When electrical magnetic wave passes through the ionosphere, it is reflected and disturbed. This feature will bring: 1) beneficial results i.e. as a media for radio signal long distance propagation; and 2) disadvantage results i.e. causing Global Positioning System (GPS) inaccuracy. Therefore it is necessary to build up an accurate ionospheric model for use in various applications. Because elec...

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...

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...

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...

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...