We give an example of two rational functions with non-equal Julia sets that generate a rational semigroup whose completely invariant Julia set is a closed line segment. We also give an example of polynomials with unequal Julia sets that generate a non nearly Abelian polynomial semigroup with the property that the Julia set of one generator is equal to the Julia set of the semigroup. These examp...

Since its first production in 1947, Arthur Miller’s All My Sons has been performed and appreciated worldwide. In academic studies on Miller, it secures an important place as a precursor, because it has encompassed such themes as father-son conflict, pursuit of success dream in the form of a traditional tragedy as well as a family and a social play. As for techniques, to begin with, the Ibsenite...

We derive uniform asymptotic expressions of some Abel sums appearing in some problems in coding theory and indicate the usefulness of these sums in other fields, like empirical processes, machine maintenance, analysis of algorithms, probabilistic number theory, queuing models, etc.

We construct an example of a series that is Abel summable but whose associated power series does not converge on angular sectors. We also give some related results.

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. They also 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 this resu...

The Abel inversion, used to reconstruct axisymmetric radial profiles from line-of-sight intensity measurements, is increasingly used to make spatially resolved combustion measurements. An Abel deconvolution is valid only when incoming rays are parallel, whereas most practical optical setups used for emission imaging consist of single-lens and multilens systems that collect light in a cone, over...

Martin Abel* *Middlebury College, 14 Old Chapel Rd, Middlebury, VT 05753 (email: mabel{at}middlebury.edu).