• 대한수학회지
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• 제45권1호
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• pp.79-95
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• 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

• 대한수학회지
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• 제55권1호
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• pp.147-160
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• 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 ${\int_{0}^{T}}{\alpha}(t)dx(t)$.

• 한국광학회지
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• 제8권2호
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• pp.154-160
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• 1997

푸리에 변환의 일반형인 분수차 푸리에 변환(fractional Fourier transform : FRT)을 근간으로 하는 분수차 상관기는 입력패턴의 위치나 모양에 따라 상관결과치가 변하는 공간 가변 특성을 갖는다. 이러한 특성을 갖는 분수차 상관기를 푸리에 변환을 이용하는 기존의 상관기와 비교하였고, 분수차에 따른 상관결과치의 변화를 분석하였다. 정확한 분수차 상관함수의 계산을 위하여 광학부품들의 정렬에 있어서 고도의 정확도와 안정도를 갖는 평판 집적 광학계를 구성하였으며, 실험결과와 계산결과를 비교함으로써 평판 집적 광학계에 의한 분수차 상관기의 구현이 매우 정확히 수행될 수 있음을 검증하였다.

• Nonlinear Functional Analysis and Applications
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• 제26권2호
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• pp.381-392
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• 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.

• International Journal of Computer Science & Network Security
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• 제24권9호
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• pp.21-29
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• 2024

Precoding of the orthogonal frequency division multiplexing (OFDM) with Walsh Hadamard transform (WHT) is known in the literature. Instead of performing WHT precoding and inverse discrete Fourier transform separately, a product of two matrix can yield a new matrix that can be applied with lower complexity. This resultant transform, T-transform, results in T-OFDM. This paper extends the limited existing work on T-OFDM significantly by presenting detailed account of its computational complexity, a lower complexity receiver design, an expression for PAPR and its cumulative distribution function (cdf), sensitivity of T-OFDM to timing synchronization errors, and novel analytical expressions signal to noise ratio (SNR) for multiple equalization techniques. Simulation results are presented to show significant improvements in PAPR performance, as well improvement in bit error rate (BER) in Rayleigh fading channel. This paper is Part II of a three-paper series on alternative transforms and many of the concepts and result refer to and stem from results in generalized multicarrier communication (GMC) system presented in Part I of this series.

• Geomechanics and Engineering
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• 제19권4호
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• pp.295-305
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• 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
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• 제3권3호
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• pp.241-262
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• 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
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• 제81권4호
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• pp.503-511
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• 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
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• 제34권4호
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• pp.211-221
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• 2004

물질을 이루고 있는 원자의 집합체에서 단 한번의 회절이 일어나는 경우의 회절이론의 개발을 소개하였다. Fourier transform으로 이루어지는 역 격자 공간에서의 역격자 공간 분포와 실 공간에서의 패터슨 함수와의 관계를 유도하고 이어 여러 가지 물질을 예로 들어 고찰하였다.

• 한국광학회지
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• 제7권4호
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• pp.333-340
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• 1996

기존 퓨리에 변환의 일반화된 형식인 분수차 퓨리에 변환을 평판집적 광학계로 구현하였다. 구현된 평판집적 광학계는 동일한 2차원 입력패턴에 대해 서로 다른 분수차를 갖는 4개의 FRT의 결과를 얻을 수 있는 구조를 가지며 모든 부품들은 레이저 빔 묘화장치를 이용하여 하나의 유리판에 동시에 제작되었다. FRT 실험결과를 계산치와 비교 분석함으로써 평판집적 광학계가 기존의 자유공간 광학계가 갖는 3차원적 광신호 전달 특성과 이에 따른 높은 신호의 공간대역폭을 가지고 매우 정확한 FTR를 수행할 수 있음을 검증하였다.