Asymptotics of Weil�CPetersson Geodesics II: Bounded Geometry and Unbounded Entropy

We use ending laminations for Weil–Petersson geodesics to establish that bounded geometry is equivalent to bounded combinatorics for Weil–Petersson geodesic segments, rays, and lines. Further, a more general notion of non-annular bounded combinatorics, which allows arbitrarily large Dehn-twisting, corresponds to an equivalent condition for Weil–Petersson geodesics. As an application, we show theWeil–Petersson geodesic flow has compact invariant subsets with arbitrarily large topological entropy.     

Duality Functors for Triple Vector Bundles

We calculate the group of dualization operations for triple vector bundles, showing that it has order 96 and not 72 as given in Mackenzie’s original treatment. The group is a nonsplit extension of S ₄ by the Klein group. Dualization operations are interpreted as functors on appropriate categories and are said to be equal if they are naturally isomorphic. The method set out here will be applied in a subsequent paper to the case of n-fold vector bundles.     

Synthesis of [5,6]-Bicyclic Heterocycles with a Ring-Junction Nitrogen Atom: Rhodium(III)-Catalyzed C−H Functionalization of Alkenyl Azoles

The first syntheses of privileged [5,6]-bicyclic heterocycles, with ring-junction nitrogen atoms, by transition metal catalyzed C−H functionalization of C-alkenyl azoles is disclosed. Several reactions are applied to alkenyl imidazoles, pyrazoles, and triazoles to provide products with nitrogen incorporated at different sites. Alkyne and diazoketone coupling partners give azolopyridines with various substitution patterns. In addition, 1,4,2-dioxazolone coupling partners yield azolopyrimidines. Furthermore, the mechanisms for the reactions are discussed and the utility of the developed approach is demonstrated by iterative application of C−H functionalization for the rapid synthesis of a patented drug candidate.     

The Weil–Petersson Isometry Group

We prove that, for 3g–3+n>1 and (g,n)(1,2), the group of Weil–Petersson isometries of the Teichmüller space T _g,n coincides with the extended mapping class group.     

Investigating cellular metabolism of synthetic azidosugars with the Staudinger ligation

The structure of sialic acid on living cells can be modulated by metabolism of unnatural biosynthetic precursors. Here we investigate the conversion of a panel of azide-functionalized mannosamine and glucosamine derivatives into cell-surface sialosides. A key tool in this study is the Staudinger ligation, a highly selective reaction between modified triarylphosphines and azides that produces an amide-linked product. A preliminary study of the mechanism of this reaction, and refined conditions for its in vivo execution, are reported. The reaction provided a means to label the glycoconjugate-bound azidosugars with biochemical probes. Finally, we demonstrate that the cell-surface Staudinger ligation is compatible with hydrazone formation from metabolically introduced ketones. These two strategies provide a means to selectively modify cell-surface glycans with exogenous probes.     

Toward a stable apoptolidin derivative: identification of isoapoptolidin and selective deglycosylation of apoptolidin

[formula: see text] Isoapoptolidin was isolated from crude fermentation extracts of the apoptolidin-producing microorganism Nocardiopsis sp. Apoptolidin isomerizes to isoapoptolidin upon treatment with methanolic triethylamine to establish a 1.4:1 equilibrium mixture of isoapoptolidin and apoptolidin. Semisynthesis of a peracetylated and deglycosylated derivative of apoptolidin is also described.     

High-throughput approaches for the discovery and optimization of new olefin polymerization catalysts

The discovery of new olefin polymerization catalysts is currently a time-intensive trial-and-error process with no guarantee of success. A fully integrated high-throughput screening workflow for the discovery of new catalysts for polyolefin production has been implemented at Symyx Technologies. The workflow includes the design of the metal-ligand libraries using custom-made computer software, automated delivery of metal precursors and ligands into the reactors using a liquid-handling robot, and a rapid primary screen that serves to assess the potential of each metalligand-activator combination as an olefin polymerization catalyst. "Hits" from the primary screen are subjected to secondary screens using a 48-cell parallel polymerization reactor. Individual polymerization reactions are monitored in real time under conditions that provide meaningful information about the performance capabilities of each catalyst. Rapid polymer characterization techniques support the primary and secondary screens. We have discovered many new and interesting catalyst classes using this technology.