• Journal of electromagnetic engineering and science
• /
• v.1 no.1
• /
• pp.54-59
• /
• 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.

• Journal of the Chungcheong Mathematical Society
• /
• v.21 no.2
• /
• pp.231-246
• /
• 2008

In this paper, we use a generalized Brownian motion process to define a generalized analytic Feynman integral. We then establish several integration formulas for generalized analytic Feynman integrals generalized analytic Fourier-Feynman transforms and generalized integral transforms of functionals in the class of functionals ${\mathbb{E}}_0$. Finally, we use these integration formulas to obtain several generalized Feynman integrals involving the generalized analytic Fourier-Feynman transform and the generalized integral transform of functionals in ${\mathbb{E}}_0$.

• Communications of the Korean Mathematical Society
• /
• v.31 no.4
• /
• pp.791-809
• /
• 2016

By introducing two fractional convolutions, we obtain the convolution theorems for fractional Fourier cosine and sine transforms. Applying these convolutions, we construct two Boehmian spaces and then we extend the fractional Fourier cosine and sine transforms from these Boehmian spaces into another Boehmian space with desired properties.

• The Pure and Applied Mathematics
• /
• v.28 no.2
• /
• pp.119-142
• /
• 2021

In this paper, we first introduce a new L_p analytic Fourier-Feynman transform with respect to subordinate Brownian motion (AFFTSB), which extends the Fourier-Feynman transform in the Wiener space. We next examine several relationships involving the L_p-AFFTSB, the convolution product, and the gradient operator for several types of functionals.

• Korean Journal of Mathematics
• /
• v.31 no.4
• /
• pp.521-536
• /
• 2023

This paper is a further development of the recent results by the author and coworker on the generalized sequential Fourier-Feynman transform for functionals in a Banach algebra Ŝ and some related functionals. We establish existence of the generalized first variation of these functionals. Also we investigate various relationships between the generalized sequential Fourier-Feynman transform, the generalized sequential convolution product and the generalized first variation of the functionals.

• Journal of Energy Engineering
• /
• v.8 no.4
• /
• pp.540-545
• /
• 1999

The classical Fourier heat conduction equation is invalid at temperatures near absolute zero or at very early times in highly transient heat transfer processes. In such situations, a hyperbolic equation model for heat conduction based on the modified Fourier law is introduced because the wave nature of heat propagation becomes dominant. The Fourier model and the hyperbolic model for heat conduction are analyzed by using the Green's function technique together with the integral transform. Analytical expressions for the heat flux and temperature distributions in a finite slab subjected to a periodic surface heating at one of its surfaces are presented and the results obtained from each model are compared with each other. The thermal wave implied b the hyperbolic model is shown to travel through a medium and to reflect back toward the origin at the other insulated surface. On the other hand, the heat by the Fourier model propagates at an infinite speed instantaneously after a thermal disturbance is felt throughout the medium.

• Korean Journal of Optics and Photonics
• /
• v.14 no.3
• /
• pp.266-271
• /
• 2003

The reflectance spectrum of optical films thicker than a few microns shows an intensity oscillation due to interference. Since the spectral period of the oscillation is inversely related to film thickness, the thickness of an optical film can be determined from the spectral frequency of the oscillation. For rapid data processing, the spectral frequency is obtained by use of a Fast Fourier Transformation technique. The conventional method of applying a Fast Fourier Transformation to the reflectance spectrum versus photon energy is modified so as to clear the ambiguity in choosing the proper effective refractive index value and to prevent the broadening of the Fourier transformed peak due to the refractive index dispersion. This technique of modified Fast Fourier Transformation is suggested by the authors for the first time to their knowledge. From the analysis of the calculated reflectance spectrum of a 30-${\mu}{\textrm}{m}$-thick dielectric film. it is shown to improve the accuracy in determining film thickness by a great amount. The improved accuracy of the modified Fast Fourier Transformation is also confirmed from the analysis of the reflectance spectra of a sample with 80-${\mu}{\textrm}{m}$-thick cover layer and 13-${\mu}{\textrm}{m}$-thick spacer layer on a PC substrate.

• Journal of the Korean Statistical Society
• /
• v.25 no.1
• /
• pp.123-131
• /
• 1996

The problerm of testing for a constant mean is considered. A Kolmogorov-Smirnov type test using the sample Fourier coefficients is suggested and its asymptotic distribution is derived. A simulation study shows that the proposed test is more powerful than the cusum type test when there is more than one change-point or there is a cyclic change.

• Proceedings of the Korean Statistical Society Conference
• /
• 2002.11a
• /
• pp.109-114
• /
• 2002

In this paper we propose a change-point estimator with left and right regressions using the sample Fourier coefficients on the orthonormal bases. The asymptotic properties of the proposed change-point estimator are established. The limiting distribution and the consistency of the estimator are derived.

• Korean Journal of Mathematics
• /
• v.16 no.1
• /
• pp.85-90
• /
• 2008

We consider Fourier multiplier operators whose symbols satisfy a generalization of $H{\ddot{o}}rmander^{\prime}s$ condition and establish their Sobolev-type mapping properties on the homogeneous Besov-Lipschitz spaces by making use of a continuous characterization of Besov-Lipschitz spaces. As an application, we derive Sobolev-type imbedding theorem.