• Corrosion Science and Technology
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• v.11 no.6
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• pp.247-256
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• 2012

Harmonic current was measured for a dummy cell with various values of resistance, and the procedure developed through the measurements was applied to the investigation of effects of the amplitude of applied frequency and applied potential on the harmonic current of a stainless steel and a carbon steel in chloride containing solutions. From the measurements of harmonic current in the dummy cell, the optimum values of applied frequency and applied potential in harmonic current measurements were found to be 1 mHz and 20 mV (or lower), respectively. Increase in harmonic current with applied frequency was observed in the case where the level of harmonic current is low as in a stainless steel. Decrease in polarization resistance was also noted in this corrosion system with either increasing applied frequency or decreasing applied potential. However, no obvious effects of applied frequency was observed on harmonic current and polarization resistance in a carbon steel in which the level of harmonic current is high.

• Kyungpook Mathematical Journal
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• v.58 no.3
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• pp.559-571
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• 2018

In this paper, we give some results on the stability of f-harmonic maps with potential from or into spheres and any Riemannian manifold. We study the constant boundary-value problems of such maps defined on a specific Cartan-Hadamard manifolds, and obtain a Liouville-type theorem. It can also be applied to the static Landau-Lifshitz equations. We also prove a Liouville theorem for f-harmonic maps with finite f-energy or slowly divergent f-energy.

• Journal of Biomedical Engineering Research
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• v.8 no.2
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• pp.223-230
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• 1987

In this paper the harmonic degrees between $\alpha$ wave and $\beta$ wave in visual evoked potential are analyzed by the bicoherence. The bicoherence analysis is based on an AR model which provides significantly better resolution than that of Fourier transform. The analysis results of visual evoked pope ntial are compared with the analysis results of background EEC. From the comparison results it is found that the harmonic degree of visual evoked potential is less than she harmonic degree of background EEG and the $\beta$ wave of visual evoke potential unlike the background EEC contains the non harmonic property of a wave more than the harmonic properity

• Bulletin of the Korean Mathematical Society
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• v.48 no.6
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• pp.1291-1302
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• 2011

We establish the local well-posedness for the Cauchy problem of the nonlinear Schr$\ddot{o}$odinger equation with harmonic potential in $H^s(\mathbb{R}^n)$, where $s{\in}\mathbb{R}$, s > 0.

• Bulletin of the Korean Chemical Society
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• v.24 no.2
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• pp.219-221
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• 2003

Rabi oscillation between bound states of a single potential is well known. However the corresponding formula between the states of two different potentials has not been obtained yet. In this work, we derive Rabi formula between the states of a coupled harmonic oscillator which may be used as a simple model for the electron transfer. The expression is similar to typical Rabi formula for a single potential. This result may be used to describe transitions between coupled diabatic potential curves.

• Journal of the Korean Mathematical Society
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• v.54 no.4
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• pp.1189-1208
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• 2017

In this paper, we study vanishing properties for $L^2$ harmonic 1-forms on a gradient shrinking Ricci soliton. We prove that if (M, g, f) is a complete oriented noncompact gradient shrinking Ricci soliton with potential function f, then there are no non-trivial $L^2$ harmonic 1-forms which are orthogonal to df. Second, we show that if the scalar curvature of the metric g is greater than or equal to (n - 2)/2, then there are no non-trivial $L^2$ harmonic 1-forms on (M, g). We also show that any multiplication of the total differential df by a function cannot be an $L^2$ harmonic 1-form unless it is trivial. Finally, we derive various integral properties involving the potential function f and $L^2$ harmonic 1-forms, and handle their applications.

• Bulletin of the Korean Chemical Society
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• v.29 no.1
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• pp.85-88
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• 2008

A direct application of the WKB quantization to the three-dimensional Coulomb potential does not yield the exact eigenenergies. The three-dimensional Coulomb potential is converted to a Morse potential by using the point canonical transformation. Then the WKB quantization is applied to the Morse potential to find a relationship between the eigenenergies of the Coulomb and those of the Morse potentials. From the relationship the exact eigenenergis of the Coulomb potential are determined. The same method is found to be also valid for the three-dimensional harmonic oscillator potential. And the Langer modified WKB quantization is algebraically derived.

• Korean Journal of Mathematics
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• v.26 no.4
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• pp.601-614
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• 2018

We consider the magnetic $Schr{\ddot{o}}dinger$ operator coupled with two different potentials. One of them is a harmonic oscillator and the other is a periodic potential. We give some periodic potential classes for which the operator has purely absolutely continuous spectrum. We also prove that for strong magnetic field or large coupling constant, there are open gaps in the spectrum and we give a lower bound on their number.

• Korean Journal of Mathematics
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• v.19 no.2
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• pp.129-147
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• 2011

In this paper we discuss the zeta-determinants of harmonic oscillators having general quadratic potentials defined on $\mathbb{R}^2$. By using change of variables we reduce the harmonic oscillators having general quadratic potentials to the standard harmonic oscillators and compute their spectra and eigenfunctions. We then discuss their zeta functions and zeta-determinants. In some special cases we compute the zeta-determinants of harmonic oscillators concretely by using the Riemann zeta function, Hurwitz zeta function and Gamma function.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.27 no.12
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• pp.81-86
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• 2013

An electric potential rise of the grounding electrode developed by the lightning stroke currents should be calculated for the purpose of effective protection of electrical and electronic equipment. In this paper, the electromagnetic model was applied to calculate the harmonic impedance of grounding electrode. Also the empirical equation related to the permittivity and resistivity of soil was used. The lightning current waveforms, which are expressed by the Heidler's equation, were used in order to calculate accurately transient electric potential rises. The transient voltage was obtained by using the simulated harmonic impedance and the lightning current in frequency domain. Finally, the transient voltages of horizontal grounding electrode(10m) under lightning stroke currents were calculated by IFFT(Inverse Fast Fourier Transform).