• Honam Mathematical Journal
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• v.27 no.4
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• pp.655-663
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• 2005

One of the basic questions concerning harmonic map is on the existence of harmonic maps satisfying a certain condition. Rigidity of a certain harmonic map can be considered as an answer for this kinds of questions. In this article, we study a rigidity property of harmonic diffeomorphisms under the condition that the inverse map is also harmonic. We show that every such a harmonic diffeomorphism is totally geodesic or conformal in two dimensional case.

• Journal of Electrical Engineering and Technology
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• v.9 no.1
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• pp.6-14
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• 2014

A new method to determine the total harmonic contributions of several customers and the utility at the point of common coupling is presented. The proposed method can quantify the individual harmonic impact of each suspicious harmonic source at the point of common coupling. The individual harmonic impact index is then used to assess the total harmonic contribution of each harmonic source. This index can be calculated by the results processed from instantaneous harmonic voltage and current phasor values. The results demonstrate the performance of the proposed method in terms of steady-state accuracy and response to time-varying operating conditions. The proposed index can be used for billing purposes to control harmonic distortion levels in power systems.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.61 no.10
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• pp.1554-1560
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• 2012

In this paper, the even harmonic current(2nd, 4th, 6th, 8th) of the arc fault current and normal current were measured in computer load and analyzed. The BPF with GIC was developed to detection of harmonic, the exact center frequency and a high degree of sharpness could be easily obtained. The total even harmonic distortion due to series arc fault in computer load was 31.2%, this value was increased 3.9 times better than the total even harmonic distortion of normal current. The results of analysis of arc fault current RMS variation rate and Peak variation rate per half-cycle, The RMS average variation rate are as follows ; the 2nd harmonic was 0.24, the 4th harmonic was 0.15, the 6th harmonic was 0.19, the 8th harmonic was 0.25, respectively. The Peak average variation rate are as follows ; the 2nd harmonic was 0.19, the 4th harmonic was 0.12, the 6th harmonic was 0.13, the 8th harmonic was 0.15, respectively. The results of this analysis utilize data to detect of series arc fault on wiring of computer load.

• Bulletin of the Korean Mathematical Society
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• v.49 no.6
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• pp.1241-1250
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• 2012

We prove the maximum principle and the comparison principle of $p$-harmonic functions via $p$-harmonic boundary of graphs. By applying the comparison principle, we also prove the solvability of the boundary value problem of $p$-harmonic functions via $p$-harmonic boundary of graphs.

• Korean Journal of Mathematics
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• v.5 no.2
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• pp.127-134
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• 1997

On the setting of the upper half-space of the euclidean n-space, we study some properties of harmonic little Bloch functions and we show that for a given harmonic little Bloch function $u$, there exists unique harmonic conjugates of $u$, which are also little Bloch functions with appropriate norm bounds.

• Journal of Power Electronics
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• v.18 no.4
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• pp.1140-1153
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• 2018

The harmonic impedance characteristic of a traction power supply system (TPSS) is necessary for taking actions to suppress the high-order harmonic resonances caused by AC electric locomotives. This paper proposes a controllable harmonic generating method (CHGM) for measuring the TPSS harmonic impedance by injecting harmonic disturbances of different frequencies and amplitudes into the TPSS. This method applies phase shifted pulse-width modulation (PSPWM) and ensures that the undesired sideband harmonics can be negligible while the desired harmonic is both controllable and adjustable. Multiple harmonics can be emitted at the same time. The implementation of the method is also presented. Simulations are carried out to validate the performance of the proposed method. Finally, experimental results on a 5 H-bridge converters platform verified the effectiveness and feasibility of the proposed method.

• Bulletin of the Korean Mathematical Society
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• v.51 no.6
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• pp.1591-1603
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• 2014

In this paper, we investigate maximum principle, convergence of sequences and angular limits for harmonic Bloch mappings. First, we give the maximum principle of harmonic Bloch mappings, which is a generalization of the classical maximum principle for harmonic mappings. Second, by using the maximum principle of harmonic Bloch mappings, we investigate the convergence of sequences for harmonic Bloch mappings. Finally, we discuss the angular limits of harmonic Bloch mappings. We show that the asymptotic values and angular limits are identical for harmonic Bloch mappings, and we further prove a result that applies also if there is no asymptotic value. A sufficient condition for a harmonic Bloch mapping has a finite angular limit is also given.

• 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.

• Journal of Electrical Engineering and Technology
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• v.12 no.2
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• pp.559-568
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• 2017

Harmonic/inter-harmonic detection and analysis is an important issue in power system signal processing. This paper proposes a fast algorithm based on matching pursuit (MP) sparse signal decomposition, which can be employed to extract the harmonic or inter-harmonic components of a distorted electric voltage/current signal. In the MP iterations, the method extracts harmonic/inter-harmonic components in order according to the spectrum peak. The Fast Fourier Transform (FFT) and nonlinear optimization techniques are used in the decomposition to realize fast and accurate estimation of the parameters. First, the frequency estimation value corresponding to the maxim spectrum peak in the present residual is obtained, and the phase corresponding to this frequency is searched in discrete sinusoids dictionary. Then the frequency and phase estimations are taken as initial values of the unknown parameters for Nelder-Mead to acquire the optimized parameters. Finally, the duration time of the disturbance is determined by comparing the inner products, and the amplitude is achieved according to the matching expression of the harmonic or inter-harmonic. Simulations and actual signal tests are performed to illustrate the effectiveness and feasibility of the proposed method.

• Communications of the Korean Mathematical Society
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• v.35 no.3
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• pp.843-854
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• 2020

The purpose of this present paper is to obtain inclusion relations between various subclasses of harmonic univalent functions by using the convolution operator associated with generalized distribution series. To be more precise, we obtain such inclusions with harmonic starlike and harmonic convex mappings in the plane.