Weierstrass Points and Regular Maps

It was shown by G. A. Jones and the first author in [8] that underlying any map on a compact orientable surface S there is a natural complex structure making S into a Riemann surface. In this paper we consider regular maps and enquire about the Weierstrass points on the underlying Riemann surface. We are particularly interested to know when these are geometric, i.e. whether they lie at vertices, face-centres or edge-centres of the map.     

Unicellular Dessins and a Uniqueness Theorem for Klein's Riemann Surface of Genus 3

If we consider the 14-sided hyperbolic polygon of Felix Kleinthat defines his famous surface of genus 3, then we observethat we have a uniform, unifacial dessin whose automorphismgroup is transitive on the edges, but not on the directed edgesof the dessin. We show that Klein's surface is the unique platonicsurface with this property. 2000 Mathematics Subject Classification30F10, 14H05.     

Quantitation of pressure-sensitive film using digital image scanning

An experimental technique is presented for measurement of contact stress distribution using Fuji Pressensor film. The development of packets of Pressensor disks for use in small areas or surfaces of complex curvature is explained. A digital-image-scanning procedure has been developed to substantially increase the spatial resolution with which stress distributions can be constructed from stained Fuji Pressensor film. The technique is developed for small, discrete disks as well as for larger, continuous sheets of Pressensor. As an illustration, sealed packets of small Pressensor disks are used to measure the stress distribution across a cadaveric juvenile femoral head under load.     

A new synthesis of 2,1-benzisothiazoles

A novel synthesis of 2,1-benzisothiazoles is described. When an o-toluidine or N-sulfinyl-o-toluidine is allowed to react with an N-sulfinylsulfonamide, a 2,1-benzisothiazole is formed.     

Belyi Uniformization of Elliptic Curves

Belyi's Theorem implies that a Riemann surface X representsa curve defined over a number field if and only if it can beexpressed as U/, where U is simply-connected and is a subgroupof finite index in a triangle group. We consider the case whenX has genus 1, and ask for which curves and number fields canbe chosen to be a lattice. As an application, we give examplesof Galois actions on Grothendieck dessins. 1991 MathematicsSubject Classification 30F10, 11G05.     

REAL BELYI THEORY

We develop a Belyi-type theory that applies to Klein surfaces,that is, (possibly non-orientable) surfaces with boundary whichcarry a dianalytic structure. In particular, we extend Belyi'sfamous theorem from Riemann surfaces to Klein surfaces.     

Synthesis of alkylaminoethanethiolsulfuric acids substituted with heterocyclic moieties

Several alkylaminoethanethiolsulfurie acids substituted with heterocyclic moieties have been synthesized to determine their effectiveness as radiation protection agents. These compounds are represented by the structure R(CH₂)₃NH(CH₂)₂S₂O₃H, where R is 8-quinoly-oxy (V), 8-quinaldyloxy (IX), 5-quinolyloxy (XII), 4-pyridyl (XVI), and 4-pyridylmethyl (XXIII). The diheterocyclic-substituted compound, 2-[bis-(2-phenyl-1, 2, 3, 2H-triazol-4-ylmethyl)amino]ethanethiolsulfuric acid (XIV) was also synthesized.     

Synthesis of substituted pyridazino[4,5-c]pyridazines

Several pyridazino[4,5-c]pyridazines substituted in the 5- and 8-positions with hydroxyl, mercapto and amino groups and in the 3-position with a methyl group or a hydrogen atom have been prepared. In the course of this work five previously unreported pyridazine derivatives have also been synthesized.