X iv : m at h - ph / 9 81 20 19 v 1 1 8 D ec 1 99 8 ON ANGLES WHOSE SQUARED TRIGONOMETRIC FUNCTIONS ARE RATIONAL

ar X iv : m at h - ph / 9 81 20 09 v 1 1 3 D ec 1 99 8 Quantum dots A survey of rigorous results

ar X iv : m at h - ph / 9 81 20 16 v 1 1 8 D ec 1 99 8 ISOMORPHISM OF HIERARCHICAL STRUCTURES

We consider hierarchical structures such as Fibonacci sequences and Penrose tilings, and examine the consequences of different choices for the definition of isomorphism. In particular we discuss the role such a choice plays with regard to matching rules for such structures.

ar X iv : m at h - ph / 9 81 20 28 v 1 2 8 D ec 1 99 8 ( q , h ) – analogue of Newton ’ s binomial formula

In this letter, the (q, h)–analogue of Newton’s binomial formula is obtained in the (q, h)–deformed quantum plane which reduces for h = 0 to the q–analogue. For (q = 1, h = 0), this is just the usual one as it should be. Moreover, the h–analogue is recovered for q = 1. Some properties of the (q, h)–binomial coefficients are also given. This result will contribute to an introduction of the (q, h...

ar X iv : g r - qc / 9 81 20 29 v 1 8 D ec 1 99 8 From Superstrings to M Theory

In this talk I will survey some of the basic facts about superstring theories in 10 dimensions and the dualities that relate them to M theory in 11 dimensions. Then I will mention some important unresolved issues.

ar X iv : m at h / 99 05 11 8 v 1 [ m at h . L O ] 1 9 M ay 1 99 9 REMARKS ON SETS RELATED TO TRIGONOMETRIC SERIES

We show that several classes of sets, like N 0-sets, Arbault sets, N-sets and pseudo-Dirichlet sets are closed under adding sets of small size.