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In order to use the well known representation of the Mellin transform as a combination of two Laplace transforms, the inverse function is represented as an expansion of Laguerre polynomials with respect to the variable . The Mellin transform of the series can be written as a Laurent series. Consequently, the coefficients of the numerical inversion procedure can be estimated. The discrete least squares approximation gives another determination of the coefficients of the series expansion. The last...
In this work, a combined form of the Laplace transform method and the Adomian decomposition method is implemented to give an approximate solution of nonlinear systems of differential equations such as fish farm model with three components nutrient, fish and mussel. The technique is described and illustrated with a numerical example.
We start with a general time-homogeneous scalar diffusion whose state space is an interval I ⊆ ℝ. If it is started at x ∈ I, then we consider the problem of imposing upper and/or lower boundary conditions at two points a,b ∈ I, where a < x < b. Using a simple integral identity, we derive general expressions for the Laplace transform of the transition density of the process, if killing or reflecting boundaries are specified. We also obtain a number of useful expressions for the Laplace transforms...
Several representations of the space of Laplace ultradistributions supported by a half line are given. A strong version of the quasi-analyticity principle of Phragmén-Lindelöf type is derived.
The space of Laplace ultradistributions supported by a convex proper cone is introduced. The Seeley type extension theorem for ultradifferentiable functions is proved. The Paley-Wiener-Schwartz type theorem for Laplace ultradistributions is shown. As an application, the structure theorem and the kernel theorem for this space of ultradistributions are given.
The paper focuses on a low-rank tensor structured representation of Slater-type and Hydrogen-like orbital basis functions that can be used in electronic structure calculations. Standard packages use the Gaussian-type basis functions which allow us to analytically evaluate the necessary integrals. Slater-type and Hydrogen-like orbital functions are physically more appropriate, but they are not analytically integrable. A numerical integration is too expensive when using the standard discretization...
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