Volumes of Hyperbolic 3-Manifolds of Betti Number at Least 3

This paper provides a new, simpler proof of the fact that thesmallest volume hyperbolic 3-manifold has betti number at least3. In the process, the best known lower bound on the volumeof such a manifold is improved.     

A momentum construction for circle-invariant Kähler metrics

Examples of Kähler metrics of constant scalar curvature are relatively scarce. Over the past two decades, several workers in geometry and physics have used symmetry reduction to construct complete Kähler metrics of constant scalar curvature by ODE methods. One fruitful idea--the ``Calabi ansatz'--is to begin with an Hermitian line bundle over a Kähler manifold, and to search for Kähler forms in some disk subbundle, where is the logarithm of the norm function and is a function of one variable.

Our main technical result (Theorem A) is the calculation of the scalar curvature for an arbitrary Kähler metric  arising from the Calabi ansatz. This suggests geometric hypotheses (which we call ``-constancy') to impose upon the base metric  and Hermitian structure  in order that the scalar curvature of  be specified by solving an ODE. We show that -constancy is ``necessary and sufficient for the Calabi ansatz to work' in the following sense. Under the assumption of -constancy, the disk bundle admits a one-parameter family of complete Kähler metrics of constant scalar curvature that restrict to on the zero section (Theorems B and D); an analogous result holds for the punctured disk bundle (Theorem C). A simple criterion determines when such a metric is Einstein. Conversely, in the absence of -constancy the Calabi ansatz yields at most one metric of constant scalar curvature, in either the disk bundle or the punctured disk bundle (Theorem E).

Many of the metrics constructed here seem to be new, including a complete, negative Einstein-Kähler metric on the disk subbundle of a stable vector bundle over a Riemann surface of genus at least two, and a complete, scalar-flat Kähler metric on  .

     

Metabolic profiling of rodent biological fluids via 1H NMR spectroscopy using a 1 mm microlitre probe

The application of a 1 mm TXI (1H/13C/15N) microlitre NMR probe with z-gradient for metabolic profiling of biofluids is described. The probe was used to provide spectral profiles for rat blood plasma using only approximately 2 microl of fluid with a range of solvent suppression techniques. Using a similar amount of fluid, spectra were obtained from rat and mouse cerebrospinal fluid, demonstrating that the probe could be used to profile rodents metabolically via biofluids previously inaccessible to NMR analysis without the need for termination.     

Dynamic behavior in diplatinum metalloreceptors

Diplatinum metalloreceptors anti-4a and anti-4b exhibit dynamic behavior in solution that is modified by anion binding. An X-ray crystal structure determination of anti-4a supports its proposed solution structure.     

Heme charge-transfer band III is vibronically coupled to the Soret band

A complete resonance Raman excitation profile of the heme charge-transfer band known as band III is presented. The data obtained throughout the near-infrared region show preresonance with the Q-band, but the data also clearly show the enhancement of a number of modes in the spectral region of band III. Only nontotally symmetric modes are observed to have resonance enhancement in the band III region. The observed resonance enhancements in modes of B(1g) symmetry are compared with the enhancements of those same modes in the excitation profiles of the Q-band of deoxy myoglobin, also presented here for this first time. The Q-band data agree well with the theory of vibronic coupling in metalloporphyrins (Shelnutt, J. A. J. Chem. Phys. 1981, 74, 6644-6657). The strong vibronic coupling of the Q-band of the deoxy form of hemes is discussed in terms of the enhancement of modes with both B(1g) and A(2g) symmetry. The comparison between the Q-band and band III reveals that, consistent with the theory, only modes of B(1g) symmetry are enhanced in the vicinity of band III. These results show that band III is vibronically coupled to the Soret band. The coupling of band III to modes with strong rhombic distortion of the heme macrocycle calls into question the hypothesis that the axial iron out-of-plane displacement is primarily responsible for the structure-dynamics correlations observed in myoglobin.     

Heterocumulene metathesis by iridium guanidinate and ureylene complexes: catalysis involving reversible insertion to form six-membered metallacycles

The four-membered metallacycles Cp*Ir((NAr)2C=Z) have been prepared for Z = NAr and Z = O. These complexes undergo facile exchange with free heterocumulenes. This exchange process can be employed to effect the rapid, catalytic metathesis of aryl carbodiimides at room temperature and the metathesis of aryl carbodiimides with aryl isocyanates at slightly elevated temperature. The exchange process appears to proceed via a novel associative mechanism involving ring expansion to form a six-membered metallacycle rather than cycloreversion to give an imido complex. Observation of key intermediates and the results of crossover experiments support this hypothesis.     

Argon rectification and the cause of light emission in single-bubble sonoluminescence

In single-bubble sonoluminescence, repeated brief flashes of light are produced in a gas bubble strongly driven by a periodic acoustic field. A startling hypothesis has been made by Lohse and co-workers [Phys. Rev. Lett. 78, 1359 (1997)] that the non-noble gases in an air bubble undergo chemical reaction into soluble products, leaving only argon. In the present work, this dissociation hypothesis is supported by simulations, although the associated temperatures of about 7000 K seem too low for bremsstrahlung, which has been proposed as the dominant light emission mechanism. This suggests that emission from water vapor and its reaction products, heretofore not included, may play an important role.     

Crystal structure and luminescence of 2,7-dimethylnaphthalene-1-carbonitrile

The title compound crystallizes in the monoclinic space group P2 ₁/c: M _r = 181.2; a = 7.119(1), b = 18.389(4), c = 7.5385(6) Å = 91.661(7)° V = 986.4(5) ų; and Z = 4. The purified material shows fluorescence similar to other naphthalene derivatives: monomer fluorescence (_max 350-370 nm) in the solid state and in dilute solutions, and excimer fluorescence (_max 421 nm) in concentrated solutions. Intense blue-green luminescence (_max 490 nm) is observed in some partially purified crystalline samples. This is attributed to phosphorescence from two isomeric bromodimethylnaphthalenecarbonitrile impurities detected by GC-MS analysis.     

Enantioselective synthesis of the 4-hydroxy buteneolide terminus of mucocin and related annonaceous acetogenins

The 4-hydroxy buteneolide terminus 3, applicable to mucocin 1 and related annonaceous acetogenins, was prepared in an expeditious manner from the selenocarbonate 2 via an intramolecular acyl radical cyclization followed by an enantioselective Lewis-acid catalyzed Keck-allylation reaction.