Poincaré Semigroup Symmetry as an Emergent Property of Unstable Systems

The notion that elementary systems correspond to irreducible representations of the Poincaré group is the starting point for this paper, which then goes on to discuss how a semigroup for the time evolution of unstable states and resonances could emerge from the underlying Poincaré symmetry. Important tools in this analysis are the Clebsch-Gordan coefficients for the Poincaré group.     

Large gaps between the zeros of the Riemann zeta function

We show that the generalized Riemann hypothesis implies that there are infinitely many consecutive zeros of the zeta function whose spacing is three times larger than the average spacing. This is deduced from the calculation of the second moment of the Riemann zeta function multiplied by a Dirichlet polynomial averaged over the zeros of the zeta function.     

Extreme values of {zeta}'({rho})

Assuming the Riemann hypothesis, we exhibit large and smallvalues of the derivative of the zeta function evaluated at thenon-trivial zeros of the zeta function. These results are provedby applying Soundararajan's resonance method.     

Enantioselective organocatalytic α-sulfenylation of substituted diketopiperazines

The asymmetric organocatalytic α-sulfenylation of substituted piperazine-2,5-diones is reported, with cinchona alkaloids as chiral Lewis bases and electrophilic sulfur transfer reagents. Catalyst loadings, the type of sulfur transfer reagent, temperature, and solvent were investigated in order to optimize the reaction conditions. The effects of ring substitution and the type of catalyst on the yield and enantioselectivity of the reaction are reported.     

Green Approaches to Field Nitrate Analysis: An Electroanalytical Perspective

The different approaches that have been taken in the development of analytical methods for the determination of nitrate within the field are reviewed. The emphasis has been placed on providing a critical appraisal of the chemistry that underpins current commercial systems and the need to remove the dependence on heavy metal and concentrated acid components. The search for more environmentally acceptable and user friendly systems has long been pursued and the present communication seeks to explore the recent development in portable testing technologies and how they might evolve in the future. In particular, the role of electrochemical techniques in the latter are investigated and their potential application compared and contrasted with the more traditional wet chemical detection strategies.     

An Automated Approach to Luminescence Lifetime and Intensity Titrations

An apparatus is described for the automated collection of luminescence emission decay curves over a wide range of analyte concentrations. The decay curves allow for determination of the excited-state lifetime or calculated steady-state intensity of a luminophore as a function of the analyte concentration. The data presented here demonstrate the use of the apparatus for pH titrations.     

Vinylferrocene homopolymer and copolymers: an electrochemical comparison.

Poly(vinylferrocene) (pVFc) homopolymer was synthesized by free radical polymerization, along with a series of pVFc-based copolymers containing either styrene, vinylanthracene or methylmethacrylate. This report details the electrochemical experiments conducted to examine the stability of the various pVFc based polymers, which is shown to be critically dependent on the extent of copolymerization. A trend was found that when the concentration of co-monomer was decreased, electrochemical stability was enhanced. Furthermore incorporation of a second monomer into the polymer chain produced a profound effect on the scan rate behaviour of the vinylferrocene moiety. As the concentration of co-monomer was decreased, the behaviour tended towards that of a diffusion controlled process. These results are of vital significance for the development of pVFc-based electrochemical sensors.     

Characterization of the network properties of poly(ethylene glycol)–acrylate hydrogels prepared by variations in the ethanol–water solvent composition during crosslinking copolymerization

The characteristics of poly(ethylene glycol) (PEG)–acrylate hydrogel networks were investigated as a function of the ethanol–water solvent composition during free‐radical crosslinking copolymerization. Macromonomer (88% ω‐methoxy‐PEG–acrylate and 10% ω‐phenoxy‐PEG–acrylate) and crosslinker (2% PEG–diacrylate) concentrations were kept constant. As the copolymerization progressed, the polymer solution in 100% ethanol became increasingly turbid, indicating the development of a heterogeneous network structure. In 100% water, however, the initially turbid polymer solution became increasingly transparent as the crosslinking copolymerization progressed. All the gels were optically clear upon equilibration in water. Kinetic studies, with attenuated total reflectance‐infrared, showed a long induction period, along with a lowered reaction rate, in 100% ethanol, and a decrease in conversion with an increase in ethanol content. These results agree with the UV analysis of the sol fractions, which indicated an increase in the amounts of unreacted PEG–acrylates with an increase in the ethanol content. The gels which were formed with a high ethanol concentration exhibited lower Young's modulus and higher swelling ability, suggesting that the network structure was significantly affected by the solvent composition during free‐radical crosslinking copolymerization. From the stress–strain and swelling experiments, the Flory–Huggins interaction parameter was evaluated. The creep characteristics of the hydrogels were modeled with two Kelvin elements. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 2677–2684, 2002