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.     

Naturally-occurring nitro compounds

Naturally-occurring nitro compounds display great structural diversity, and a wide range of biological activities. This review summarizes current information on the structures of naturally-occurring nitro compounds and on the biosynthesis of the nitro group.     

Unusual electrical resistivity behavior of carbon fibers

PAN-based fibers, heat-treated to ≈1300°C having elastic moduli ≈35 Msi (240 GPa), exhibit an unusual maximum in the resistivity at low temperature (≈30 K), and the temperature coefficient of resistance remains positive to 1.5 K. Measurement of resistivity are reported, and the results discussed in terms of models for the electronic states of this disordered material. It is speculated that the behavior is related to anomalies observed in the specific heat of bulk carbons heat treated to similar temperatures.     

Galvanomagnetic effects in graphite—I: Low field data and the densities of free carriers

Measurements of the galvanomagnetic properties of highly-oriented pyrolytic graphite have been made in the field range 0.001–1.5 T at 298, 77.4 and 4.2 K, with selected measurements to higher fields and ～1.2K. Specimens of graphite were chosen with properties approximating those of purified natural crystals (single crystals) of graphite. Attention is drawn to differences in the properties of these materials. The data are analyzed with particular emphasis on the density of free carriers and its dependence on temperature, since earlier work had shown that experimental results were appreciably different from theoretical predictions.     

Predation, death, and survival in a biofilm: Bdellovibrio investigated by atomic force microscopy

Biofilms are complex microbial communities that are resistant to attack by bacteriophages and to removal by drugs and chemicals. Here we use atomic force microscopy (AFM) to image the attack on Escherichia coli biofilms by Bdellovibrio bacteriovorus 109J. Bdellovibrio is a small, predatory bacterium that invades and devours other Gram-negative bacteria. We demonstrate that under dilute nutrient conditions, bdellovibrios can prevent the formation of simple bacterial biofilms and destroy established biofilms; under richer conditions the prey bacteria persist and are not eradicated, but may be shifted toward solution populations. Using AFM we explore these bacterial interactions with more detail and accuracy than available by more traditional staining assays or optical microscopy. AFM also allows us to investigate the nanoscale morphological changes of the predator, especially those related to motility. This demonstration of Bdellovibrio's successful predation in a biofilm inspires us to consider ways that it might be used productively for industrial, medical, agricultural, and biodefensive purposes.