The C library libkww provides functions to compute the Kohlrausch–Williams– Watts function, i.e., the Laplace–Fourier transform of the stretched (or compressed) exponential function exp(−t) for exponents β between 0.1 and 1.9 with double precision. Analytic error bounds are derived for the low and high frequency series expansions. For intermediate frequencies, the numeric integration is enormou...

Integral transforms play an important rôle in Analytic number theory, the part of Number theory where problems of a number-theoretic nature are solved by the use of various methods from Analysis. The most common integral transforms that are used are: Mellin transforms (Robert Hjalmar Mellin, 18541933), Laplace transforms (Pierre-Simon, marquis de Laplace, 1749-1827) and Fourier transforms (Jose...

Abstract In this paper we study the almost everywhere convergence of the expansions related to the self-adjoint extension of the Laplace operator. The sufficient conditions for summability is obtained. For the orders of Riesz means, which greater than critical index N−1 2 we established the estimation for maximal operator of the Riesz means. Note that when order α of Riesz means is less than cr...

This paper discusses static and dynamic response of nanoplate resting on an orthotropic visco-Pasternak foundation based on Eringen’s nonlocal theory. Graphene sheet modeled as nanoplate which is assumed to be orthotropic and viscoelastic. By considering the Mindlin plate theory and viscoelastic Kelvin-Voigt model, equations of motion are derived using Hamilton’s principle which are then solved...

In this paper we describe two numerical methods by which the relaxation modulus and memory function of a polymer can be determined from a set of discrete linear viscoelastic storage and loss moduli measurements. The first method involves expressing the linear viscoelastic data by means of a rational function (with certain constraints) and then taking the Laplace transform of that function. The ...

Conventional Fourier analysis has many schemes for different types of signals. They are Fourier transform (FT), Fourier series (FS), discrete-time Fourier transform (DTFT), and discrete Fourier transform (DFT). The goal of this correspondence is to develop two absent schemes of fractional Fourier analysis methods. The proposed methods are fractional Fourier series (FRFS) and discrete-time fract...

We continue a program generalizing classical results from the analysis on symmetric cones to Dunkl setting for root systems of type A A ...

Report II is concerned with the extended results of distance function wavelets (DFW). The fractional DFW transforms are first addressed relating to the fractal geometry and the fractional derivative, and then, the discrete Helmholtz-Fourier transform is briefly presented. The Green second identity may be an alternative devise in developing the theoretical framework of the DFW transform and seri...