Every nonreflexive subspace of fails the fixed point property

The main result of this paper is that every nonreflexive subspace of fails the fixed point property for closed, bounded, convex subsets of and nonexpansive (or contractive) mappings on . Combined with a theorem of Maurey we get that for subspaces of , is reflexive if and only if has the fixed point property. For general Banach spaces the question as to whether reflexivity implies the fixed point property and the converse question are both still open.

     

Design, synthesis and evaluation of furanocoumarin monomers as inhibitors of CYP3A4

A number of furanocoumarins isolated from grapefruit juice have been found to inhibit CYP3A4 activity in vitro. In this study, we have designed and synthesised a range of analogues based on bergamottin to investigate the relationship between chemical structure and inhibition of CYP3A4 activity. Studies were performed using human liver microsomes and human intestinal S9 fraction, with testosterone as the marker substrate. With the exception of the coumarin and phenolic furanocoumarin derivatives, which were inactive, the alkyloxy-furanocoumarin analogues were found to inhibit CYP3A4 activity in a dose dependent manner, with observed IC50 values ranging from 0.13 +/- 0.03 to 49.3 +/- 1.9 microM. The unsaturated furan derivatives were found to exhibit time-dependent inhibition, showing a 2-, 4- and 14-fold increase in potency for 6',7'-epoxybergamottin, 6',7'-dihydroxybergamottin and bergamottin, respectively after a preincubation period of ten minutes. Reduction of the furan moiety resulted in an 11-fold decrease in inhibitory potency, suggesting that this functional group is key to the interaction between these compounds and CYP3A4.     

Preparation of a Rapidly Forming Poly(ferrocenylsilane)‐Poly(ethylene glycol)‐based Hydrogel by a Thiol‐Michael Addition Click Reaction

The synthesis of a rapidly forming redox responsive poly(ferrocenylsilane)‐poly(ethylene glycol) (PFS‐PEG)‐based hydrogel is described, achieved by a thiol‐Michael addition click reaction. PFS bearing acrylate side groups (PFS‐acryl) was synthesized by side group modification of poly(ferrocenyl(3‐iodopropyl)methylsilane) (PFS‐I) and characterized by ¹H NMR, ¹³C NMR, and FT‐IR spectroscopy. The equilibrium swelling ratio, morphology, rheology, and redox responsive properties of the PFS‐PEG‐based hydrogel are reported.

     

Unique reconstruction of band-limited signals by a Mallat-Zhong wavelet transform algorithm

We show that uniqueness and existence for signal reconstruction from multiscale edges in the Mallat and Zhong algorithm become possible if we restrict our signals to Paley-Wiener space, band-limit our wavelets, and irregularly sample at the wavelet transform (absolute) maxima—the edges—while possibly including (enough) extra points at each level. We do this in a setting that closely resembles the numerical analysis setting of Mallat and Zhong and that seems to capture something of the essence of their (practical) reconstruction method. Our work builds on a uniqueness result for reconstructing an L² signal from irregular sampling of its wavelet transform of Grochenig and the related work of Benedetto, Heller, Mallat, and Zhong. We show that the rate of convergence for this reconstruction algorithm is geometric and computable in advance. Finally, we consider the effect on the rate of convergence of not sampling enough local maxima.     

Enhancement of latent fingermarks on non-porous surfaces using anti-L-amino acid antibodies conjugated to gold nanoparticles

Enantioselective anti-L-amino acid antibodies conjugated to gold nanoparticles are shown to facilitate the detection of latent fingermarks by interacting with amino acids present in friction ridge secretions. This antibody-based system is particularly effective for the enhancement of aged and dried fingermarks on non-porous surfaces, an area unexploited by current techniques.     

Pressure dependent mechanistic branching in the formation pathways of secondary organic aerosol from cyclic-alkene gas-phase ozonolysis

The gas-phase ozonolysis of cyclic-alkenes (1-methyl-cyclohexene, methylene-cyclohexane, α-pinene, β-pinene) is studied with respect to the pressure dependent formation of secondary organic aerosol (SOA). We find that SOA formation is substantially suppressed at lower pressures for all alkenes under study. The suppression coincides with the formation of ketene (α-pinene, 1-methyl-cyclohexene), ethene (1-methyl-cyclohexene) and the increased formation of CO (all alkenes) at lower reaction pressures. The formation of these products is independent of the presence of an OH scavenger and explained by an increased chemical activation of intermediate species in the hydroperoxide channel after the OH elimination. These findings underline the central role of the hydroperoxide pathway for SOA formation and give insight into the gas-phase ozonolysis mechanism after the stage of the Criegee intermediate chemistry.     

The Mazur product map on Hardy-type sequence spaces

We study certain Hardy-type sequence spaces Hp and , 1?p?∞, which are analogues of ?^∞ and c₀, respectively. We show that the Mazur product is not onto for every p∈(1,∞) with q=p⁻¹(p−1). We present corollaries for spaces defined via weighted ?p seminorms and for c₀. The latter corollary provides a new solution of Mazur's Problem 8 in the Scottish Book.