• Tribology and Lubricants
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• v.17 no.5
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• pp.373-379
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• 2001

The problem of interest is formulating elastic contact problem of a layered semi-infinite solid in terms of Fourier integral. The plane strain problem is considered for a solid composed of homogeneous isotropic two layers with different mechanical properties. General solutions for the subsurface stress and deformation field of frictionless elastic bodies under normal loading using of Fourier transformation technique are obtained. The numerical results for the stress distribution of coated solid for some particular cases are given.

• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.1101-1121
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• 2008

One proposes an approach to fractional Fourier's transform, or Fourier's transform of fractional order, which applies to functions which are fractional differentiable but are not necessarily differentiable, in such a manner that they cannot be analyzed by using the so-called Caputo-Djrbashian fractional derivative. Firstly, as a preliminary, one defines fractional sine and cosine functions, therefore one obtains Fourier's series of fractional order. Then one defines the fractional Fourier's transform. The main properties of this fractal transformation are exhibited, the Parseval equation is obtained as well as the fractional Fourier inversion theorem. The prospect of application for this new tool is the spectral density analysis of signals, in signal processing, and the analysis of some partial differential equations of fractional order.

• Journal of the Korean Society of Safety
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• v.20 no.3 s.71
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• pp.64-70
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• 2005

In this literature, fault detection and classification of faulty induction motors are carried out through Z-index and frequency analysis. Above frequency analysis refer Fourier transformation and Wavelet transformation. Z-index is defined as the similar form of energy function, also the faulty and healthy conditions are classified through Z-index. For the detection and classification feature extraction for the fault detection of an induction motor is carried out using the information from stator current. Fourier and Wavelet transforms are applied to detect the characteristics under the healthy and various faulty conditions. We can obtain feature vectors from two transformations, and the results illustrate that the feature vectors are complementary each other.

• The Pure and Applied Mathematics
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• v.14 no.4
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• pp.317-333
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• 2007

In 2002, the author and professor Ryu introduced the concept of analogue of Wiener measure. In this paper, we prove the existence theorem of Fourier-Feynman transform on analogue of Wiener measure in $L_2-norm$ sense.

• Geophysics and Geophysical Exploration
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• v.17 no.3
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• pp.129-136
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• 2014

Electromagnetic (EM) methods are generally divided into frequency-domain EM (FDEM) and time-domain EM (TDEM) methods, depending on the source waveform. The FDEM and TDEM fields are mathematically related by the Fourier transformation, and the TDEM field can thus be obtained as the Fourier transformation of FDEM data. For modeling in time-domain, we can use fast frequency-domain modeling codes and then convert the results to the time domain with a suitable numerical method. Thus, frequency-to-time transformations are of interest to EM methods, which is generally attained through fast Fourier transform. However, faster frequency-to-time transformation is required for the 3D inversion of TDEM data or for the processing of vast air-borne TDEM data. The diffusion expansion method (DEM) is one of smart frequency-to-time transformation methods. In DEM, the EM field is expanded into a sequence of diffusion functions with a known frequency dependence, but with unknown diffusion-times that must be chosen based on the data to be transformed. Especially, accuracy of DEM is sensitive to the diffusion-time. In this study, we developed a method to determine the optimum range of diffusion-time values, minimizing the RMS error of the frequency-domain data approximated by the diffusion expansion. We confirmed that this method produces accurate results over a wider time range for a homogeneous half-space and two-layered model.

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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• 1999.06a
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• pp.73-79
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• 1999

Finite element equations by using fast Fourier transformation were formulated for studying temperatures resulting from frictional heating in sliding systems. The equations include the effect of velocity of moving components. The program developed by using FFT-FEM that combines Fourier transform techniques and the finite element method, was applied to the sliding bearing system. Numerical prediction obtained by FFT-FEM was in an excellent agreement of experimental temperature measurements.

• Bulletin of the Korean Mathematical Society
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• v.38 no.1
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• pp.7-16
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• 2001

We study the Fourier transformation on the Gelfand-Bruhat space of type S and characterize this space by means of Fourier transform on a locally compact abelian group G. Also, we extend Bochner-Schwartz theorem to the dual space of the Gelfand-Bruhat space and the space of Fourier hyperfunctions on G. respectively.

• Tribology and Lubricants
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• v.16 no.3
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• pp.218-222
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• 2000

Finite element equations by using fast Fourier transformation were formulated for studying temperatures resulting from frictional heating in sliding systems. The equations include the effect of velocity of moving components. The program developed by using FFT-FEM that combines Fourier transform techniques and the finite element method, was applied to the sliding bearing system. Numerical prediction obtained by FFT-FEM was in an excellent agreement of experimental temperature measurements.

• Korean Journal of Mathematics
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• v.9 no.2
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• pp.133-147
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• 2001

In this paper, we introduce the concepts of multiple $L_p$ analytic Fourier-Feynman transform ($1{\leq}p$ < ${\infty})$ and a convolution product of functionals on abstract Wiener space and verify the existence of the multiple $L_p$ analytic Fourier-Feynman transform for functionls in the Fresnel class. Moreover, we verify that the Fresnel class is closed under the $L_p$ analytic Fourier-Feynman transformation and the convolution product, respectively. And we establish some relationships among the multiple $L_p$ analytic Fourier-Feynman transform and the convolution product on the Fresnel class.

• Proceedings of the KIEE Conference
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• 1996.07c
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• pp.1523-1525
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• 1996

Partial discharges(PD) in air insulated electric power systems cause power loss, produce interfering electromagnetic radiation, and can indicate incipient failure. An understanding of PD in air gap is clearly important. The Wavelet transformation is an extended method of fourier transformation. The fourier method is a powerful tool for signal analysis, but it can't include informations for time. However tile wavelet transformation analysis can include on the informations of time and frequency at the same time. In this paper we apply the wavelet transformation to the PD signals in needle-plane air gap for tile purpose of analysis of developing aspects of PD. We can analyze the developing aspects of PD, namely, PD current, repetition rates, width of pulse distribution region, pulseless region and frequencies distribution of PD pulses.