Efficient asymmetric synthesis of the vasopeptidase inhibitor BMS-189921

[reaction: see text] An efficient asymmetric synthesis of the vasopeptidase inhibitor BMS-189921 was accomplished. Two short enantioselective syntheses of the common key intermediate (S)-alpha-aminoazepinone 6b were developed. Olefin 3 was converted to 6b via asymmetric hydrogenation. Alternatively, enyne 12 was converted to racemic alpha-aminoazepinone 15b, which was transformed to 6b by a practical dynamic resolution.     

Catalytic asymmetric vinylation of ketone enolates

[see reaction]. A protocol for the catalytic asymmetric vinylation of ketone enolates has been developed. Key to the success of this process was the development of new electron-rich chiral monodentate ligands.     

Inequalities for <Emphasis Type="Bold">cd</Emphasis>-Indices of Joins and Products of Polytopes

The cd-index is a polynomial which encodes the flag f-vector of a convex polytope. For polytopes U and V, we determine explicit recurrences for computing the cd-index of the free join and the cd-index of the Cartesian product U x V. As an application of these recurrences, we prove the inequality involving the cd-indices of three polytopes.     

Experimental evidence for a light and broad scalar resonance in D(+) --> pi(-)pi(+)pi(+) decay

From a sample of 1172 +/- 61 D(+)-->pi(-)pi(+)pi(+) decays, we find gamma(D(+)-->pi(-)pi(+)pi(+))/gamma(D(+)-->K-pi(+)pi(+)) = 0.0311 +/- 0.0018(+0.0016)(-0.0026). Using a coherent amplitude analysis to fit the Dalitz plot of these decays, we find strong evidence that a scalar resonance of mass 478(+24)(-23) +/- 17 MeV/c(2) and width 324(+42)(-40) +/- 21 MeV/c(2) accounts for approximately half of all decays.     

Perturbed Dolbeault operators and the homology Todd class

This paper discusses the role played by perturbed Dolbeault operators in relating the coherent sheaf and elliptic operator perspectives on the homology of projective varieties. Among the consequences are index formulas for perturbed Dolbeault operators.

     

Methods for calculating the desorption rate of an isolated molecule from a surface: Water on MgO(0 0 1)

We present two types of Molecular Dynamics (MD) simulation for calculating the desorption rate of molecules from a surface. In the first, the molecules move freely between two surfaces, and the desorption rate is obtained either by counting the number of desorption events in a given time, or by looking at the average density of the molecules as a function of distance from the surface and then applying transition state theory (TST). In the second, the potential of mean force (PMF) for a molecule is determined as a function of distance from the surface and the desorption rate is obtained by means of TST. The methods are applied to water on the MgO(0 0 1) surface at low coverage. Classical potentials are used so that long simulations can be performed, to minimise statistical errors. The two sets of MD simulations agree well at high temperatures. The PMF method reproduces the 0 K adsorption energy of the molecule to within 5 meV, and finds that the well depth of the PMF is not linear with temperature. This implies the prefactor frequency f in the Polanyi-Wigner equation is a function of temperature, increasing at lower temperatures due to the reduction of the available configuration space associated with an adsorbed molecule compared with a free molecule.     

Dehn filling in relatively hyperbolic groups

We introduce a number of new tools for the study of relatively hyperbolic groups. First, given a relatively hyperbolic group G, we construct a nice combinatorial Gromov hyperbolic model space acted on properly by G, which reflects the relative hyperbolicity of G in many natural ways. Second, we construct two useful bicombings on this space. The first of these, preferred paths, is combinatorial in nature and allows us to define the second, a relatively hyperbolic version of a construction of Mineyev. As an application, we prove a group-theoretic analog of the Gromov-Thurston 2π Theorem in the context of relatively hyperbolic groups. The first author was supported in part by NSF Grant DMS-0504251. The second author was supported in part by an NSF Mathematical Sciences Post-doctoral Research Fellowship. Both authors thank the NSF for their support. Most of this work was done while both authors were Taussky-Todd Fellows at Caltech.