Finite nonabelian p-groups all of whose subgroups are q-self dual

A finite p-group G is q-self dual if every quotient of G is isomorphic to a subgroup of G. Here, we determine finite 2-groups G all of whose subgroups are q-self dual (Theorem 3) and in case p > 2 we get a classification of such groups only under the additional assumptions that Ω1(G) is abelian (Theorem 4).

On the Non-Holonomic Character of Logarithms, Powers, and the $n$th Prime Function

We establish that the sequences formed by logarithms and by "fractional" powers of integers, as well as the sequence of prime numbers, are non-holonomic, thereby answering three open problems of Gerhold [El. J. Comb. 11 (2004), R87]. Our proofs depend on basic complex analysis, namely a conjunction of the Structure Theorem for singularities of solutions to linear differential equations and of an Abelian theorem. A brief discussion is offered regarding the scope of singularity-based methods and several naturally occurring sequences are proved to be non-holonomic.

The Laplace transform on a class of Boehmians

The one-sided Laplace transform is defined on a space of generalised functions called transformable Boehmians. The space of one-sided Laplace transformable distributions is shown to be a proper subspace of transformable Boehmians. Some basic properties of the Laplace transform are investigated. An inversion formula and an Abelian theorem of the final type are obtained.

Abelian theorem for the Stieltjes transform of distributions

First, a definition is given of the Stieltjes transform of distributions which contains some well-known. Then, a structural theorem for distributions havingS-asymptotic is proved. This makes possible to prove two theorems of the Abelian type valued for Stieltjes transforms of distributions given in different ways.