A Note on the Almost Everywhere Convergence to Initial Data for Some Evolution Equations

The weighted Lebesgue spaces of initial data for which almost everywhere convergence of the heat equation holds was only very recently characterized. In this note we show that the same weighted space of initial data is optimal for the heat–diffusion parabolic equations involving the harmonic oscillator and the Ornstein–Uhlenbeck operator.     

A limit theorem for continuous selectors

Any (measurable) function K from Rⁿ to R defines an operator K acting on random variables X by K(X) = K(X₁,..., X_n), where the X_j are independent copies of X. The main result of this paper concerns continuous selectors H, continuous functions defined in Rn and such that H(x₁, x₂,..., x_n) ∈ {x₁, x₂,..., x_n}. For each such continuous selector H (except for projections onto a single coordinate) there is a unique point ω_H in the interval (0, 1) so that, for any random variable X, the iterates H^(N) acting on X converge in distribution as N → ∞ to the ωH-quantile of X.     

A simple Markov chain structure for the evolution of credit ratings

We focus on continuous Markov chains as a model to describe the evolution of credit ratings. In this work it is checked whether a simple, tridiagonal type of generator provides a good approximation to a general one. Three different tridiagonal approximations are proposed and their performance is checked against two generators, corresponding to a volatile and a stable period, respectively. Copyright © 2007 John Wiley & Sons, Ltd.     

Coinage Metal–Glutathione Thiolates as a New Class of Supramolecular Hydrogelators

Summary: Coinage metal salts (e.g. Au^III, Ag^I and Cu^II salts) readily react with thiols to give the corresponding metal(I) thiolates. These thiolate species are known to either self-assemble into insoluble polymeric species or to form soluble oligomers, depending on the nature of the thiol ligand. Here we demonstrate that this self-assembling ability can be applied to create supramolecular hydrogels. Glutathione (GSH), a naturally occurring tripeptide, has been used in combination with Au^III, Ag^I and Cu^II salts to obtain pH responsive hydrogels that are able to gelate 100 times their weight in water.     

Reactivity of 2-halo-2H-azirines. 1. Reactions with nucleophiles.

Nucleophilic substitution reactions of 2-halo-2H-azirines 1a, 1b, 1d, and 1e with potassium phthalimide and aniline allowed the preparation of new substituted 2H-azirines 2-5. The reactions of 2-bromo-2H-azirine 1a with methylamine led to the synthesis of alpha-diimines 7 and 8. 2-Halo-2H-azirines were also established as building blocks for the synthesis of a range of heterocyclic compounds, namely, quinoxalines 10a-10d, 3-oxazoline 14, and 2H-[1,4]oxazines 18 and 20. X-ray crystal structures of alpha-diimine 7, 3-oxazoline 14, and 2H-[1,4]oxazine 18 are reported.     

Direct (1)H NMR spectroscopy of dissolved organic matter in natural waters

Nuclear magnetic resonance (NMR) spectroscopy arguably provides the greatest insight into the overall chemical composition of dissolved organic matter (DOM). However, in a standard 5 mm NMR probe, a sample of sea water at natural abundance only contains ca. 500-600 ng of organic matter, distributed among the heterogeneous components of DOM. Additionally, the intensity of the water signal, which may be many orders of magnitude greater than the signals from DOM, makes the detection and analysis of DOM at natural abundance extremely demanding. Here, we demonstrate, that although challenging, the application of an improved water suppression technique allows NMR spectra of DOM to be obtained directly (i.e without pre-concentration) for major bodies of water, including rivers, lakes and the ocean. The technique described here provides a compositional overview of an intact sample, permitting researchers to investigate and assess the impact of concentration, isolation and extraction procedures that are employed routinely. Also the technique permits NMR to be performed on 'precious' samples for which traditional isolations are not possible, for example, water from ice cores and pore water, which are key in hydrology and for paleoclimatic reconstruction.     

Glass breaks like metal,but at the nanometer scale

We report in situ atomic force microscopy experiments which reveal the presence of nanoscale damage cavities ahead of a stress-corrosion crack tip in glass. Their presence might explain the departure from linear elasticity observed in the vicinity of a crack tip in glass. Such a ductile fracture mechanism, widely observed in the case of metallic materials at the micrometer scale, might be also at the origin of the striking similarity of the morphologies of fracture surfaces of glass and metallic alloys at different length scales.     

Total and inorganic mercury determination in fish tissue by flow injection cold vapour atomic fluorescence spectrometry

A simple and reliable method for Hg determination in fish samples has been developed. Lyophilised fish tissue samples were extracted in a 25% (w/v) tetramethylammonium hydroxide (TMAH) solution; the extracts were then analysed by FI-CVAFS. This method can be used to determine total and inorganic Hg, using the same FI manifold. For total Hg determination, a 0.1% (w/v) KMnO₄ solution was added to the FI manifold at the sample zone, followed by the addition of a 0.5% (w/v) SnCl₂ solution, whereas inorganic Hg was determined by adding a 0.1% (w/v) L-cysteine solution followed by a 1.0% (w/v) SnCl₂ solution to the FI system. The organic fraction was determined as the difference between total and inorganic Hg. Sample preparation, reagent consumption and parameters that can influence the FI-CVAFS performance were also evaluated. The limit of detection for this method is 3.7 ng g^?1 for total Hg and 4.3 ng g^?1 for inorganic Hg. The relative standard deviation for a 1.0 µg L^?1 CH₃Hg standard solution (n = 20) was 1.1%, and 1.3% for a 1.0 µg L^–1 Hg²⁺ standard solution (n = 20). Accuracy was assessed by the analysis of Certified Reference Material (dogfish: DORM-2, NRCC). Recoveries of 99.1% for total Hg and 93.9% inorganic Hg were obtained. Mercury losses were not observed when sample solutions were re-analysed after a seven day period of storage at 4°C.     

Improvements in the electrochemical generation of arsine at gold electrodes as a sample introduction strategy for arsenic determination in well-water samples by atomic absorption spectrometry

The development and evaluation of a cathode consisting of a gold electrode covered by a polyaniline film, PANI/Au modified electrode, for electrochemical generation of arsine is described. The efficiency of arsine production using the new electrode was ascertained by comparison with corresponding hydride generation atomic absorption spectroscopy determinations of arsenic (As) in aqueous standards. The PANI/Au modified electrodes provide better sensitivity, accuracy and precision than the pure Au cathodes. The PANI/Au cathodes were prepared by controlled electrodeposition cycles of polyaniline films on top of Au electrodes. Cathodes obtained after 10 electrodeposition cycles showed the best performance, while the ones obtained after five voltammetry cycles produced films too thin and those obtained after 20 voltammetry cycles produced films too thick for the purpose of this work. Under optimised conditions, the As limit of detection in aqueous solutions, according to the (3σ) criterion, was 2.48 µg L^?1. For accuracy determination, the modified electrode was applied to quantification of As(III) in acidified aqueous solutions of the certified standard reference material, NIST SRM 1643d, and in well-water samples containing possible interfering ions. Application of the Student’s t-test showed no significant difference between the expected and obtained results of the NIST SRM standard analysis at the 95% confidence level. Values for six replicate determinations of As(III) in the well-water samples showed close agreement with values obtained by analyses using hydride generation atomic absorption. Recoveries were in the range of 95–105% at test for acceptable accuracy in the analysis of real samples.     

Alternative mechanisms for cyanide anion exchange with acetonitrile

Mechanisms for the recently observed exchange of cyanide anion in acetonitrile have been investigated by means of semi-empirical MNDO molecular orbital calculations. A prototropic type mechanism $\text{via}$ a cyclopropane intermediate is the most likely candidate. The previously proposed concerted migration is indicated to be the least favourable reaction pathway.