• Journal of the Korean Mathematical Society
• /
• v.45 no.1
• /
• pp.79-95
• /
• 2008

The local existence of solutions for the initial-boundary value problem of a generalized Boussinesq equation on the half line is considered. The approach consists of replacing he Fourier transform in the initial value problem by the Laplace transform and making use of modern methods for the study of nonlinear dispersive wave equation

• Journal of the Korean Mathematical Society
• /
• v.55 no.1
• /
• pp.147-160
• /
• 2018

In this article, we establish translation theorems for the analytic Fourier-Feynman transform of functionals in non-stationary Gaussian processes on Wiener space. We then proceed to show that these general translation theorems can be applied to two well-known classes of functionals; namely, the Banach algebra S introduced by Cameron and Storvick, and the space ${\mathcal{B}}^{(P)}_{\mathcal{A}}$ consisting of functionals of the form $F(x)=f({\langle}{\alpha}_1,x{\rangle},{\ldots},{\langle}{\alpha}_n,x{\rangle})$, where ${\langle}{\alpha},x{\rangle}$ denotes the Paley-Wiener-Zygmund stochastic integral ${\int_{0}^{T}}{\alpha}(t)dx(t)$.

• Korean Journal of Optics and Photonics
• /
• v.8 no.2
• /
• pp.154-160
• /
• 1997

On the base of the fractional Fourier transform(FRT) which is known as a generalized form of the conventional Fourier transform, the fractional correlation has been implemented. Shift-variance property of the fraction correlation has been evaluated and compared with the shift-invariance of the conventional correlation. The fractional correlation operation has been implemented by using a planar optics configuration which integrates all of the optical components on a single glass substrate. A good agreement between the experimental and calculated results has been obtained.

• Nonlinear Functional Analysis and Applications
• /
• v.26 no.2
• /
• pp.381-392
• /
• 2021

During the last several decades, a great variety of fractional kinetic equations involving diverse special functions have been broadly and usefully employed in describing and solving several important problems of physics and astrophysics. In this paper, we aim to find solutions of a type of fractional kinetic equations associated with the (p, q)-extended 𝜏 -hypergeometric function and the (p, q)-extended 𝜏 -confluent hypergeometric function, by mainly using the Laplace transform. It is noted that the main employed techniques for this chosen type of fractional kinetic equations are Laplace transform, Sumudu transform, Laplace and Sumudu transforms, Laplace and Fourier transforms, P_𝛘-transform, and an alternative method.

• Geomechanics and Engineering
• /
• v.19 no.4
• /
• pp.295-305
• /
• 2019

The present paper is concerned with the investigation of disturbances in orthotropic thermoelastic medium by using fractional order heat conduction equation with three phase lags due to thermomechanical sources. Laplace and Fourier transform techniques are used to solve the problem. The expressions for displacement components, stress components and temperature change are derived in transformed domain and further in physical domain using numerical inversion techniques. The effect of fractional parameter based on its conductivity i.e., ($0<{\alpha}<1$ for weak, ${\alpha}=1$ for normal, $1<{\alpha}{\leq}2$ for strong conductivity) is depicted graphically on various components.

• Composite Materials and Engineering
• /
• v.3 no.3
• /
• pp.241-262
• /
• 2021

In this article, we studied the effect of two-temperature in a two-dimensional orthotropic thermoelastic media with fractional order heat transfer in generalized thermoelasticity with three-phase-lags due to thermomechanical sources. The boundary of the surface is subjected to linearly distributed and concentrated loads (mechanical and thermal source). The solution of the problem is obtained with the help of Laplace and Fourier transform techniques. The expressions for displacement components, stress components and conductive temperature are derived in transformed domain. Numerical inversion technique is used to obtain the results in physical domain. The effect of two-temperature on all the physical quantities has been depicted with the help graphs. Some special cases are also discussed in the present investigation.

• Structural Engineering and Mechanics
• /
• v.81 no.4
• /
• pp.503-511
• /
• 2022

In this article, we have examined the effect of fractional order parameter in a two-dimensional orthotropic magneto-thermoelastic solid in generalized thermoelasticity without energy dissipation with fractional order heat transfer in the context of hall current, rotation and two-temperature due to normal force. Laplace and Fourier transform techniques are used to obtain the solution of the problem. The expressions for displacement components, stress components, current density components and conductive temperature are obtained in transformed domain and then in physical domain by using numerical inversion method. The effect of fractional parameter on all the components has been depicted through graphs. Some special cases are also discussed in the present investigation.

• Applied Microscopy
• /
• v.34 no.4
• /
• pp.211-221
• /
• 2004

In this review, the kinematical scattering theorems are explained by means of Fourier transformation of the assemblies of atoms. The reciprocal space and the generalized Patterson function are introduced. The scatterings of real monatomic gas or liqiud and the hydrogen atoms are described as examples.

• Korean Journal of Optics and Photonics
• /
• v.7 no.4
• /
• pp.333-340
• /
• 1996

We have implemented a planar integrated optics for the fractional Fourier transform (FRT) which has recently been developed as a generalized form of the conventional Fourier transform. FRT optical systems provide versatile tools for analyzing signals and designing hardwares, but require high accuracy and stability in the arrangement of optical components because of their shift-variant characteristic. The planar optical FRT setup composed of free-space optical components integrated on a single glass block makes the FRT of 2-dimensional(2-D) input patterns through the 3-D glass-space. Therefore, taking advantage of the compactness, easy alignment and thermal/mechanical stability, the planar optics can provide a useful approach to realizing an optical fractional correlation system in a practical way. In the experiment, we have obtained accurate FRT results by using the planar integrated optics with 4 different fractional orders of 0.25, 0.5, 0.75, and 1.0.

• ETRI Journal
• /
• v.46 no.3
• /
• pp.392-403
• /
• 2024

Even though generalized frequency division multiplexing is an alternative waveform method expected to replace the orthogonal frequency division multiplexing in the future, its implementation must alleviate channel effects. Least-squares (LS), a low-complexity channel estimation technique, could be improved by using the discrete Fourier transform (DFT) without increasing complexity. Unlike the usage of the LS method, the DFT-based method requires the receiver to know the channel impulse response (CIR) length, which is unknown. This study introduces a simple, yet effective, CIR length estimator by utilizing LS estimation. As the cyclic prefix (CP) length is commonly set to be longer than the CIR length, it is possible to search through the first samples if CP is larger than a threshold set using the remaining samples. An adaptive scale is also designed to lower the error probability of the estimation, and a simple signal-to-interference-noise ratio estimation is also proposed by utilizing a sparse preamble to support the use of the scale. A software simulation is used to show the ability of the proposed system to estimate the CIR length. Due to shorter CIR length of rural area, the performance is slightly poorer compared to urban environment. Nevertheless, satisfactory performance is shown for both environments.