Certain functions useful for representing axisymmetric refractive-index distributions are shown to have exact solutions for Abel transformation of the resulting angular deflection data.

We study the Abel differential equations that admits either a generalized Weierstrass first integral or a generalized Weierstrass inverse integrating factor.

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...

Abstract In the case of radiography of a cylindrically symmetric object, the Abel transform is useful for describing the tomographic measurement operator. The inverse of this operator is unbounded, so regularization is required for the computation of satisfactory inversions. We introduce the use of the total variation seminorm for this purpose, and prove the existence and uniqueness of solution...

1. Abel, D. C. (red.). (1992). Theories of human nature: classical and contemporary readings. New York: Mc- Graw-Hill. Google Scholar

By means of series–rearrangements and finite differences, elementary proofs are presented for the well–known convolution identities of Abel and Hagen–Rothe.