• 대한수학회지
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• 제60권5호
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• pp.1087-1107
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• 2023

Let E be an elliptic curve defined over ℚ of conductor N, c the Manin constant of E, and m the product of Tamagawa numbers of E at prime divisors of N. Let K be an imaginary quadratic field where all prime divisors of N split in K, P_K the Heegner point in E(K), and III(E/K) the Shafarevich-Tate group of E over K. Let 2u_K be the number of roots of unity contained in K. Gross and Zagier conjectured that if P_K has infinite order in E(K), then the integer c · m · u_K · |III(E/K)| $\frac{1}{2}$ is divisible by |E(ℚ)_tor|. In this paper, we prove that this conjecture is true if E(ℚ)_tor ≅ ℤ/2ℤ or ℤ/4ℤ except for two explicit families of curves. Further, we show these exceptions can be removed under Stein-Watkins conjecture.

• 대한수학회논문집
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• 제27권4호
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• pp.689-699
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• 2012

(S, *) is a semigroup S equipped with a unary operation "*". This work is devoted to a class of unary semigroups, namely E-$inversive$ *-$semigroups$. A unary semigroup (S, *) is called an E-inversive *-semigroup if the following identities hold: $$x^*xx^*=x^*$$, $$(x^*)^*=xx^*x$$, $$(xy)^*=y^*x^*$$. In this paper, E-inversive *-semigroups are characterized by several methods. Furthermore, congruences on these semigroups are also studied.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2005년도 추계학술대회 학술발표 논문집 제15권 제2호
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• pp.345-348
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• 2005

In this paper, we suggested an evaluation model for satisfaction of e-Learning. This model was composed decision of evaluation criteria, analysis of consciousness structure for evaluation factors using the Fuzzy Structural Modeling method, decision of weights for evaluation factors considering intersectional dependence relations and evaluation of satisfaction of e-Learning. The case study of this model was done for comparative analysis between teachers and students of e-Learning in high school.

• Korean Journal of Mathematics
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• 제13권1호
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• pp.1-11
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• 2005

The purpose of the present paper is to introduce a new concept of the E($^*{\kappa}$)-connection ${\Gamma}^{\nu}_{{\lambda}{\mu}}$, which is both Einstein and ($^*{\kappa}$)-connection, and to obtain a necessary and sufficient condition for the existence of the unique E($^*{\kappa}$)-connection in $n-^*g$-UFT. Next, under this condition, we shall obtain a surveyable tensorial representation of the unique E($^*{\kappa}$)-connection in $n-^*g$-UFT.

• 대한수학회논문집
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• 제27권3호
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• pp.497-503
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• 2012

In this paper, we study elliptic curves E over $\mathbb{Q}$ such that the 3-torsion subgroup E[3] is split as ${\mu}_3{\oplus}\mathbb{Z}/3{\mathbb{Z}}$. For a non-zero intege $m$, let $C_m$ denote the curve $x^3+y^3=m$. We consider the relation between the set of integral points of $C_m$ and the elliptic curves E with $E[3]{\simeq}{\mu}_3{\oplus}\mathbb{Z}/3{\mathbb{Z}}$.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2005년도 제36회 하계학술대회 논문집 A
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• pp.402-404
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• 2005

This paper represents the amapcity calculation method of power cables installed in a concrete construction above a bridge which is exposed to solar radiation.

• Journal of Information Processing Systems
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• 제7권3호
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• pp.549-560
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• 2011

Vote validity proof and verification is an efficiency bottleneck and privacy drawback in homomorphic e-voting. The existing vote validity proof technique is inefficient and only achieves honest-verifier zero knowledge. In this paper, an efficient proof and verification technique is proposed to guarantee vote validity in homomorphic e-voting. The new proof technique is mainly based on hash function operations that only need a very small number of costly public key cryptographic operations. It can handle untrusted verifiers and achieve stronger zero knowledge privacy. As a result, the efficiency and privacy of homomorphic e-voting applications will be significantly improved.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1989년도 추계학술대회 논문집 학회본부
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• pp.53-57
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• 1989

Until now, method of equivalent circuit is generally used in analyzing the characteristic of the synchronous alternator. But this method can't apply when loads are connected to alternator. In this paper, we analyzed the load characteristic of the synchronous alternator with permanant magnet using 2-dimensional finite element method having voltage source. The loads of a alternator are battary and diodes which are used to rectify. also, we used half periodic boundary condition in the F.E.M calculation

• Journal of Dairy Science and Biotechnology
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• 제34권1호
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• pp.43-49
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• 2016

Emulsion PCR (ePCR) has recently gained interest in the areas of food safety and biotechnology owing to its highly specific and sensitive performance in the amplification of target DNA. To facilitate the applications of ePCR to food safety and biotechnology, this paper describes the principles of ePCR and the factors that should be considered in designing ePCR. In addition, current research and applications related to ePCR are discussed.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제2권1호
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• pp.88-93
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• 1998

It is frequently important to approximate a rational B$\acute{e}$zier curve by an integral, i.e., polynomial one. This need will arise when a rational B$\acute{e}$zier curve is produced in one CAD system and is to be imported into another system, which can only handle polynomial curves. The objective of this paper is to present an algorithm to approximate rational B$\acute{e}$zier curves with polynomial curves of higher degree.