Wild universally pierced arcs

Acyclic Groups and Wild Arcs

We discuss two classes of acyclic groups that are commutator subgroups of finitely presented groups with infinite cyclic abelianization. The first is algebraic and includes groups first exhibited by Baumslag & Gruenberg, of which it is shown that Epstein’s acyclic group is a special case. The second class is geometric, and is shown to include a number of wild arc groups in the literature. 0. In...

Threshold reduction in pierced microdisk lasers

GaAs microdisk lasers with holes pierced through the disk surface are investigated for their threshold characteristics. Disks are fabricated with either a single hole or two diametrically opposite holes at various distances from the disk outer edge. Even though the disk area is reduced by only 1%, we find that the lasing threshold for a disk with one hole is reduced by up to 50% compared to a d...

t-Pancyclic Arcs in Tournaments

Let $T$ be a non-trivial tournament. An arc is emph{$t$-pancyclic} in $T$, if it is contained in a cycle of length $ell$ for every $tleq ell leq |V(T)|$. Let $p^t(T)$ denote the number of $t$-pancyclic arcs in $T$ and $h^t(T)$ the maximum number of $t$-pancyclic arcs contained in the same Hamiltonian cycle of $T$. Moon ({em J. Combin. Inform. System Sci.}, {bf 19} (1994), 207-214) showed that $...

Universally Composable Undeniable Signature

How to define the security of undeniable signature schemes is a challenging task. This paper presents two security definitions of undeniable signature schemes which are more useful or natural than the existing definition. It then proves their equivalence. We first define the UC-security, where UC means universal composability. We next show that there exists a UC-secure undeniable signature sche...

Deformation of a free interface pierced by a tilted cylinder