p-adic Proofs of congruences for the Bernoulli numbers

Many of the classical theorems for the Bernoulli numbers, particularly those congruences needed in the study of irregular primes, follow easily from the existence of the (p ? 1)st roots of unity in the ring of p-adic integers. Proofs are given for the von Staudt-Clausen theorem, the theorem of J. C. Adams, the Friedmann-Tamarkine congruence, a theorem of Vandiver, special cases of the congruences of Voronoi, Kummer, and Carlitz, and the congruences of E. Lehmer.     

The initiation,evaluation and selection of operational research projects

This paper discusses the problems involved in conducting successful Operational Research within a large organisation and suggests ways of overcoming them. It describes ways in which Operational Research projects arise, methods of assessing their relative merits, and methods used by the authors to obtain a suitable portfolio of projects. It is argued that an Operational Research Group should apply to its own project planning the scientific approach that it advocates for others.     

Kinetics of the solvolysis of chloropentacyanocobaltate (III) ions in mixtures of ethane-1,2-diol or ethanonitrile with water

The kinetics of the solvolysis of [Co(CN)₅Cl]^3? ions have been investigated in mixtures formed by the addition of ethane-1,2-diol or ethanonitrile to water where the physical properties indicate little enhancement of structure in water-rich conditions. The effect on the kinetics of this solvolysis of this lack of structural change in the solvent shows in the linearity of the variation of log (rate constant) with the reciprocal of the dielectric constant for the addition of ethane-1,2-diol to water and the absence of any prominent extrema in the enthalpy or entropy of activation using either co-solvent. However, the effect of changes in solvation on the solvolysis with these two co-solvents appears to operate in a similar manner to the effects found when the hydrophobic co-solvent propan-2-ol is added to water. The application of a free energy cycle to the process of the initial state going to the transition state for this dissociative process suggests that, with both co-solvents, [Co(CN)₅]^2? in the transition state is more stable than [Co(CN)₅Cl]^3? in the initial state. © John Wiley & Sons, Inc.     

A journey through quality control

The Euroanalysis VII conference in Vienna included a two-day session: Quality Assurance in Analytical Chemistry. The contributions comprised 15 lectures devoted to: intra-laboratory quality measures, inter-laboratory control, formal aspects and accreditation and implementation. The paper presents an overview of the main items developed by the contributors.A survey on the session on Quality Assurance in Analytical Chemistry of Euroanalysis VIIThe authors thank the organizers of EUROANALYSIS VII and in particular Dr. B. Griepink and Dr. E. Maier of the Community Bureau of Reference (BCR) of the CEC for their support and considerable contributions.     

Pathways to Nanocrystalline III-V (13–15) Compound Semiconductors

Discussed in this review are various solution-phase methodologies and specific chemical reactions involving molecular precursors and/or species derived there-from which have been utilized to synthesize various binary and ternary nanocrystalline III-V (13–15) compound semiconductors.     

Multiplicities of secondary hadrons produced in vp and vp charged current interactions

In an experiment with the hydrogen bubble chamber BEBC at CERN multiplicities of hadrons produced in νp and $\text{v}\text{p}$ interactions have been investigated. Results are presented on the multiplicities of charged hadrons and neutral pions, forward and backward multiplicities of charged hadrons and correlations between forward and backward multiplicities. Comparisons are made with hadronic reactions and e⁺e^? annihilation. In the framework of the quark-parton model the data imply similar charged multiplicities for the fragments of a u- and a d-quark, and a larger multiplicities for the fragments of a uu- than for a ud-diquark. The correlation data suggest independent fragmentation of the quark and diquark for hadronic masses above ～ 7 GeV and local charge compensation within an event.