Abstract I seems to be widely believed that the Fourier and Laplace transforms are simply related to each other. Nothing could be further from the truth. The Fourier transform is the basis for the Hilbert vector-space expansion of signals. The Laplace transform is the basis of system functions, that are causal. The Fourier transform does not naturally include the step function, which must be sh...

The theory of fuzzy transform (F-transform, for short) has been developed extensively in recent years. Based on the current successes of F-transform, we expect that in the future, F-transform will become as successful and as widely used as the well-known transforms such as Laplace, Fourier, and wavelet transforms. The most successful applications of F-transform are in the fields of image proces...

the present study is the first to analyze the dynamic response of a poroelastic beam subjected to a moving force. moreover, the influences of attached mass-spring systems and non-ideal supports (with local movements in the supporting points or base due to the presence of factors such as gaps, unbalanced masses, and friction or seismic excitations) on the responses were investigated. non-ideal s...

We discuss and derive the analytical solution for three basic problems of the so-called timefractional telegraph equation. The Cauchy and Signaling problems are solved by means of juxtaposition of transforms of the Laplace and Fourier transforms in variable t and x, respectively. the appropriate structures and negative prosperities for their Green functions are provided. The boundary problem in...

From a suitable integral representation of the Laplace transform of a positive semi–definite quadratic form of independent real random variables with not necessarily identical densities a univariate integral representation is derived for the cumulative distribution function of the sample variance of i.i.d. random variables with a gamma density, supplementing former formulas of the author. Furth...

In this paper, the classic coupled Magneto-thermo-elasticity model of hollow and solid cylinders under radial-symmetric loading condition (r, t) is considered. A full analytical and the direct method based on Fourier Hankel series and Laplace transform is used, and an exact unique solution of the classic coupled equations is presented. The thermal and mechanical boundary conditions, the body fo...

Inverting the Laplace transform is a paradigm for exponentially ill-posed problems. For a class of operators, including the Laplace transform, we give forward and inverse formulae that have fast implementations using the fast Fourier transform. These formulae lead easily to regularized inverses whose effects on noise and filtered data can be precisely described. Our results give cogent reasons ...

in this paper, we apply the laplace decomposition method to obtain a series solutions of the burgers-huxley and burgers-fisher equations. the technique is based on the application of laplace transform to nonlinear partial differential equations. the method does not need linearization, weak nonlinearity assumptions or perturbation theory and the nonlinear terms can be easily handled by using the...

The aim of the article is to demonstrate the use of the Laplace transform to the evaluation of consols’ present value under different streams of returns (dividends). Consols (or perpetual bonds, perpetuities) are bonds with no maturity, which means that interest is paid to a bondholder perpetually (usually annually) forever. The present value of a consol, when constant interest is paid, is simp...