• Title/Summary/Keyword: Fourier Function

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Fourier Transformations (TEM 관련 이론해설 (2): Fourier 변환)

  • Lee, Hwack-Joo
    • Applied Microscopy
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    • v.32 no.3
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    • pp.195-204
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    • 2002
  • In this review, the fundamental concepts of delta function, convolution integral and Fourier transformation are discussed. The applications of Fourier transformation to slit function, two very narrow slits, two slits of appreciable width, periodic array of narrow slits, arbitary periodic function, diffraction gratings and gaussian functions are also introduced.

A REPRESENTATION FOR AN INVERSE GENERALIZED FOURIER-FEYNMAN TRANSFORM ASSOCIATED WITH GAUSSIAN PROCESS ON FUNCTION SPACE

  • Choi, Jae Gil
    • The Pure and Applied Mathematics
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    • v.28 no.4
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    • pp.281-296
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    • 2021
  • In this paper, we suggest a representation for an inverse transform of the generalized Fourier-Feynman transform on the function space Ca,b[0, T]. The function space Ca,b[0, T] is induced by the generalized Brownian motion process with mean function a(t) and variance function b(t). To do this, we study the generalized Fourier-Feynman transform associated with the Gaussian process Ƶk of exponential-type functionals. We then establish that a composition of the Ƶk-generalized Fourier-Feynman transforms acts like an inverse generalized Fourier-Feynman transform.

Economies of Scale in Multiproduct Firms;Evidence from Air Transport Industry (항공운송산업의 비용분석을 통한 규모의 경제성 추정;초월대수(Translog)비용함수와 푸리에(Fourier) 신축함수 비교 분석을 중심으로)

  • Kim, Je-Chul;Huh, Seok-Min;Lee, Dong-Hui;Lee, Young-Soo
    • Journal of the Korean Society for Aviation and Aeronautics
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    • v.14 no.4
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    • pp.38-47
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    • 2006
  • This study analyzes the expense structure of the air transport industry, based on the cost and income data of 18 major airlines, estimates the economic effectiveness of scale and conducts comparative analysis. As for the method of analysis, Translog cost function and the Fourier flexible function were used. The result showed that big companies had the economy of scale based on the Translog cost function, while the Fourier flexible function led to a estimation that expanding the input is not recommended, for the expansion of scale entails the poor economy of scale. It can be presumed that the economy of scale was estimated according to the U shape of the Translog cost function in the given data. On the other hand, the Fourier flexible cost function approaches the unknown function, as it is a Fourier series, and correctly infers the economy of scale based on the analyzed data. As for the flag carrier's economy of scale, it was inferred that the economy of scale existed by any of two functions. Therefore, the conclusion was that further expanding the scale will not cause any problem.

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Convolution product and generalized analytic Fourier-Feynman transforms

  • Chang, Seung-Jun
    • Communications of the Korean Mathematical Society
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    • v.11 no.3
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    • pp.707-723
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    • 1996
  • We first define the concept of the generalized analytic Fourier-Feynman transforms of a class of functionals on function space induced by a generalized Brownian motion process and study of functionals which plays on important role in physical problem of the form $ F(x) = {\int^{T}_{0} f(t, x(t))dt} $ where f is a complex-valued function on $[0, T] \times R$. We next show that the generalized analytic Fourier-Feynman transform of the convolution product is a product of generalized analytic Fourier-Feynman transform of functionals on functin space.

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GENERALIZED FOURIER-WIENER FUNCTION SPACE TRANSFORMS

  • Chang, Seung-Jun;Chung, Hyun-Soo
    • Journal of the Korean Mathematical Society
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    • v.46 no.2
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    • pp.327-345
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    • 2009
  • In this paper, we define generalized Fourier-Hermite functionals on a function space $C_{a,b}[0,\;T]$ to obtain a complete orthonormal set in $L_2(C_{a,b}[0,\;T])$ where $C_{a,b}[0,\;T]$ is a very general function space. We then proceed to give a necessary and sufficient condition that a functional F in $L_2(C_{a,b}[0,\;T])$ has a generalized Fourier-Wiener function space transform ${\cal{F}}_{\sqrt{2},i}(F)$ also belonging to $L_2(C_{a,b}[0,\;T])$.

Dyadic Green`s Function for an Unbounded Anisotropic Medium in Cylindrical Coordinates

  • Kai Li;Park, Seong-Ook;Pan, Wei-Yan
    • Journal of electromagnetic engineering and science
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    • v.1 no.1
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    • pp.54-59
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    • 2001
  • The dyadic Green`s function for an unbounded anisotropic medium is treated analytically in the Fourier domain. The Green`s function, which is expressed as a triple Fourier integral, can be next reduced to a double integral by performing the integral, by performing the integration over the longitudinal Fourier variable or the transverse Fourier variable. The singular behavior of Green`s is discussed for the general anisotropic case.

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CONDITIONAL GENERALIZED FOURIER-FEYNMAN TRANSFORM AND CONDITIONAL CONVOLUTION PRODUCT ON A BANACH ALGEBRA

  • Chang, Seung-Jun;Choi, Jae-Gil
    • Bulletin of the Korean Mathematical Society
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    • v.41 no.1
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    • pp.73-93
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    • 2004
  • In [10], Chang and Skoug used a generalized Brownian motion process to define a generalized analytic Feynman integral and a generalized analytic Fourier-Feynman transform. In this paper we define the conditional generalized Fourier-Feynman transform and conditional generalized convolution product on function space. We then establish some relationships between the conditional generalized Fourier-Feynman transform and conditional generalized convolution product for functionals on function space that belonging to a Banach algebra.

RELATIONSHIPS BETWEEN INTEGRAL TRANSFORMS AND CONVOLUTIONS ON AN ANALOGUE OF WIENER SPACE

  • Cho, Dong Hyun
    • Honam Mathematical Journal
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    • v.35 no.1
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    • pp.51-71
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    • 2013
  • In the present paper, we evaluate the analytic conditional Fourier-Feynman transforms and convolution products of unbounded function which is the product of the cylinder function and the function in a Banach algebra which is defined on an analogue o Wiener space and useful in the Feynman integration theories and quantum mechanics. We then investigate the inverse transforms of the function with their relationships and finally prove that th analytic conditional Fourier-Feynman transforms of the conditional convolution products for the functions, can be expressed in terms of the product of the conditional Fourier-Feynman transforms of each function.

FOURIER'S TRANSFORM OF FRACTIONAL ORDER VIA MITTAG-LEFFLER FUNCTION AND MODIFIED RIEMANN-LIOUVILLE DERIVATIVE

  • Jumarie, Guy
    • 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.

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SURVEY OF GIBBS PHENOMENON FROM FOURIER SERIES TO HYBRID SAMPLING SERIES

  • SHIM HONG TAE;PARK CHIN HONG
    • Journal of applied mathematics & informatics
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    • v.17 no.1_2_3
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    • pp.719-736
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    • 2005
  • An understanding of Fourier series and their generalization is important for physics and engineering students, as much for mathematical and physical insight as for applications. Students are usually confused by the so-called Gibbs' phenomenon, an overshoot between a discontinuous function and its approximation by a Fourier series as the number of terms in the series becomes indefinitely large. In this paper we give short story of Gibbs phenomenon in chronological order.