Multiple scattering in random media

The paper is an application of a general microscopic approach to the theory of the average scattering matrix for a particle interacting with random scatterers. We present a detailed treatment for the case of uncorrelated positions of the scatterers. First, the general two-body additive approximation is used to truncate the hierarchy of correlation functions for fluctuations. It is shown that the self-energy is accurate through the fourth power of the individual scattering amplitude. Second, the hierarchy is terminated at the next stage. The self-energy is correct to the sixth power of the scattering amplitude.Work supported in part by the National Science Foundation under Contract No. NSF DMR 79-23213.     

Homotopy groups of -contact toric manifolds

Contact toric manifolds of Reeb type are a subclass of contact toric manifolds which have the property that they are classified by the images of the associated moment maps. We compute their first and second homotopy group terms of the images of the moment map. We also explain why they are -contact.

     

Convergence of Perturbation Expansions in Fermionic Models. Part 1: Nonperturbative Bounds

An estimate on the operator norm of an abstract fermionic renormalization group map is derived. This abstract estimate is applied in another paper to construct the thermodynamic Greens functions of a two dimensional, weakly coupled fermion gas with an asymmetric Fermi curve. The estimate derived here is strong enough to control everything but the sum of all quartic contributions to the Greens functions.Research supported in part by the Natural Sciences and Engineering Research Council of Canada and the Forschungsinstitut für Mathematik, ETH Zürich.     

A Two Dimensional Fermi Liquid. Part 3: The Fermi Surface

We show that the particle number density derived from the thermodynamic Greens function at temperature zero constructed in the second part of this series has a jump across the Fermi curve, a basic property of a Fermi liquid. We further show that the two particle thermodynamic Greens function at temperature zero has the regularity behavior expected in a Fermi liquid.Research supported in part by the Natural Sciences and Engineering Research Council of Canada and the Forschunginstitut für Mathematik, ETH Zürich.     

NMR assignment of protein side chains using residue-correlated labeling and NOE spectra

A new approach for the isotopic labeling of proteins is proposed that aims to facilitate side chain resonance assignments. Residue-correlated (RC) labeling is achieved by the expression of a protein on a medium containing a mixture of labeled, e.g., [U-13C,15N]amino acids, and NMR silent, [U-2H]amino acids. De novo synthesis of amino acids was suppressed by feedback inhibition by the amino acids in the growth medium and by the addition of beta-chloro-L-alanine, a transaminase inhibitor. Incorporation of these amino acids into synthesized proteins results in a relative diminution of inter-residue NOE interactions and a relative enhancement of intra-residue NOEs. Comparison of the resulting NOE spectra with those obtained from a uniformly labeled sample allows identification of intra-residue NOE peaks. Thus, this approach provides direct information for sidechain assignments in the NOE spectra, which are subsequently used for structural analysis. We have demonstrated the feasibility of this strategy for the 143 amino acid nuclease inhibitor NuiA, both at 35 degrees C, corresponding to a rotational correlation time of 9.5 ns, and at 5 degrees C, corresponding to a rotational correlation time of 22 ns.