• Journal of the Korean Mathematical Society
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• v.52 no.5
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• pp.907-928
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• 2015

We show in many cases that the Siegel-Ramachandra invariants generate the ray class fields over imaginary quadratic fields. As its application we revisit the class number one problem done by Heegner and Stark, and present a new proof by making use of inequality argument together with Shimura's reciprocity law.

• Journal of Electrical Engineering and Technology
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• v.9 no.1
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• pp.190-196
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• 2014

In this paper, the characteristics of a defective elliptical aluminum plate are analyzed by three different eddy current testing probes; T/R, T/T, and Impedance probes. The analysis was done by 3D finite element method, and the impedance change of real and imaginary voltage values were analyzed.

• Journal of the Korean Mathematical Society
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• v.55 no.1
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• pp.131-146
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• 2018

We generate ring class fields of imaginary quadratic fields in terms of the special values of certain eta-quotients, which are related to the relative norms of Siegel-Ramachandra invariants. These give us minimal polynomials with relatively small coefficients from which we are able to solve certain quadratic Diophantine equations concerning non-convenient numbers.

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1357-1365
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• 2013

We find a lower bound on the number of real/inert imagi-nary/ramified imaginary quadratic extensions of the function field $\mathbb{F}_q(t)$ whose ideal class groups have an element of a fixed order, where $q$ is a power of 2.

• Bulletin of the Korean Mathematical Society
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• v.45 no.4
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• pp.709-715
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• 2008

We construct certain ring class fields over an imaginary quadratic field by making use of Shimura's canonical models and extend the result of Chen-Yui ([1] Theorem 3.7.5(2)) to the case where (a, b, N) $\neq$ N or (a/N, N) $\neq$ 1 for a positive integer N > 1.

• Communications of the Korean Mathematical Society
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• v.22 no.3
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• pp.331-351
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• 2007

Let k be an imaginary quadratic field, h the complex upper half plane, and let $\tau{\in}h{\cap}k$, $q=e^{{\pi}i\tau}$. We find a lot of algebraic properties derived from theta functions, and by using this we explore some new algebraic numbers from Rogers-Ramanujan continued fractions.

• ETRI Journal
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• v.26 no.2
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• pp.161-166
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• 2004

AC electrical properties of organic light-emitting diodes with poly(2-methoxy-5-(2'-ethyl-hexyloxy)-1,4-phenylenevinylene) (MEH-PPV), poly[2,5-bia(dimethyloctylsilyl)-1,4-phenylenevinylene] (BDMOS-PPV), and tris-(8-hydroxyquinolate)-aluminum $(AlQ_3)$ as light-emitting materials are studied. The frequency-dependent real and imaginary parts of impedance were fitted using an equivalent circuit. We found that the conduction mechanism is a space-charge limited current with exponential trap distribution.

• 한국초전도학회:학술대회논문집
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• v.13
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• pp.68-68
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• 2003

• Transactions of the Korean Society of Mechanical Engineers B
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• v.29 no.1 s.232
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• pp.71-79
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• 2005

For the non-premixed interacting jet flames, it has been reported that if eight small nozzles are arranged along the circle of $40{\sim}72$ times the diameter of single jet, the flames are not extinguished even in 200m/s. In this research, experiments were extended to the partially premixed cases to reduce both flame temperature and NOx emission. Nine nozzles were used- eight was evenly located along the perimeter of the imaginary circle and one at the geometric centre. The space between nozzles, S, the equivalence ratio, ${\phi}$, the exit velocity and the role of the jet from the centre nozzle were considered. Normally, flame was lifted and flame base was located inside the imaginary circle made by the nozzle. As nozzles went away from each other, blowout velocity increased and then decreased. The maximum blowout velocity diminished with the addition of air to the fuel stream. When the fuel and/or oxidizer were not fed through the centre nozzle, the maximum blowout velocity obtained by varying S and ${\phi}$ was around 160m/s. Optimum nozzle separation distance at which peak blowout velocity obtained also decreased with ${\phi}$ decrease. Flame base became leaner as approaching to the blowout. It seemed that lots of air was supplied to the flame stabilizing region by the entrainment and partially premixing. To approve this idea and to enhance the blowout velocity, fuel was supplied to the centre region. With the small amount of fuel through the centre nozzle, partially premixed flame could be sustained till sonic velocities. It seemed that the stabilizing mechanism in partially premixed interacting flame was different from that of non-premixed case because one was stabilized by the fuel supply through the centre nozzle but the other destabilized.

• 한국연소학회:학술대회논문집
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• 2004.11a
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• pp.79-84
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• 2004

For the non-premixed interacting jet flames, it has been reported that if eight small nozzles are arranged along the circle of 40 $^{\sim}$ 72 times the diameter of single jet, the flames are not extinguished over 2oom/s. In this research, experiments were extended to the partially premixed cases to reduce both flame temperature and NOx emission. Nine nozzles were used- eight was evenly located along the perimeter of the imaginary circle and one at the geometric centre. The space between nozzles, S, the equivalence ratio, ${\Phi}$, the exit velocity and the role of the jet from the centre nozzle were considered. Normally, flame was lifted and flame base was located inside the imaginary circle made by the nozzle. As nozzles went away from each other, blowout velocity increased and then decreased. The maximum blowout velocity diminished with the addition of air to the fuel stream. When the fuel and/or oxidizer were not fed through the centre nozzle, the maximum blowout velocity obtained by varying Sand ${\Phi}$ was around 160m/s. Optimum nozzle separation distance at which peak blowout velocity obtained also decreased with ${\Phi}$ decrease. Flame base became leaner as approaching to the blowout. It seemed that lots of air was supplied to the flame stabilizing region by the entrainment and partially premixing. To approve this idea and to enhance the blowout velocity, fuel was supplied to the centre region. With the small amount of fuel through the centre nozzle, partially premixed flame could be sustained till sonic velocities. It seemed that the stabilizing mechanism in partially premixed interacting flame was different from that of non-premixed case because one was stabilized by the fuel supply through the centre nozzle but the other destabilized.