A Closed Contour of Integration in Regge Calculus

The analytic structure of the Regge action on a cone in d dimensions over a boundary of arbitrary topology is determined in simplicial minisuperspace. The minisuperspace is defined by the assignment of a single internal edge length to all 1-simplices emanating from the cone vertex, and a single boundary edge length to all 1-simplices lying on the boundary. The Regge action is analyzed in the space of complex edge lengths, and it is shown that there are three finite branch points in this complex plane. A closed contour of integration encircling the branch points is shown to yield a convergent real wave function. This closed contour can be deformed to a steepest descent contour for all sizes of the bounding universe. In general, the contour yields an oscillating wave function for universes of size greater than a critical value which depends on the topology of the bounding universe. For values less than the critical value the wave function exhibits exponential behaviour. It is shown that the critical value is positive for spherical topology in arbitrary dimensions. In three dimensions we compute the critical value for a boundary universe of arbitrary genus, while in four and five dimensions we study examples of product manifolds and connected sums.     

Real Places and Torus Bundles

If M is a hyperbolic once-punctured torus bundle over S ¹, then the trace field of M has no real places.     

Twisted K-Theory and K-Theory of Bundle Gerbes

In this note we introduce the notion of bundle gerbe K-theory and investigate the relation to twisted K-theory. We provide some examples. Possible applications of bundle gerbe K-theory to the classification of K-brane charges in nontrivial backgrounds are briefly discussed. Received: 29 June 2001 / Accepted: 15 October 2001     

Molecularly Designed Stabilized Asymmetric Hollow Fiber Membranes for Aggressive Natural Gas Separation

New rigid polyimides with bulky CF₃ groups were synthesized and engineered into high‐performance hollow fiber membranes. The enhanced rotational barrier provided by properly positioned CF₃ side groups prohibited fiber transition layer collapse during cross‐linking, thereby greatly improving CO₂/CH₄ separation performance compared to conventional materials for aggressive natural gas feeds.     

Individually addressable microelectrode array for monitoring oxygen and nitric oxide release

We have fabricated a six individual addressable gold working electrode microarray. The device is wirebonded to an eight-pin DIL package that can be easily interconnected to an external multi-channel potentiostat. A polyion complex film coating on the electrode surface provides a suitable coating for the growth of cells. The responses of oxygen and nitric oxide were assessed on uncoated and coated devices using electroanalytical methods. The film coating reduced the diffusion current by approximately 20% in both cases. No changes in the electrochemical mechanism were observed. Simultaneous recordings were obtained for 2 h in the presence of the cells, thus the device is stable for the duration of the bioanalytical measurements. Measurements were conducted to study the simultaneous changes in oxygen and nitric oxide levels in cultured fibroblast cells in the presence of growth hormones that cause cell proliferation. Increases in oxygen consumption of the cells were coupled with increases in nitric oxide levels when in the presence of the growth hormones. Use of a biological detergent to cause an oxidative burst resulted in a large increase in the current for potentials set to detect nitric oxide and oxygen.     

Diastereoselective Friedel-Crafts alkylation of indoles with chiral alpha-phenyl benzylic cations. Asymmetric synthesis of anti-1,1,2-triarylalkanes

The reactions of chiral benzyl carbocations bearing alpha-phenyl substituents with N-sulfonylated indoles afford 1,1,2-triarylalkanes with anti-selectivities. This outcome is a reversal of facial diastereoselectivity relative to Bach's alpha-alkyl-bearing benzyl cations. The reactions are promoted by either a Br?nsted acid (TFA) or Lewis acid (BF3.OEt2), offering differential diastereoselectivities and reactivities. The electronic properties of both reacting partners strongly influence the reaction rates and the product diastereoselectivities and appear to operate under kinetic control. This chemistry provides an efficient access to sterically congested tetrasubstituted ethanes.     

Constructing the Spectrum of Packings and Coverings for the Complete Graph with Stars with up to Five Edges

The packing and covering problems have been considered for several classes of graphs. For instance, Bryant et. al. have investigated the packing problem for paths and cycles, and the packing and covering problems for 3-cubes. The packing and covering problems were settled for stars with up to six edges by Roditty. In this paper, for every possible leave graph (excess graph), we find a corresponding maximum packing (minimum covering) of the complete graph with stars with up to five edges.     

Synthesis of the C9-C29 fragments of ajudazols A and B

The syntheses of both C9-C29 fragments 3 and 4 of the myxobacteria metabolites ajudazols A (1) and B (2) are described. The key steps were a cyclodehydration to form the oxazole, Sonogashira coupling to form the C18-C19 bond and a P-2 Ni mediated partial alkyne hydrogenation to install the C17-C18 Z-alkene. The C15 alkene in the ajudazol A fragment 3 was introduced in the final steps by elimination of the corresponding primary alcohol.