• 대한수학회논문집
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• 제16권4호
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• pp.595-606
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• 2001

Using p-adic class number formula, we derive a congru-ence relation for class numbers of the simplest cubic fields which can be considered as a cubic analogue of Ankeny-Artin-Chowlas theo-rem, Furthermore, we give an elementary proof for an upper bound for the class numbers of the simplest cubic fields.

• 충청수학회지
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• 제27권2호
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• pp.205-210
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• 2014

The author with C. H. Kim and Y. Lee constructed infinite families of elliptic curves over cubic number fields K with prescribed torsion groups which occur infinitely often. In this paper, we examine the Galois structures of such cubic number fields K for the families of elliptic curves with cyclic torsion.

• 대한수학회지
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• 제58권1호
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• pp.123-132
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• 2021

Let K be a number field and L a finite abelian extension of K. Let E be an elliptic curve defined over K. The restriction of scalars ResKLE decomposes (up to isogeny) into abelian varieties over K $$Res^L_KE{\sim}{\bigoplus_{F{\in}S}}A_F,$$ where S is the set of cyclic extensions of K in L. It is known that if L is a quadratic extension, then AL is the quadratic twist of E. In this paper, we consider the case that K is a number field containing a primitive third root of unity, $L=K({\sqrt[3]{D}})$ is the cyclic cubic extension of K for some D ∈ K×/(K×)3, E = Ea : y2 = x3 + a is an elliptic curve with j-invariant 0 defined over K, and EaD : y2 = x3 + aD2 is the cubic twist of Ea. In this case, we prove AL is isogenous over K to $E_a^D{\times}E_a^{D^2}$ and a property of the Selmer rank of AL, which is a cubic analogue of a theorem of Mazur and Rubin on quadratic twists.

• Journal of Advanced Marine Engineering and Technology
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• 제22권6호
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• pp.935-941
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• 1998

Experiments were carried out for a cubic cavity flow. Contrinuous shear stress is supplied by driven flow for high Reynolds number and three kinds of aspect ratios. Velocity vectors are obtained by PIV and they are used as velocity components for Poisson equation for pressure, Related boundary conditions and no-slip condition at solid wall and the linear velocity extrapolation on the upper side of cavity are well examined for the present study. For calculation of pressure resolution of grid is basically $40{\times}40$ and 2-dimensional uniform mesh using MSC staggered grid is adopted. The flow field within the cavity maintains a forced-vortex formation and almost of the shear stress from the driving inflow is transformed into rotating flow energy and the size of the distorted forced-vortex increases with increment of Reynolds number

• 한국통신학회논문지
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• 제36권10C호
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• pp.614-620
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• 2011

현재 가장 많이 쓰이는 공개키 암호시스템 중 하나인 RSA는 매우 큰 합성수 N의 인수분해가 어렵다는 것에 기반을 두고 있다. 120자리보다 큰 합성수를 인수분해하는데 가장 효율적인 알고리즘으로 알려진 Number Field Sieve (NFS)는 법 N에 대하여 공통근을 갖는 두 다항식 선택한 후에, sieving, linear algebra, square root 단계를 차례대로 거친다. 최근의 많은 연구 결과에 따르면 다항식을 얼마나 적합하게 선택하느냐에 따라 sieving step에서의 복잡도가 크게 달라질 수 있다는 것이 알려져 있다. Sieving 다항식은 차수가 같은 두 다항식을 선택하는 것이 이상적이며 두 개의 2차 다항식을 선택하는 방법은 이미 Montgomery가 제시하였다. 이 논문에서는 5항 등 비수열 방법을 이용하여 두 개의 3차 다항식 선택방법을 제시하고자 한다.

• 한국전기전자재료학회:학술대회논문집
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• 한국전기전자재료학회 2001년도 추계학술대회 논문집 Vol.14 No.1
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• pp.451-454
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• 2001

The ionic conductivity of cubic solid solutions in the system $Y_{2}O_{3}-ZrO_{2}$ prepared by SHS was examined. Conductivity-temperature data obtained at $1000^{\circ}C$ in atmosphere of low oxygen partial pressure ($10^{-40}$ atm) for $Y_{2}O_{3}-ZrO_{2}$ cubic solid solutions indicated that these materials could be reduced, the degree of reduction being related to the measuring electric field. At low impressed fields no reduction was observed. Thus, these conductivity data give a transference number for the oxygen ion in $Y_{2}O_{3}-ZrO_{2}$ cubic solid solutions greater than 0.99.

• 한국전기전자재료학회:학술대회논문집
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• 한국전기전자재료학회 2001년도 추계학술대회 논문집
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• pp.451-454
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• 2001

The ionic conductivity of cubic solid solutions in the system Y$_2$O$_3$-ZrO$_2$ prepared by SHS was examined. Conductivity-temperature data obtained at 1000$^{\circ}C$ in atmosphere of low oxygen partial pressure (10$\^$-40/ atm) for Y$_2$O$_3$-ZrO$_2$ cubic solid solutions indicated that these materials could be reduced, the degree of reduction being related to the measuring electric field. At low impressed fields no reduction was observed. Thus, these conductivity data give a transference number for the oxygen ion in Y$_2$O$_3$-ZrO$_2$ cubic solid solutions greater than 0.99.

• Journal of Advanced Marine Engineering and Technology
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• 제21권5호
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• pp.557-563
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• 1997

The unsteady flow in three-dimensional cubic cavity with narrow channel at upper region is investigated experimentally for three kinds of Reynolds number, 1*10/sup 4/, 3*10/sup 4/ and 5*10/sup 4/ based on the cavity width and cavity inlet mean flow velocity. Instant velocity vectors are obtained simultaneously at whole field by PIV(Particle Image Velocimetry). Wall pressure distributions are estimated using Poisson equation from the velocity data. Results of PIV reveal that severe unsteady flow fluctuation within the cavity are remarkable at all Reynolds numbers and sheared mixing layer phenomena are also found at the region where inlet driving flow is collided with the clock-wise rotating main primary vortex. Instant velocity profiles reveal that deformed forced vortex formation is observed throughout the entire region and spanwise kinetic energy migration is conspicuous.

• 환경영향평가
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• 제18권6호
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• pp.411-417
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• 2009

Lately the master plan for the Four Major Rivers Restoration Project has been released by the Ministry of Land and Maritime Affairs and relevant ministries. According to the master plan compared with the interim report made on 15 December 2008, the number of weirs for irrigation has increased from 5 to 16, the amount of dredging has increased from 220 million cubic metres to 570 million cubic metres, and the total cost estimated has increased from 14 trillion won to 22 trillion won. A critical review of the master plan by some research group will be summarized focused upon budget, objectives, securing water resource, dredging, and flood control etc. After various experts' forums and field surveys, it is concluded that the government should implement a joint-research program on assessing the impact of the project together with experts and citizens' groups as co-partners, in order to truly save or restore the four major rivers.

• 한국전기전자재료학회논문지
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• 제15권4호
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• pp.349-355
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• 2002

The ionic conductivity of cubic solid solutions in the systems of CaO-$ZrO_2$, $Y_2O_3-ZrO_2$ prepared by SHS was examined. The higher conductivity appears to be related to a lower activation energy rather than to the number of oxygen vacancies dictated by composition. Conductivity-temperature data was obtained at 1000 $^{\circ}C$ in atmosphere of low oxygen partial pressure (~$10^{-40}$ atm) for $Y_2O_3-ZrO_2$ cubic solid solutions. The data indicated that these materials could be reduced, and the decree of reduction would be related with the measuring electric field.