• Korean Journal of Mathematics
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• v.26 no.2
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• pp.293-297
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• 2018

In the paper [4], we constructed 3-part of the Hilbert class field of imaginary quadratic fields whose class number is divisible exactly by 3. In this paper, we extend the result for any odd prime p.

• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.747-756
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• 2007

In this paper we give an example of imaginary quadratic number field k such that every ideal of k becomes principal in some proper subfields of the Hilbert class field of k.

• Journal for History of Mathematics
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• v.13 no.2
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• pp.151-160
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• 2000

In this paper we prove that for all irreducible complex characters of a finite group, there exist F-representations and a finite degree field extension F ⊇ Q, where Q is the rational number field.

• Honam Mathematical Journal
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• v.36 no.1
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• pp.147-155
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• 2014

Let D be a square-free positive integer and let $K_D=\mathbb{Q}(\sqrt{-D})$ be the imaginary quadratic field. And let $h_D$ be the class number of the number field $K_D$. In this paper, we show the following: If D=l or 4l, where l is a prime number with $l{\equiv}3$ (mod 4), then $h_D$ is odd.

• Journal of the Korean Mathematical Society
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• v.54 no.4
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• pp.1345-1356
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• 2017

For a given number field K, we show that the ranks of elliptic curves over K are uniformly finitely bounded if and only if the weak Mordell-Weil property holds in all (some) ultrapowers $^*K$ of K. We introduce the nonstandard weak Mordell-Weil property for $^*K$ considering each Mordell-Weil group as $^*{\mathbb{Z}}$-module, where $^*{\mathbb{Z}}$ is an ultrapower of ${\mathbb{Z}}$, and we show that the nonstandard weak Mordell-Weil property is equivalent to the weak Mordell-Weil property in $^*K$. In a saturated nonstandard number field, there is a nonstandard ring of integers $^*{\mathbb{Z}}$, which is definable. We can consider definable abelian groups as $^*{\mathbb{Z}}$-modules so that the nonstandard weak Mordell-Weil property is well-defined, and we conclude that the nonstandard weak Mordell-Weil property and the weak Mordell-Weil property are equivalent. We have valuations induced from prime numbers in nonstandard rational number fields, and using these valuations, we identify two nonstandard rational numbers.

• Journal of computational fluids engineering
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• v.16 no.4
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• pp.100-109
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• 2011

Large eddy simulation(LES) of fully developed turbulent pipe flow has been performed to investigate the effect of Reynolds number on the flow field at $Re_{\tau}$=180, 395, 590 based on friction velocity and pipe radius. A dynamic subgrid-scale model for the turbulent subgrid-scale stresses was employed to close the governing equations. The mean flow properties, mean velocity profiles and turbulent intensities obtained from the present LES are in good agreement with the previous numerical and experimental results currently available. The Reynolds number effects were observed in the higher-order statistics(Skewness and Flatness factor). Furthermore, the budgets of the Reynolds stresses and turbulent kinetic energy were computed and analyzed to elucidate the effect of Reynolds number on the turbulent structures.

• Journal of KSNVE
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• v.8 no.2
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• pp.283-288
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• 1998

If one wants to control the noise from a duct, then one must have sufficient number of sensors and actuators so that the control system is observable and controllable. A number of sensors and actuators for control of radiating noise from a duct have to be incorporated with the number of modes which one wants to control. These considerations motivated the present study that considers a control system which has less microphones and actuators than required. In this work, by theoretical analysis and numerical simulation, the control performance and robust reliability of such a kind of control system is investigated in terms of sound-field variables and control system variables. Then the possibility of implementation of the robust radiation power control system is verified by theoretical analysis and numerical simulation. In addition, the control performance of the control system is verified by experiment.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.05a
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• pp.486-489
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• 2004

The NAH based on the inverse BEM is used to reconstruct the source field, which is advantageous in dealing with the irregular source. In the implementation of this technique, a large number of pressure measurements is required because an over-determined pressure data set is required. These conditions accordingly cause the increase of measurement time and associated effort along with the error due to mal-positioning. The purpose of this study is to reduce such inconveniences: Instead of increasing the number of field pressure data, the number of transfer paths between the source and the receiver is increased by placing rigid scattering body in-between the source and receiver. For validating the usefulness and effectiveness of the method, the numerical analyses of interior problem are demonstrated. As a result, it is thought that the proposed method enables the measurement at smaller number of sensor positions and the monitoring of surface vibration with less experimental effects than before.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.61 no.12
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• pp.1944-1947
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• 2012

In this work, we investigated quench characteristics of matrix-type superconducting fault current limiters (MFCLs) according to the turn number of reactors. The reactors used in MFCLs apply magnetic field to superconducting elements within reactors when fault currents surge into MFCL systems. It makes the fast and simultaneous quenches between superconducting elements. Also reactors decrease the fault power burden of superconducting elements by bypassing the partial fault currents to itself, when quench occurs. These structure proposed in this work can be expected to achieve much more current limiting capacity even though it uses less superconductors compared with other type SFCLs. Three reactors were made by Bakelite. These reactors with the turn number of 190, 380 and 570, had the length of 270 mm and diameter of 80 mm. We reported experimental results, including fault currents, fault voltages and resistance in superconducting elements according to the turn number of reactors. We confirmed that experimental results will be useful in next future plan for the real power grid.

• East Asian mathematical journal
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• v.28 no.2
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• pp.135-158
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• 2012

The ideals of the rings of integers are used to induce rational number system as operators(=group homomorphisms). We modify this inducing method to be effective in teaching rational numbers in secondary school. Indeed, this modification provides a nice model for explaining the equality property to define addition and multiplication of rational numbers. Also this will give some explicit ideas for students to understand the concept of 'field' efficiently comparing with the integer number system.