• Journal of the Korean Mathematical Society
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• v.61 no.2
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• pp.377-393
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• 2024

In this paper, we study the positive solutions to a discrete harmonic function for a random walk satisfying finite range and ellipticity conditions, killed at the boundary of an unbounded cylinder in ℤ^d. We first prove the existence and uniqueness of positive solutions, and then establish that all the positive solutions are generated by two special solutions, which are exponential growth at one end and exponential decay at the other. Our method is based on maximum principle and a Harnack type inequality.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.55 no.9
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• pp.384-391
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• 2006

The harmonic currents generated along with the operating speed of electrical railroad traction are very difficult to analyze because of its nonlinear characteristics. This paper therefore presents probabilistic approach for the evaluation of harmonic currents about the operating speed of the arbitrary single traction. To use probabilistic method for railroad system, PDF(Probability Density Function) using measuring data based on the realistic h 따 monic currents per operating speed is calculated. Measuring data of harmonic current per operating speed is obtained using the result data of PSCAD/EMTDC dynamic simulation based on an IAT(Intra Airport Transit) in Incheon International Airport. The means(expected values) and variances of harmonic currents of single traction also are obtained by the PDF of the operating traction speed and harmonic currents. The uncertainty of harmonic currents can be calculated through the mean and variance of PDF. The probability of harmonic currents generated with the operating of arbitrary many tractions is calculated by the convolution of functions. The harmonics of different number of tractions are systematically investigated to assess the TDD(Total Demand Distortion) for the railroad system. The calculation of TDD was carried out using Monte-Carlo Simulations(MSCs) and the results of TDD evaluation of the power quality in the IAT power feeding system.

• Journal of the Korea Society for Simulation
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• v.10 no.4
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• pp.1-10
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• 2001

For the simulation of piping vibrations in petrochemical plants, forcing functions mainly depend upon the equipment working mechanism and vibration resources in the piping systems. In general, harmonic function is used to simulate rotary equipment. Mechanical driving frequencies, wave functions, and response spectrum are used to simulate reciprocating compressors, surge vibration of long transfer piping, and seismic/wind vibration, respectively. In this study, the general suggestions for forcing functions were reviewed and proposed the forcing function to simulate the spray injection system inside the pipe in which two different fluids are distributed uniformly. To confirm the results, the scheme was applied for a real piping system. The vibration mode of the real system was consistent with the 4th mode (26.725 Hz) obtained by simulation using the forcing function presented in this study.

• East Asian mathematical journal
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• v.33 no.3
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• pp.309-315
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• 2017

In this paper, we investigate the regularities of the hyper-complex valued functions of the split quaternion variables. We define several differential operators for the split qunaternionic function. We research several left split regular functions for each differential operators. We also investigate split harmonic functions. And we find the corresponding Cauchy-Riemann system and the corresponding Cauchy theorem for each regular functions on the split quaternion field.

• Journal of the Korean Mathematical Society
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• v.55 no.5
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• pp.1103-1129
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• 2018

In this paper, we show several vanishing type theorems for p-harmonic ${\ell}$-forms on Riemannian manifolds ($p{\geq}2$). First of all, we consider complete non-compact immersed submanifolds $M^n$ of $N^{n+m}$ with flat normal bundle, we prove that any p-harmonic ${\ell}$-form on M is trivial if N has pure curvature tensor and M satisfies some geometric conditions. Then, we obtain a vanishing theorem on Riemannian manifolds with a weighted $Poincar{\acute{e}}$ inequality. Final, we investigate complete simply connected, locally conformally flat Riemannian manifolds M and point out that there is no nontrivial p-harmonic ${\ell}$-form on M provided that the Ricci curvature has suitable bound.

• Transactions on Electrical and Electronic Materials
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• v.15 no.4
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• pp.182-188
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• 2014

When the windowed DFT algorithm is applied in harmonic measurements, the problem of initial-phase sensitivity will be encountered, this has an effect on harmonic amplitude accuracy. In this paper, the origin of initial-phase sensitivity is analyzed and the main factors that influence the level of initial-phase sensitivity are demonstrated. A method of reducing initial-phase sensitivity is proposed to increase the stability of harmonic measurements. We found that initial-phase sensitivity is determined by the side lobe peak level of the window functions when synchronous deviation is fixed. In addition, increasing the length of the time recorded can be used to remove initial-phase sensitivity. The correctness and validity of our conclusions have been confirmed through numerical results and field tests.

• Proceedings of the KIPE Conference
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• 2004.07b
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• pp.587-591
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• 2004

This paper proposes a novel current compensation technique that can eliminate the harmonic currents included in line currents without computation of harmonic current components. A current controller with fast dynamics for an active filter is described. Harmonic currents are directly controlled without the need for sensing and computing the harmonic current of the load current, thus simplifying the control system. Current compensation is done in the time domain, allowing a fast time response. The DC voltage control loop keeps the voltage across the DC capacitor constant. High power factor control by an active filter is described. All control functions are implemented in software using a single-chip microcontroller, thus simplifying the control circuit. Any current-controlled synchronous rectifier can be used as a shunt active filter through only the simple modification of the software and the addition of current sensors. It is shown through experimental results that the proposed controller gives good performance for the shunt active filter.

• Proceedings of the KIEE Conference
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• 2005.07a
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• pp.214-216
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• 2005

A magnitude of generated harmonic currents along with the operation of traction has nonlinear characteristics. The harmonic currents generated along with the operating speed of electrical railroad traction is to analyze very difficulty. This paper therefore presents probabilistic approach for the harmonic currents evaluation about the operating speed of the arbitrary single traction. To use probabilistic method for railroad system, probability density function(PDF) using measuring data based on the realistic harmonic currents per operating speed is calculated. Mean and variance of harmonic currents of single traction also are obtained the PDF of the operating speed and electrical railroad traction model. Uncertainty of harmonic currents expects to results through mean and variance with PDF. The probability of harmonic currents generated with the operating of arbitrary many tractions is calculated by the convolution of functions. The harmonics of different number of tractions are systematically investigated. It is assessed by the total demand distortion(TDD) for the railroad system.

• Communications of the Korean Mathematical Society
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• v.5 no.1
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• pp.119-122
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• 1990

• Journal of the Korean Mathematical Society
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• v.10 no.2
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• pp.73-75
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• 1973