• Communications of the Korean Mathematical Society
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• v.16 no.4
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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.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.2
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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.

• Journal of the Korean Mathematical Society
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• v.58 no.1
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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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• v.22 no.6
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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

• The Journal of Korean Institute of Communications and Information Sciences
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• v.36 no.10C
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• pp.614-620
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• 2011

RSA, the most commonly used public-key cryptosystem, is based on the difficulty of factoring very large integers. The fastest known factoring algorithm is the Number Field Sieve(NFS). NFS first chooses two polynomials having common root modulo N and consists of the following four major steps; 1. Polynomial Selection 2. Sieving 3. Matrix 4. Square Root, of which the most time consuming step is the Sieving step. However, in recent years, the importance of the Polynomial Selection step has been studied widely, because one can save a lot of time and memory in sieving and matrix step if one chooses optimal polynomial for NFS. One of the ideal ways of choosing sieving polynomial is to choose two polynomials with same degree. Montgomery proposed the method of selecting two (nonlinear) quadratic sieving polynomials. We proposed two cubic polynomials using 5-term geometric progression.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2001.11b
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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.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2001.11a
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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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• v.21 no.5
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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.

• Journal of Environmental Impact Assessment
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• v.18 no.6
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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.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.15 no.4
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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.