In this work we propose a criterion to apply the Abel inversion in the case of a small set of experimental data to be used in laboratory plasmas. The Nestor-Olsen method, spline interpolation, and Fourier transform Abel inversion have been compared in order to study the influence of statistical noise and the number of sampled data. The application of this criterion permits us to obtain a radial...

For the constant frequency case, we introduce a special type of Ermakov-Pinney equations with nonlinear dissipation based on the corresponding Chiellini integrable Abel equation. General solutions of these equations are obtained following the Abel equation route. Based on particular solutions, we also provide general solutions containing a factor with the phase of the Milne type. In addition, t...

Lemma introduced the Abel-type matrix Aα,t defined by ank = ( k+α k ) tk+1 n (1− tn)α+1, where α>−1, 0< tn < 1, for all n, and limtn = 1; and studied it as mappings into . In this paper, we extend our study of this matrix and investigate its translativity in the setting.

Recently, Chen, Hou and Jin used both Abel’s lemma on summation by parts and Zeilberger’s algorithm to generate recurrence relations for definite summations. Meanwhile, they proposed the Abel-Gosper method to evaluate some indefinite sums involving harmonic numbers. In this paper, we use the Abel-Gosper method to prove an identity involving the generalized harmonic numbers. Special cases of thi...

In this paper, we define a certain Hodge-theoretic structure for an arbitrary variety X over the complex number field by using the theory of mixed Hodge module due to Morihiko Saito. We call it an arithmetic Hodge structure of X. It is shown that extension groups of arithmetic Hodge structure do not vanish even for degree ≥ 2. Moreover, we define higher Abel-Jacobi maps from Bloch’s higher Chow...

A direct almost Bernstein operational matrix of integration is used to propose a stable algorithm for numerical inversion of the generalized Abel integral equation. The applicability of the earlier proposed methods was restricted to the numerical inversion of a part of the generalized Abel integral equation. The method is quite accurate and stable as illustrated by applying it to intensity data...