Super Riemann surfaces: Uniformization and Teichmüller theory

Teichmüller theory for super Riemann surfaces is rigorously developed using the supermanifold theory of Rogers. In the case of trivial topology in the soul directions, relevant for superstring applications, the following results are proven. The super Teichmüller space is a complex super-orbifold whose body is the ordinary Teichmüller space of the associated Riemann surfaces with spin structure. For genusg>1 it has 3g-3 complex even and 2g-2 complex odd dimensions. The super modular group which reduces super Teichmüller space to super moduli space is the ordinary modular group; there are no new discrete modular transformations in the odd directions. The boundary of super Teichmüller space contains not only super Riemann surfaces with pinched bodies, but Rogers supermanifolds having nontrivial topology in the odd dimensions as well. We also prove the uniformization theorem for super Riemann surfaces and discuss their representation by discrete supergroups of Fuchsian and Schottky type and by Beltrami differentials. Finally we present partial results for the more difficult problem of classifying super Riemann surfaces of arbitrary topology.Enrico Fermi Fellow. Research supported by the NSF (PHY 83-01221) and DOE (DE-AC02-82-ER-40073).     

A novel approach towards intermolecular stabilization of para-quinone methides. First complexation of the elusive, simplest quinone methide, 4-methylene-2,5-cyclohexadien-1-one

A novel approach towards the intermolecular stabilization of "simple" (i.e. methylene-unsubstituted) p-quinone methides (QMs) by their coordination to a transition-metal center is described. 4-Bromomethyl phenols, protected by a silyl group, were employed as the QM precursors and cis-chelating diphosphine Pd0 complexes were chosen as the metal precursors, since they have strong back-bonding interactions with the electron-poor QM moiety. Removal of the silyl protecting-group from the corresponding [LPd(benzyl)Br] complex (L=bisphosphine) with fluoride results in the spontaneous rearrangement of the unobserved zwitterionic Pd(II) complex into the QM-Pd0 complex. The feasibility of this approach was demonstrated in the synthesis of the structurally characterized Pd0 complex of BHT-QM (4), a biologically relevant metabolite of 2,6-di-tert-butyl-p-cresol, and the synthesis of the complex of 4-methylene-2,5-cyclohexadien-1-one (11), the simplest, and so far unobserved QM molecule. These complexes exhibit a remarkable thermal stability and do not react with alcohol or water. In both cases, the use of an appropriate incoming ligand allowed the release of the coordinated QM into the reaction media in which it was effectively trapped by added nucleophiles.     

Set systems with no union of cardinality 0 modulom

Letq be a prime power. It is shown that for any hypergraph = {F ₁,...,F _d(q–1)+1} whose maximal degree isd, there exists Ø ₀ , such that 0 (modq).     

Precise measurement of Γ(Λ0 → p + e− + ν)/Γ(Λ0 → p + π−)

Based on a sample of 10 000 events of the decay $\text{Λ}{}^0\text{→ p + e}{}^{\mathrm{?}}\text{+}\text{ν}\text{,}\text{the ratio}\text{Γ(Λ}{}^0\text{→ pe}\text{ν}\text{)/Γ(Λ}{}^0\text{→ pπ}{}^{\mathrm{?}}\text{)}$ is found to be (1.313 ± 0.024) × 10^?3. From this, the absolute rate for the process is calculated to be (3.204 ± 0.068) × 10⁶ s^?1 .     

Real time computation

We introduce a concept of real-time computation by a Turing machine. The relative strengths of one-tape versus two-tape machines is established by a new method of proofs of impossibility of actual computations. This research was supported in part by National Science Foundation grant GP-228 to Harvard University. This paper was written while the author was visiting at the Computation Laboratory of Harvard University during the summer of 1963.     

Phase Diagram Behaviors for Rod/Plate Liquid Crystal Mixtures

We present a simple theory of rod/plate liquid-crystal mixtures in which the angle-dependent pair interactions are assumed to be of second-rank form. Calculations are reported for varying relative anisotropies of the “rods” and “plates”. Temperature vs. mole-fraction phase diagrams show successive isotropic (I) → uniaxial ( U) and U → biaxial ( B) transitions which are first- and second-order, respectively. For each pair of species there exists a special composition ( x _rod*) for which cooling of the isotropic phase leads directly (and continuously) to a biaxial liquid. As X _rod approaches X _rod* from either side, the first-orderness of the I → U transition (i.e. discontinuities in volume, order parameter, etc.) becomes vanishingly small. Furthermore the transition temperature of the rod-(plate-) solvent is found to be depressed when “doped” by not-too-anisotropic plates (rods) and elevated when doped by sufficiently anisotropic plates (rods). These behaviors are explained in terms of simple excluded volume considerations and compared with recent experimental data on rod/plate mixtures.     

Novel Surface Modification of Sulfur by Plasma Polymerization and its Application in Dissimilar Rubber-Rubber Blends

In this study, surface modification of elemental sulfur by plasma polymerization with acetylene, perfluorohexane and acrylic acid is described, with the aim of changing the surface properties of sulfur without losing the bulk properties and reactivities in the vulcanization process. Significant improvements are obtained in dissimilar elastomer blends using the encapsulated sulfur powders. The conditions for the plasma polymerization were varied in order to obtain the optimal performance of the modified sulfur. The imperfections in the shell structure, obtained with plasma polymers, act as gateways to release sulfur for the vulcanization reaction.