eta(\tau)^{24}}({\bar{{\rho}}{\eta}}(\frac{\tau+1}{2})^8+{\eta}(\frac{\tau+2}{2})^8)^2$$ is holomorphic for Im ${\tau}$ > 0, and has the property $$g(\tau+1)=g(\tau),\;g(-\frac{1}{\tau})={\tau}^{12}g(\tau)$$. (Theorem)

• 한국철도학회:학술대회논문집
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• 한국철도학회 2011년도 춘계학술대회 논문집
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• pp.1195-1201
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• 2011

Since the release of safety standard IEC 61508 which defines functional safety of electronic safety-related systems, SIL(Safety Integrity Level) certification for railway systems has gained lots of attention lately. In this paper, we propose a new design technique of the computer board for train control systems with high reliability and safety. The board is designed with TMR(Triple Modular Redundancy) using a certified SIL3 Texas Instrument(TI)'s TMS570 MCU(Micro-Controller Unit) to guarantee safety and reliability. TMR for the control device is implemented on FPGA(Field Programmable Gate Array) which integrates a comparator, a CAN(Controller Area Network) communication module, built-in self-error checking, error discriminant function to improve the reliability of the board. Even if a malfunction of a processing module occurs, the safety control function based on the proposed technique lets the system operate properly by detecting and masking the malfunction. An RTOS (Real Time Operation System) called FreeRTOS is ported on the board so that reliable and stable operation and convenient software development can be provided.