EquivariantL-theory I

W.L. was supported by DFG     

On the solution of nonlinear equations in interval arithmetic

We consider the problem of finding a simple zero of a continuously differentiable functionf:R ⁿ R ⁿ . There is given an intervalvectorX ₀ ^I containing one zero off, and we will construct a contracting sequence of intervalvectors enclosing this zero. This can be done by Newton's method, which gives quadratic convergence, but requires inversion of an intervalmatrix at each step of the iteration. Alefeld and Herzberger, [1], give a modification of Newton's method, without the necessity of inversion, the convergence being superlinear. We give a slight modification of the latter method, with the property that the sequence of interval widths is dominated by a quadratically convergent sequence.     

Utilization of flow injection with hydrazine reduction and photometric detection for the determination of nitrate in rain-water

The hydrazine reduction method for determination of nitrate at the parts per million level is adapted to flow injection sample processing of rain-water. Reagent composition and physical variables were evaluated and optimized. Forty samples per hour can be processed. A precision of better than 3% is possible in the range of 1.0–10.0 ppm nitrate. Results for nitrate obtained from 9 rain-water samples agreed favorably with those determined by ion chromatography.     

Sperm whale clicks: directionality and source level revisited

In sperm whales (Physeter catodon L. 1758) the nose is vastly hypertrophied, accounting for about one-third of the length or weight of an adult male. Norris and Harvey [in Animal Orientation and Navigation, NASA SP-262 (1972), pp. 397-417] ascribed a sound-generating function to this organ complex. A sound generator weighing upward of 10 tons and with a cross-section of 1 m is expected to generate high-intensity, directional sounds. This prediction from the Norris and Harvey theory is not supported by published data for sperm whale clicks (source levels of 180 dB re 1 microPa and little, if any, directionality). Either the theory is not borne out or the data is not representative for the capabilities of the sound-generating mechanism. To increase the amount of relevant data, a five-hydrophone array, suspended from three platforms separated by 1 km and linked by radio, was deployed at the slope of the continental shelf off Andenes, Norway, in the summers of 1997 and 1998. With this system, source levels up to 223 dB re 1 microPa peRMS were recorded. Also, source level differences of 35 dB for the same click at different directions were seen, which are interpreted as evidence for high directionality. This implicates sonar as a possible function of the clicks. Thus, previously published properties of sperm whale clicks underestimate the capabilities of the sound generator and therefore cannot falsify the Norris and Harvey theory.     

The primary photodynamics of aqueous nitrate: formation of peroxynitrite

We have examined the photochemical reactions occurring after irradiation at 200 nm of the aqueous nitrate ion, NO3(-)(aq). Using femtosecond transient absorption spectroscopy over the range 194-388 nm, we have characterized the formation and subsequent relaxation of the primary photoproducts of nitrate photolysis. The dominant photoproduct is the cis-isomer of peroxynitrite, which accounts for 48% of the excited state molecules initially produced. A slightly smaller fraction, 44%, of the excited molecules return to the electronic ground state of NO3(-) and relax to the vibrational ground state in 2 ps. The remaining 8% of the molecules initially excited react via the *NO + *O2(-) or the NO- + O2 dissociation channels. Formation of NO2(-) and *NO2 is not observed, suggesting that the previous observations of these species in steady-state photolysis are caused by reactions occurring on a longer time scale.     

Structural basis for cyclophellitol inhibition of a beta-glucosidase

The structural basis for beta-glucosidase inhibition by cyclophellitol is demonstrated using X-ray crystallography, enzyme kinetics and mass spectrometry.     

Methylated β-cyclodextrins: influence of degree and pattern of substitution on the thermodynamics of complexation with tauro- and glyco-conjugated bile salts

The complexation of 6 bile salts with various methylated β-cyclodextrins was studied to elucidate how the degree and pattern of substitution affects the binding. The structures of the CDs were determined by mass spectrometry and NMR techniques, and the structures of the inclusion complexes were characterized from the complexation-induced shifts of (13)C nuclei as well as by 2D ROESY NMR. Thermodynamic data were generated using isothermal titration calorimetry. The structure-properties analysis showed that methylation at O3 hinders complexation by partially blocking the cavity entrance, while methyl groups at O2 promote complexation by extending the hydrophobic cavity. Like in the case of 2-hydroxypropylated cyclodextrins, the methyl substituents cause an increased release of ordered water from the hydration shell of the bile salts, resulting in a strong increase in both the enthalpy and the entropy of complexation with increased number of methyl substituents. Due to enthalpy-entropy compensation the effect on the stability constant is relatively limited. However, when all hydroxyl groups are methylated, the rigid structure of the free cyclodextrin is lost and the complexes are severely destabilized due to very unfavorable entropies.     

Mechanistic insights for block copolymer morphologies: how do worms form vesicles?

Amphiphilic diblock copolymers composed of two covalently linked, chemically distinct chains can be considered to be biological mimics of cell membrane-forming lipid molecules, but with typically more than an order of magnitude increase in molecular weight. These macromolecular amphiphiles are known to form a wide range of nanostructures (spheres, worms, vesicles, etc.) in solvents that are selective for one of the blocks. However, such self-assembly is usually limited to dilute copolymer solutions (<1%), which is a significant disadvantage for potential commercial applications such as drug delivery and coatings. In principle, this problem can be circumvented by polymerization-induced block copolymer self-assembly. Here we detail the synthesis and subsequent in situ self-assembly of amphiphilic AB diblock copolymers in a one pot concentrated aqueous dispersion polymerization formulation. We show that spherical micelles, wormlike micelles, and vesicles can be predictably and efficiently obtained (within 2 h of polymerization, >99% monomer conversion) at relatively high solids in purely aqueous solution. Furthermore, careful monitoring of the in situ polymerization by transmission electron microscopy reveals various novel intermediate structures (including branched worms, partially coalesced worms, nascent bilayers, "octopi", "jellyfish", and finally pure vesicles) that provide important mechanistic insights regarding the evolution of the particle morphology during the sphere-to-worm and worm-to-vesicle transitions. This environmentally benign approach (which involves no toxic solvents, is conducted at relatively high solids, and requires no additional processing) is readily amenable to industrial scale-up, since it is based on commercially available starting materials.