Landau levels and Riemann zeros

The number N(E) of complex zeros of the Riemann zeta function with positive imaginary part less than E is the sum of a "smooth" function N[over ](E) and a "fluctuation." Berry and Keating have shown that the asymptotic expansion of N[over ](E) counts states of positive energy less than E in a "regularized" semiclassical model with classical Hamiltonian H=xp. For a different regularization, Connes has shown that it counts states "missing" from a continuum. Here we show how the "absorption spectrum" model of Connes emerges as the lowest Landau level limit of a specific quantum-mechanical model for a charged particle on a planar surface in an electric potential and uniform magnetic field. We suggest a role for the higher Landau levels in the fluctuation part of N(E).     

SusChem – Berlin points to future priorities

The European Technology Platform (ETP) for Sustainable Chemistry (SusChem) is of key importance to all involved in molecular science in Europe. SusChem is addressing head‐on the challenge of developing sustainable technologies, based on chemistry, chemical engineering and industrial biotechnology that will deliver future prosperity and health for everyone.     

An Approach to Bus-Crew Roster Design in London Regional Transport

An outline is given of the bus-crew rostering problem in London Regional Transport. A method is developed for producing a skeleton roster, this skeleton being composed of standard units which contain fixed patterns of working. The aim is to determine the number of units, and then position them in a suitable sequence so that various operating objectives and constraints are met. A primary objective is to produce an even spread of weekend working through the roster. A method for producing the roster skeleton is described which formed the basis of an experimental approach to the automatic production of detailed crew rosters. Trials indicated that the procedure was capable of quickly producing rosters of sufficiently high quality to justify further development.     

Transmission Mössbauer Analysis of Nanophased Oxides Formed on High Strength Steels

Hyperfine Interactions - Nanophased oxides found in the corrosion coatings of atmospherically weathered steels have properties that are scientifically significant and industrially important....     

Hydrolysis kinetics of photoexcited 6-methoxyquinoline in aqueous acetonitrile solutions

6-Methoxyquinoline undergoes pseudo-first-order hydrolysis and its conjugate acid, second-order proton abstraction by hydroxide ion, in the lowest excited singlet state. The proton transfer kinetics in water containing acetonitrile up to a mole fraction of about 0.1 have been evaluated as a function of acetonitrile concentration. At mole fractions above 0.13 of acetonitrile, proton transfer does not occur. At mole fractions below 0.1 steady-state and pulsed-source fluorimetries show the rate constant for hydrolysis to decrease exponentially with the mole fraction of acetonitrile. This is believed to be due to penetration of the aqueous solvent cage of the 6-methoxyquinoline by acetonitrile rather than to specific solvation by the organic cosolvent. The rate of neutralization of the conjugate acid by hydroxide ion is found to vary only slightly and depends on the bulk dielectric properties of the solvent.     

A novel method for the synthesis of 6,7-unsubstituted pyrrolo[3,2-d]pyrimidines

The synthesis of 2,4-dimethoxypyrrolo[3,2-$\text{d}$]pyrimidine ($\text{4}$) is described. This facile, 3-step synthesis involves the bromination of 2,4-dimethoxy-6-methyl-5-nitropyrimidine ($\text{1}$), and the subsequent conversion of compound $\text{1}$ into compound $\text{4}$.