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The Fourier-Laplace Transform—A Conjugate Link Between the Material Brain and the Conscious Mind [PDF]
Frontiers in Human Neuroscience, 2021 Recent attempts to establish the quantum boundaries of life is pursued. A pre-existing view of quantum biology is supplemented by the formulation of modern advances in theoretical chemical physics and quantum chemistry. The extension to open system dynamics entails a self-referential amplification supporting the signature of life as well as ...
Erkki J Brândas
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Solving Generalized Heat and Generalized Laplace Equations Using Fractional Fourier Transform
Fractal and Fractional, 2023 In the present work, the main objective is to find the solution of the generalized heat and generalized Laplace equations using the fractional Fourier transform, which is a general form of the solution of the heat equation and Laplace equation using the ...
Sri Sulasteri +4 more
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Fractal and Fractional, 2022 In this paper, we establish two approximation theorems for the multidimensional fractional Fourier transform via appropriate convolutions. As applications, we study the boundary and initial problems of the Laplace and heat equations with chirp functions.
Yinuo Yang +3 more
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On the Connection between Spherical Laplace Transform and Non-Euclidean Fourier Analysis
Mathematics, 2020 We prove that, if the coefficients of a Fourier−Legendre expansion satisfy a suitable Hausdorff-type condition, then the series converges to a function which admits a holomorphic extension to a cut-plane. Next, we introduce a Laplace-type transform
Enrico De Micheli
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Duality of Shehu transform with other well known transforms and application to fractional order differential equations. [PDF]
PLoS ONEIntegral transforms are used in many research articles in the literature, due to their interesting applications in the solutions of problems of applied science and engineering.
Nabil Mlaiki +4 more
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Fourier/Laplace Transforms and Ruin Probabilities [PDF]
ASTIN Bulletin, 2002 AbstractIn this paper we use Fourier/Laplace transforms to evaluate numerically relevant probabilities in ruin theory as an application to insurance. The transform of a function is split in two: the real and the imaginary parts. We use an inversion formula based on the real part only, to get the original function.By using an appropriate algorithm to ...
Lima, Fátima D. E. +2 more
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The Fourier–Laplace Transformation and Material Law Operators [PDF]
, 2021 AbstractIn this chapter we introduce the Fourier–Laplace transformation and use it to define operator-valued functions of ∂t,ν; the so-called material law operators. These operators will play a crucial role when we deal with partial differential equations.
Christian Seifert +2 more
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The Generalized Fourier Transform: A Unified Framework for the Fourier, Laplace, Mellin and Z Transforms [PDF]
IEEE Transactions on Signal Processing, 2021 <div>This paper introduces Generalized Fourier transform (GFT) that is an extension or the generalization of the Fourier transform (FT). The Unilateral Laplace transform (LT) is observed to be the special case of GFT. GFT, as proposed in this work, contributes significantly to the scholarly literature.
Pushpendra Singh +2 more
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Transient non-Fourier thermal interactions of two parallel cracks in porous metal foam
Case Studies in Thermal Engineering, 2023 Experimental evidence shows heat conduction in the porous media would be non-Fourier under specific circumstances. The novelty of this research lies in considerations of the non-Fourier effect and the interactions of two parallel thermally insulated ...
San Zhang +4 more
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A Laplace transform finite difference scheme for the Fisher-KPP equation
Journal of Algorithms & Computational Technology, 2021 This paper proposes a numerical approach to the solution of the Fisher-KPP reaction-diffusion equation in which the space variable is developed using a purely finite difference scheme and the time development is obtained using a hybrid Laplace Transform ...
Colin L Defreitas, Steve J Kane
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