Einstein metrics and the number of smooth structures on a four-manifold

We prove that for every natural number k there are simply connected topological four-manifolds which have at least k distinct smooth structures supporting Einstein metrics, and also have infinitely many distinct smooth structures not supporting Einstein metrics. Moreover, all these smooth structures become diffeomorphic to each other after connected sum with only one copy of the complex projective plane. We prove that manifolds with these properties cover a large geographical area.     

Trapped ion chain as a neural network: error resistant quantum computation

We demonstrate the possibility of realizing a neural network in a chain of trapped ions with induced long range interactions. Such models permit one to store information distributed over the whole system. The storage capacity of such a network, which depends on the phonon spectrum of the system, can be controlled by changing the external trapping potential. We analyze the implementation of error resistant universal quantum information processing in such systems.     

Isotope ratio monitoring gas chromatography/Mass spectrometry of D/H by high temperature conversion isotope ratio mass spectrometry

Of all the elements, hydrogen has the largest naturally occurring variations in the ratio of its stable isotopes (D/H). It is for this reason that there has been a strong desire to add hydrogen to the list of elements amenable to isotope ratio monitoring gas chromatography/mass spectrometry (irm-GC/MS). In irm-GC/MS the sample is entrained in helium as the carrier gas, which is also ionized and separated in the isotope ratio mass spectrometer (IRMS). Because of the low abundance of deuterium in nature, precise and accurate on-line monitoring of D/H ratios with an IRMS requires that low energy helium ions be kept out of the m/z 3 collector, which requires the use of an energy filter. A clean mass 3 (HD(+.)) signal which is independent of a large helium load in the electron impact ion source is essential in order to reach the sensitivity required for D/H analysis of capillary GC peaks. A new IRMS system, the DELTA(plus)XL(trade mark), has been designed for high precision, high accuracy measurements of transient signals of hydrogen gas. It incorporates a retardation lens integrated into the m/z 3 Faraday cup collector. Following GC separation, the hydrogen bound in organic compounds must be quantitatively converted into H(2) gas prior to analysis in the IRMS. Quantitative conversion is achieved by high temperature conversion (TC) at temperatures >1400 degrees C. Measurements of D/H ratios of individual organic compounds in complicated natural mixtures can now be made to a precision of 2 per thousand (delta notation) or, better, with typical sample amounts of approximately 200 ng per compound. Initial applications have focused on compounds of interest to petroleum research (biomarkers and natural gas components), food and flavor control (vanillin and ethanol), and metabolic studies (fatty acids and steroids). Copyright 1999 John Wiley & Sons, Ltd.     

Clustering of critical points in Lefschetz fibrations and the symplectic Szpiro inequality

We prove upper bounds for the number of critical points in semi- stable symplectic Lefschetz fibrations. We also obtain a new lower bound for the number of nonseparating vanishing cycles in Lefschetz pencils and reprove the known lower bounds for the commutator lengths of Dehn twists.

     

Symplectic Lefschetz fibrations of curves as gonal coverings

We show that after a finite base change every symplectic Lefschetz fibration ${f \colon X \rightarrow B}$ of genus g >  3 curves over a closed oriented surface becomes a finite covering of degree ${\frac{g}{2} + 1}$ or ${\frac{g}{2} + \frac{3}{2}}$ of a family of spheres over a Riemann surface, with a branch locus admitting complex algebraic curves as local models. In the case of fibers of genus 4, it is shown that after a 2:1 base change the family admits a trigonal covering to a symplectic ruled surface, with symplectic branch locus.     

Absence of Gradients and Nernstian Equilibrium Stripping (AGNES) for the determination of [Zn] in estuarine waters

Zinc (Zn) has been classified as a “Specific Pollutant” under Annex VIII of the EU Water Framework Directive by two thirds of the EU member states. As a result, the UK Environmental Quality Standard (EQS) for Transitional and Coastal (TrAC) Waters has been reduced from 612 nM to 121 nM total dissolved Zn. It is widely accepted that the free metal ion ([Zn²⁺]) is the most bioavailable fraction, but there are few techniques available to determine its concentration in these waters. In this work, Absence of Gradients and Nernstian Equilibrium Stripping (AGNES) has been applied, for the first time, to determine [Zn²⁺] in estuarine waters. The AGNES method had a mean RSD of ±18%, a (deposition time dependent) limit of detection of 0.73 nM and a [Zn²⁺] recovery of 112 ± 19% from a certified reference material (BCR-505; Estuarine Water). AGNES results for 13 estuarine samples (salinity 0.1–31.9) compared well (P = 0.02) with Competitive Ligand Exchange Cathodic Stripping Voltammetry (CLE-AdCSV) except for one sample. AGNES requires minimal sample manipulation, is unaffected by adsorption of interfering species at the electrode surface and allows direct determination of free zinc ion concentrations. Therefore AGNES results can be used in conjunction with ecotoxicological studies and speciation modelling to set and test compliance with water quality standards.     

The determination of trace metals in estuarine and coastal waters using a voltammetric in situ profiling system

This work presents the optimisation, validation and field deployment of a voltammetric in situ profiling (VIP) system for the simultaneous determinations of dynamic Cd(II), Cu(II) and Pb(II) in estuarine and coastal waters. Systematic studies in NaNO3 (as a supporting electrolyte) and seawater, indicated that variations in ionic strength, pH and dissolved oxygen did not affect the response of the instrument, whereas an Arrhenius type temperature response was observed. The VIP instrument allows the determination of 2-3 samples h(-1), and has a detection limit (defined as 3sigma) in seawater for Cd(II): 23 pM, Cu(II): 1.13 nM, and Pb(II): 23 pM. The VIP system accurately measured the total dissolved concentrations of Cd(II), Cu(II) and Pb(II) in two certified reference materials; SLRS-3, a river water, and SLEW-2, an estuarine water. Field evaluation of the instrumentation and analytical methods was achieved through a series of surveys in the Plym Estuary (Devon, UK), from which environmental data are presented.