Assessment of trace metal binding kinetics in the resin phase of diffusive gradients in thin films

The dynamic technique of diffusive gradients in thin films (DGT), that measures metal speciation in situ, has found wide environmental application. Simple interpretation of the metal accumulation in terms of a solution concentration has assumed that trace metals do not penetrate beyond the surface of the binding layer, but penetration, although theoretically discussed has not yet been directly measured. Multiple binding layers were used to enable analysis of different depths of a DGT binding phase (Chelex-100 or iminodiacetate resins). In simple metal solution (no ligand) at pH 7, metal penetration to the back layer was low and similar for all metals. However, at lower pH up to 42% of an individual metal accumulated in the back resin layer. This was most noticeable for Mn at pH 4 and 5, but Cd and Co were also affected at pH 4. These results were consistent with rate limited binding, particularly for Mn. A kinetic model successfully fitted the data and allowed derivation of a binding rate constant and the mean distance that metals penetrate into a resin gel (λ_M). Only for Mn, Co and Cd were experimentally derived λ_M values greater than the diameter of a Chelex-100 resin bead. For most situations, then, the penetration into the binding layer is negligible and binding of trace metal ions can be regarded as instantaneous, validating the simple use and interpretation of DGT. For weakly binding metals at low pH the slower binding allows penetration, which may affect the DGT measurement.     

Lability criteria in diffusive gradients in thin films

The penetration of metal complexes into the resin layer of DGT (diffusive gradients in thin films) devices greatly influences the measured metal accumulation, unless the complexes are either totally inert or perfectly labile. Lability criteria to predict the contribution of complexes in DGT measurements are reported. The key role of the resin thickness is highlighted. For complexes that are partially labile to the DGT measurement, their dissociation inside the resin domain is the main source of metal accumulation. This phenomenon explains the practical independence of the lability degree of a complex in a DGT device with respect to the ligand concentration. Transient DGT regimes, reflecting the times required to replenish the gel and resin domains up to the steady-state profile of the complex, are also examined. Low lability complexes (lability degree between 0.1 and 0.2) exhibit the longest transient regimes and therefore require longer deployment times to ensure accurate DGT measurements.     

Quasi-periodic continued fractions

Using recent work of Adamczewski and Bugeaud, we are able to relax the conditions given by Baker to establish transcendence in the class of quasi-periodic continued fractions.     

A simple model for a two-stage chemical reaction with diffusion

We analyse the evolution of a two-stage chemical reaction betweentwo neighbouring plumes of reactants. Under the assumption thatthe plumes are approximately Gaussian we derive a system ofordinary differential equations for the total amount, the centroidand the variance of each reactant. We compare the solution ofthese equations with full numerical simulation of the reaction.Excellent agreement is obtained, with solution of the near-Gaussianmodel requiring considerably less computational effort thanthe full simulations. Of key importance is the yield of thereaction, and we discuss this feature in particular.     

Propagator theory of quantum-wire transmission

In the tight-binding formalism, the Green function (GF) is cast in the site representation, and can be interpreted as a propagator of information from one site to another. A general propagator theory is developed that encompasses the present GF treatments of electron transport in molecular wires and the scanning tunnelling and ballistic electron emission microscopes. Finally, the question of a multi-contact quantum circuit is addressed.     

An examination of HMM‐based investment strategies for asset allocation

We develop and analyse investment strategies relying on hidden Markov model approaches. In particular, we use filtering techniques to aid an investor in his decision to allocate all of his investment fund to either growth or value stocks at a given time. As this allows the investor to switch between growth and value stocks, we call this first strategy a switching investment strategy. This switching strategy is compared with the strategies of purely investing in growth or value stocks by tracking the quarterly terminal wealth of a hypothetical portfolio for each strategy. Using the data sets on Russell 3000 growth index and Russell 3000 value index compiled by Russell Investment Services for the period 1995–2008, we find that the overall risk‐adjusted performance of the switching strategy is better than that of solely investing in either one of the indices. We also consider a second strategy referred to as a mixed investment strategy which enables the investor to allocate an optimal proportion of his investment between growth and value stocks given a level of risk aversion. Numerical demonstrations are provided using the same data sets on Russell 3000 growth and value indices. The switching investment strategy yields the best or second best Sharpe ratio as compared with those obtained from the pure index strategies and mixed strategy in 14 intervals. The performance of the mixed investment strategy under the HMM setting is also compared with that of the classical mean–variance approach. To make the comparison valid, we choose the same level of risk aversion for each set‐up. Our findings show that the mixed investment strategy within the HMM framework gives higher Sharpe ratios in 5 intervals of the time series than that given by the standard mean–variance approach. The calculated weights through time from the strategy incorporating the HMM set‐up are more stable. A simulation analysis further shows a higher performance stability of the HMM strategies compared with the pure strategies and the mean–variance strategy. Copyright © 2009 John Wiley & Sons, Ltd.     

Cartesian Dynamics of Simple Molecules X Linear Quadratomics (C∞v Symmetry)

The vibrations of linear ABC₂ type molecules with C_∞V point group are analysed in terms of Cartesian co-ordinates. Algebraic expressions for the three stretching and two bending normal mode frequencies are derived in terms of longitudinal and transverse force constants, atomic masses and bond lengths. Values of non-valence interaction parameters are transferred from A₂B₂ (D_∞h) molecules, and values of the principal force constants are adjusted to reproduce the observed frequencies for a number of asymmetric halogen derivatives of acetylene. Normal mode frequencies of various isotopic species are also calculated. The nature of the computed eigenvectors for these molecules is briefly discussed. It is found that the carbon-carbon and carbon-hydrogen valence interactions remain approximately constant for these molecules, whereas the carbon-halogen bonds show a weakening trend with increasing halogen mass.