Tracking poles and representing Hankel operators directly from data

Summary We propose and analyse a method of estimating the poles near the unit circleT of a functionG whose values are given at a grid of points onT: we give an algorithm for performing this estimation and prove a convergence theorem. The method is to identify the phase for an estimate by considering the peaks of the absolute value ofG onT, and then to estimate the modulus by seeking a bestL ² fit toG over a small arc by a first order rational function. These pole estimates lead to the construction of a basis ofL ² which is well suited to the numerical representation of the Hankel operator with symbolG and thereby to the numerical solution of the Nehari problem (computing the bestH , analytic, approximation toG relative to theL norm), as analysed in [HY]. We present the results of numerical tests of these algorithms.Partially supported by grants from the AFOSR and NSF     

Recent advances in the synthesis of well-defined glycopolymers

Glycopolymers are receiving increasing interest due to their application in areas, such as glycomics, medicine, biotechnology, sensors, and separation science. Consequently, new methods for their synthesis are constantly being developed, with an increasing emphasis on the preparation of well-defined polymers and on the production of complex macromolecular architectures such as stars. This review covers recent developments in the synthesis of glycopolymers, with a particular emphasis on (i) the use of controlled radical polymerization to prepare well-defined glycopolymers from unprotected monomers and (ii) postpolymerization modification strategies using reactive polymer precursors (including “click” reactions). Recent work on the production of glycosylated polypeptides, which are under investigation as mimics of naturally occurring glycoproteins, is also included. The authors offer some suggestions as to future developments and remaining challenges in this topical area of polymer chemistry. © 2007 Wiley Periodicals, Inc. J Polym Sci PartA: Polym Chem45: 2059–2072, 2007     

Unexpectedly fast cis/trans isomerization of Xaa-Pro peptide bonds in disulfide-constrained cyclic peptides

Acyclic dithiol and cyclic disulfide forms of the peptides Ac-Cys-Pro-Xaa-Cys-NH2 (Xaa = Phe, His, Tyr, Gly, and Thr) and Ac-Cys-Gly-Pro-Cys-NH2 and the peptide Ac-Ala-Gly-Pro-Ala-NH2 were synthesized and characterized by mass spectrometry and NMR spectroscopy. Rate constants kct and ktc for cis-to-trans and trans-to-cis isomerization, respectively, across the Cys-Pro or Gly-Pro peptide bonds were determined by magnetization transfer NMR techniques over a range of temperatures, and activation parameters were derived from the temperature dependence of the rate constants. It was found that constraints imposed by the disulfide bond confer an unexpected rate enhancement for cis/trans isomerization, ranging from a factor of 2 to 13. It is proposed that the rate enhancements are a result of an intramolecular catalysis mechanism in which the NH proton of the Pro-Xaa peptide bond hydrogen bonds to the proline nitrogen in the transition state. The peptides Ac-Cys-Pro-Xaa-Cys-NH2 and Ac-Cys-Gly-Pro-Cys-NH2 are model compounds for proline-containing active sites of the thioredoxin superfamily of oxidoreductase enzymes; the results suggest that the backbones of the active sites of the oxidized form of these enzymes may have unusual conformational flexibility.     

Shubnikov-de Haas effects in Bi2Se3 with high carrier concentrations

Shubnikov-de Haas frequencies were measured in highly degenerate n-type Bi₂Se₃ having a higher carrier density (～9 × 10²⁵m^-3) than previously reported. The Fermi surface was found to be elongated along the trigonal axis, fitting a spheroidal model with an axial ratio of 5.0 for angles up to θ = 45°. Comparison of the number of carriers obtained from Hall measurements with that obtained from the Shubnikov-de Haas measurement supports the contention that the lowest conduction band minimum is a single surface located in the center of the Brillouin zone. The higher effective mass (0.25 m₀) found for these carrier concentrations indicates that the band is non-parabolic.     

Biosynthesis of hydroxydiphenylacetylene by regiospecific monooxygenation

Bacterial monooxygenase enzymes catalyze a regiospecific single-step hydroxylation of diphenylacetylene to yield meta- and para-hydroxydiphenylacetylene.     

Influence of Cyclodextrins on the Kinetics of Oxidation of Amino Acids and BSA by Hydrazyl Radicals

The kinetics of oxidation of amino acids (Arg, His, Lys, Phe, Thr and Tyr), a dipeptide (Gly-His), and BSA (bovine serum albumin) by two persistent water soluble free radicals of the hydrazyl type has been studied.The rate decreases in the order Arg>Lys>Tyr>Thr>HisBSAPheGly-His with bothfree radicals. Addition to the reaction mixture of - and -cyclodextrin decreases the oxidation rate, probably due to amino acidencapsulation in the cyclodextrin cavity. -Cyclodextrin protects more efficiently against oxidation than -cyclodextrin.     

The microscopic investigation of structures of moving flux lines by neutron and muon techniques

We have used a variety of microscopic techniques to reveal the structure and motion of flux line arrangements, when the flux lines in low T _c type II superconductors are caused to move by a transport current. Using small-angle neutron scattering by the flux line lattice (FLL), we are able to demonstrate directly the alignment by motion of the nearest-neighbor FLL direction. This tends to be parallel to the direction of flux line motion, as had been suspected from two-dimensional simulations. We also see the destruction of the ordered FLL by plastic flow and the bending of flux lines. Another technique that our collaboration has employed is the direct measurement of flux line motion, using the ultra-high-resolution spectroscopy of the neutron spin-echo technique to observe the energy change of neutrons diffracted by moving flux lines. The muon spin rotation (μSR) technique gives the distribution of values of magnetic field within the FLL. We have recently succeeded in performing μSR measurements while the FLL is moving. Such measurements give complementary information about the local speed and orientation of the FLL motion. We conclude by discussing the possible application of this technique to thin film superconductors.