Weakly Compact Homomorphisms Between Small Algebras of Analytic Functions

The weak compactness of the composition operator C(f) = f acting on the uniform algebra of analytic uniformly continuousfunctions on the unit ball of a Banach space with the approximationproperty is characterized in terms of . The relationship betweenweak compactness and compactness of these composition operatorsand general homomorphisms is also discussed. 2000 MathematicsSubject Classification 46J15 (primary), 46E15, 46G20 (secondary).     

Electroactive Films of Alternately Layered Polycations and Iron-Sulfur Protein Putidaredoxin on Gold

Layered, electrochemically active films of bacterial iron-sulfur protein putidaredoxin (Pdx) and poly(dimethyldiallyammonium) (PDDA) polycations were constructed on gold electrodes coated with mercaptopropane sulfonate (MPS) and on quartz slides. Second-derivative UV-vis spectra suggested similar structures of Pdx in films and solutions at pH 7. Direct electrochemistry was achieved between Pdx and gold electrodes in these films, with significantly better electrochemical reversibility than in cast Nafion-lipid-Pdx films. A formal potential dispersion model gave a good fit to square wave voltammograms by regression analysis and was used to estimate an average apparent rate constant of 4.5 s(-1). Reduced Pdx in the polyion films did not react with its natural redox partner cytochrome P450(cam) because of unfavorable thermodynamics in the film environment. Copyright 2000 Academic Press.     

Convex-Concave Extensions

In this paper we introduce a new notion which we call convex-concave extensions. Convex-concave extensions provide for given nonlinear functions convex lower bound functions and concave upper bound functions, and can be viewed as a generalization of interval extensions. Convex-concave extensions can approximate the shape of a given function in a better way than interval extensions which deliver only constant lower and upper bounds for the range. Therefore, convex-concave extensions can be applied in a more flexible manner. For example, they can be used to construct convex relaxations. Moreover, it is demonstrated that in many cases the overestimation which is due to interval extensions can be drastically reduced. Applications and some numerical examples, including constrained global optimization problems of large scale, are presented.     

Electronic states and phosphorescence of dendron functionalized platinum(II) acetylides

The photophysical properties of bis((4-(phenylethynyl)phenyl)ethynyl)bis(tributylphosphine) platinum(II) with 2,2-bis(methylol)propionic acid (bis-MPA) dendritic substituents were studied. The fluorescence emission decay upon excitation in the UV (typically 350-380 nm) was rapid, in the order of 1 ns or shorter. In oxygen-saturated tetrahydrofuran solvent, the phosphorescence decay time was in the order of 200 ns. Bright phosphorescence at 530 nm was found for dendrimers under certain conditions. The associated phosphorescence decay time considerably increased to above 100-200 μs at higher concentrations (30-100 μM), and in oxygen-evacuated samples. Thus, it was clarified that the strongest triplet quenching was caused by oxygen dissolved in the sample, since it was possible to reversibly go between the bright and quenched phosphorescent state by freeze-thaw pumping cycles. The bright phosphorescence formed spontaneously for the cases with the larger dendritic substituents is implying a chromophore protecting effect. From time-dependent density functional calculations, the electronic structure of a few low-lying singlet and triplet states are discussed. A new mechanism for efficient triplet state formation and phosphorescence of Pt-ethynyls is proposed. Here, a fast relaxation via internal conversion takes the excited population of the dominant π→π* excitation into a lower singlet state of ligand-to-metal charge transfer character of πσ* type. This allows an efficient inter system crossing to the triplet state manifold.     

Accurate Backbone 13C and 15N Chemical Shift Tensors in Galectin-3 Determined by MAS NMR and QM/MM: Details of Structure and Environment Matter

Chemical shift tensors obtained from solid-state NMR spectroscopy are very sensitive reporters of structure and dynamics in proteins. While accurate ¹³C and ¹⁵N chemical shift tensors are accessible by magic angle spinning (MAS) NMR, their quantum mechanical calculations remain challenging, particularly for ¹⁵N atoms. Here we compare experimentally determined backbone ¹³C^α and ¹⁵N^H chemical shift tensors by MAS NMR with hybrid quantum mechanics/molecular mechanics/molecular dynamics (MD-QM/MM) calculations for the carbohydrate-binding domain of galectin-3. Excellent agreement between experimental and computed ¹⁵N^H chemical shift anisotropy values was obtained using the Amber ff15ipq force field when solvent dynamics was taken into account in the calculation. Our results establish important benchmark conditions for improving the accuracy of chemical shift calculations in proteins and may aid in the validation of protein structure models derived by MAS NMR.     

Cascade synthesis of polyoxygenated 6H,11H-[2]benzopyrano-[4,3-c][1]benzopyran-11-ones

2-(methoxymethoxymethyl)aryllead triacetates, obtained in situ from the corresponding arylboronic acids, reacted with 4-hydroxycoumarins, leading to 3-(2-methoxymethoxymethyl)aryl-4-hydroxycoumarin derivatives in good to high yields. These compounds underwent a cascade sequence of reactions, deprotection-halogenation-annulation, to afford polyoxygenated tetracyclic 6H,11H-[2]benzopyrano-[4,3-c] [1]benzopyran-11-ones in good yields. Some compounds showed a moderate cytotoxicity against human epithelial mammary HBL100 cells.     

On the notion of a rotating fluid force induced by swirling flow

The Bently/Muszynska (B/M) model shows that oil whirl and oil whip are both self-sustained vibrations associated with two unstable modes of a rotor–fluid system. The model includes a rotating fluid damping and inertia force. In certain configurations, the rotating damping force overcomes the frictional internal damping of the rotor and pushes the rotor into a stable limit cycle of circular orbiting. Such a notion of a rotating fluid force is based on bulk-flow models of fluid-filled clearances that could be approximated as narrow since the tangential velocity of the fluid then translates to one angular velocity at a certain radial distance defined by an average radius. This paper scrutinizes the assumption of a rotating fluid inertia force and pinpoints the additional inertial effects of the swirling flow as the gap width increases. These effects are clarified by deriving the equation of motion of a body with a mass subjected to motion-induced fluid forces of a confined swirling flow. We show that the inertial effects of the swirling flow counteract the destabilizing effect of the rotating damping force. However, if the body mass is larger than the displaced fluid mass, instability follows. The frequency of the unstable mode is unchanged by the additional inertial effects and is always equal to the frequency of the damping that induces the instability.     

Diffusion tensor fiber tractography of the olfactory tract

Magnetic resonance diffusion tensor imaging with fiber tracking is used for 3-dimensional visualization of the nervous system. Peripheral nerves and all cranial nerves, except for the olfactory tract, have previously been visualized. The olfactory tracts are difficult to depict with diffusion-weighted imaging due to the high sensitivity to susceptibility artifacts at the base of the skull. Here we report an optimized single-shot diffusion-weighted echo planar imaging sequence that can visualize the olfactory tracts with fiber tracking. Five healthy individuals were examined, and the olfactory tracts could be fiber tracked with the diffusion-weighted sequence. For comparison and as a negative control, an anosmic patient was examined. No olfactory tracts were visualized on T2-weighted nor diffusion-weighted fiber tracking images. Measuring diffusion in the olfactory tracts promise to facilitate the identification of different hyposmic and anosmic conditions.