With a change of variables the Abel transform gives the projection of a 2-D distribution with circular symmetry. Thus the Abel inversion formula allows one to determine the radial dependence of such a distribution from its projection. However, this inversion formula is very sensitive to noise in the projection data. When the projection data are derived from radiographic measurements, further di...

Radio occultation (RO) has been proven to be a powerful technique for ionospheric electron density profile (EDP) retrieval. The Abel inversion currently used in RO EDP retrieval has degraded performance in regions with large horizontal gradients because of an assumption of spherical symmetry as indicated by many studies. Some alternative methods have been proposed in the past; the global ionosp...

the methods applied to regularization of the ill-posed problems can be classified under “direct” and “indirect” methods. practice has shown that the effects of different regularization techniques on an ill-posed problem are not the same, and as such each ill-posed problem requires its own investigation in order to identify its most suitable regularization method. in the geoid computations witho...

The morphic Abel-Jacobi map is the analogue of the classical Abel-Jacobi map one obtains by using Lawson and morphic (co)homology in place of the usual singular (co)homology. It thus gives a map from the group of r-cycles on a complex variety that are algebraically equivalent to zero to a certain “Jacobian” built from the Lawson homology groups viewed as inductive limits of mixed Hodge structur...

In this paper,The concept of a (∈,∈ ∨q)-fuzzy ideal in an ordered Abel-Grassmann groupoid is introduced. In partcicular, left regular ordered Abel-Grassmann groupoids are characterized by using the (∈ ,∈ ∨q)-fuzzy ideals.

The methods applied to regularization of the ill-posed problems can be classified under “direct” and “indirect” methods. Practice has shown that the effects of different regularization techniques on an ill-posed problem are not the same, and as such each ill-posed problem requires its own investigation in order to identify its most suitable regularization method. In the geoid computations witho...

Reconstructing images from ill-posed inverse problems often utilizes total variation regularization in order to recover discontinuities in the data while also removing noise and other artifacts. Total variation regularization has been successful in recovering images for (noisy) Abel transformed data, where object boundaries and data support will lead to sharp edges in the reconstructed image. I...

In this paper we intend to offer new numerical methods to solve the second-order fuzzy Abel-Volterraintegro-differential equations under the generalized $H$-differentiability. The existence and uniqueness of thesolution and convergence of the proposed methods are proved in details and the efficiency of the methods is illustrated through a numerical example.

In this paper, we consider the number of 2-protected nodes in random digital trees. For tries, Gaither, Homma, Sellke and Ward (2012) and Gaither and Ward (2013) derived asymptotic expansions for mean and variance. We re-derive their results (with some corrections) and show their conjectured central limit theorem. This will be done by recent unified approaches by Fuchs, Hwang and Zacharovas (20...