• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.521-535
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• 2022

In this paper, we introduce the k-Hankel-Wigner transform on R in some problems of time-frequency analysis. As a first point, we present some harmonic analysis results such as Plancherel's, Parseval's and an inversion formulas for this transform. Next, we prove a Heisenberg's uncertainty principle and a Calderón's reproducing formula for this transform. We conclude this paper by studying an extremal function for this transform.

• Kyungpook Mathematical Journal
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• v.63 no.3
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• pp.425-435
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• 2023

The classical Hardy Theorem on R states that a function f and its Fourier transform cannot be simultaneously very small; this fact was generalized by Miyachi in terms of L¹ + L^∞ and log⁺-functions. In this paper, we consider the k-Hankel transform, which is a deformation of the Hankel transform by a parameter k > 0 arising from Dunkl's theory. We study Miyachi's theorem for the k-Hankel transform on ℝ^d.

• Proceedings of the KIEE Conference
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• 2011.07a
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• pp.43-44
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• 2011

S-Transform은 어떠한 신호의 변환 후 원 신호의 주파수 및 크기를 모두 알 수 있는 효과적인 방법이다. 따라서, 본 논문에서는 IEEE에서 제시한 전력품질 이벤트의 분류를 기반으로 S-Transform 기반의 전력품질 이벤트의 측정지수를 제안하였다. 제안한 측정지수의 효율성을 검증하기 위하여, ATPDraw를 이용하여 고장 및 비선형 부하를 모의하였다. 그 결과를 이용하여 S-Transform을 수행하여 제안된 측정지수의 효율성을 검증하였다.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.61 no.5
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• pp.657-663
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• 2012

Recently, by increasing of devices which are sensitive to power quality, the deterioration of power quality has been accelerated. For this reason, the social and economic losses are increased. So not only correct measurement and evaluation, but also countermeasure for improvement of power quality is surely necessary for both electric power supplier and consumer. In this paper, the discrimination algorithm for events and variation occurred in distribution systems using S-transform is proposed. Firstly, we review for events and variations that occur in distribution system. Next, we simulate events and variations on various conditions using ElectroMagnetic Transient Program(EMTP). For the simulation, the IEEE 13 Node Test Feeder and KEPCO's distribution system is modeled. Finally, for the analysis, a modified wavelet transform known as S-transform is adopted to find out the characteristics of each events and variations.

• 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 Chungcheong Mathematical Society
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• v.35 no.2
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• pp.177-196
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• 2022

The Elzaki Transform method is fuzzified to fuzzy Elzaki Transform by Rehab Ali Khudair. In this article, we propose a Double fuzzy Elzaki transform (DFET) method to solving fuzzy partial differential equations (FPDEs) and we prove some properties and theorems of DFET, fundamental results of DFET for fuzzy partial derivatives of the n^th order, construct the Procedure to find the solution of FPDEs by DFET, provide duality relation of Double Fuzzy Laplace Transform (DFLT) and Double Fuzzy Sumudu Transform(DFST) with proposed Transform. Also we solve the Fuzzy Poisson's equation and fuzzy Telegraph equation to show the DFET method is a powerful mathematical tool for solving FPDEs analytically.

• Journal of the Korean Chemical Society
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• v.37 no.4
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• pp.371-377
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• 1993

Fourier Transform UV/VIS spectrometer has been modified for emission spectroscopy with the technique of supersonic expansion, in which the unstable molecular radical $CH_3S$ has been generated in a jet by a high voltage DC discharge. The fluorescence spectra of the supersonically cooled radical have been recorded on a Fourier Transform UV/VIS spectrometer. The ratio of signal to noise of the spectra has been improved substantially. Also the rotational structure has been clearly resolved for $CH_3S$ molecular radical.

• Korean Journal of Mathematics
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• v.29 no.2
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• pp.321-332
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• 2021

This paper is a further development of the recent results by the authors on the generalized sequential Fourier-Feynman transform for functionals in a Banach algebra Ŝ and some related functionals. We investigate various relationships between the generalized sequential Fourier-Feynman transform and the generalized sequential convolution product of functionals. Parseval's relation for the generalized sequential Fourier-Feynman transform is also given.

• Journal of applied mathematics & informatics
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• v.41 no.1
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• pp.83-93
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• 2023

We would like to consider Laplace transform of the form of fg, the form of product, and applies it to Burger's equation in general case. This topic has not yet been addressed, and the methodology of this article is done by considerations with respect to several approaches about the transform of the form of f g and the mean value theorem for integrals. This paper has meaning in that the integral transform method is applied to solving nonlinear equations.

• Journal of electromagnetic engineering and science
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• v.14 no.3
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• pp.273-277
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• 2014

In this research, integral transform technique for electromagnetic scattering formulation is reviewed. Electromagnetic boundary-value problems are presented to demonstrate how the integral transforms are utilized in electromagnetic propagation, antennas, and electromagnetic interference/compatibility. Various canonical structures of slotted conductors are used for illustration; moreover, Fourier transform, Hankel transform, Mellin transform, Kontorovich-Lebedev transform, and Weber transform are presented. Starting from each integral transform definition, the general procedures for solving Helmholtz's equation or Laplace's equation for the potentials in the unbounded region are reviewed. The boundary conditions of field continuity are incorporated into particular formulations. Salient features of each integral transform technique are discussed.