Contractive projections with contractive complement in Lp space

Using the concepts of conditional expectation and independence of subalgebras, we characterize those contractive projections, P, on L_p, over a probability measure space, having the property that I − P is contractive. By contractive projection we mean a linear operator, P, on the Lebesgue space, L_p, 1 < p < ∞, ≠2, with P² = P, ∥ = 1.     

Metallbindungsphänomene: Alkoholat-Aggregate als unmittelbare Teilnehmer an Eliminierungsreaktionen

In solvents of low polarity it is neither a monomolecular nor a dissociated alcoholal species which effects dehydrohalogenation of vic-dihaloalkanes and vic-dihalocycloalkanes but rather a dimeric, trimeric or tetrameric alcoholate aggregate. This behavior has important implications for the stereochemical outcome of such elimination reactions.     

Remarks on the set-valued integrals of Debreu and Aumann

Some recently obtained sufficient conditions for the weak compactness of subsets of L¹(m, X) are used to show that for functions whose values are compact, convex subsets of a Banach space the Debreu integral, when it exists, is the same as the Aumann integral. Here no assumption is made concerning the reflexivity of X. This result extends to functions whose values are weakly compact, convex subsets of Banach space.     

Turbulence decay rate as a measure of flow dimensionality

The dimensionality of turbulence in fluid layers determines their properties. We study electromagnetically driven flows in finite-depth fluid layers and show that eddy viscosity, which appears as a result of three-dimensional motions, leads to increased bottom damping. The anomaly coefficient, which characterizes the deviation of damping from the one derived using a quasi-two-dimensional model, can be used as a measure of the flow dimensionality. Experiments in turbulent layers show that when the anomaly coefficient becomes high, the turbulent inverse energy cascade is suppressed. In the opposite limit turbulence can self-organize into a coherent flow.     

Rank metric codes and zeta functions

We define the rank metric zeta function of a code as a generating function of its normalized q-binomial moments. We show that, as in the Hamming case, the zeta function gives a generating function for the weight enumerators of rank metric codes. We further prove a functional equation and derive an upper bound for the minimum distance in terms of the reciprocal roots of the zeta function. Finally, we show invariance under suitable puncturing and shortening operators and study the distribution of zeroes of the zeta function for a family of codes.     

A Schiff-base cross-linked supramolecular polymer containing diiminophenol compartments and its interaction with copper(II) ions

We report here the preparation of a Schiff-base linked organic polymer 1 based on linkages containing the potent supramolecular aggregator benzene-1,3,5-tricarboxamide, connected through 2,6-diiminophenol metal binding pockets into a cross-linked polymer. The morphological and physical properties of this material are studied using electron microscopy techniques, thermal analysis, NMR, fluorescence spectroscopy and gas adsorption studies. The interaction of the polymer 1 with Cu^II ions is then investigated by soaking the material with methanolic copper acetate solution, and studying the resulting aggregates using EDX microscopy and FTIR spectroscopy. A small-molecule model compound 2 is also prepared and crystallographically characterised to act as a spectroscopic comparison, providing strong evidence that 1 interacts with copper ions through a nucleation/seeding mechanism for the growth of microcrystalline copper acetate deposits, rather than via chemisorption of the copper ions within the diiminophenol binding pockets. Preliminary results suggest a similar mechanism for Co^II adsorption, while Zn^II ions exhibit a separate interaction mode.     

The leachability of some natural and man-made radionuclides from soil and sediments on acid attack

A radiotracer study was made of the leachability of some natural and man-made radionuclides from soils and sediments subjected to attack by various acid mixtures. Particular attention was paid to the nuclides²³⁸U,²³²Th, Pa (as²³³Pa) and Np (as²³⁹Np), since for these neutron activation can be used to study recoveries and/or to induce in situ radionuclides in samples. Thus conventional NAA allowed determination of total²³⁸U and²³²Th instrumentally, and also enabled analysis of leachates and residues by radiochemical or instrumental NAA. Activation of these nuclides produced samples endogenously labelled with²³³Pa and²³⁹Np whose behaviour on acid dissolution/leaching could be examined. Furthermore, comparison of neutron irradiated and non-irradiated samples allowed us to investigate the possibility of increased leachability induced by nuclear recoil reactions; however, this effect was negligible. We also investigated the acid leaching of americium adsorbed on the surface of sediment. In general, unsatisfactory leaching recoveries were found for²³³Pa,²³⁹Np and²³²Th for most materials, indicating the need for total dissolution procedures.     

Phenothiazinium-based photobactericidal materials

Photosensitisers based on the phenothiazinium chromophore have been reported to be bactericidal on illumination via a singlet oxygen-mediated mechanism. The current work reports on the immobilisation of the methylene blue analogue, new methylene blue, in polymer resins, and the preliminary development of photobactericidal materials. The resultant materials exhibited measurable levels of singlet oxygen and were photobactericidal against both Staphylococcus epidermidis and Escherichia coli. Such materials may be of use in surface disinfection/infection control in the healthcare milieu.