Twice Q-polynomial distance-regular graphs of diameter 4

It is known that a distance-regular graph with valency k at least three admits at most two Qpolynomial structures. We show that all distance-regular graphs with diameter four and valency at least three admitting two Q-polynomial structures are either dual bipartite or almost dual bipartite. By the work of Dickie(1995) this implies that any distance-regular graph with diameter d at least four and valency at least three admitting two Q-polynomial structures is, provided it is not a Hadamard graph, either the cube H(d, 2)with d even, the half cube 1/2H(2d + 1, 2), the folded cube?H(2d + 1, 2), or the dual polar graph on [2A2d-1(q)]with q 2 a prime power.     

Lagrangian and Eulerian models for simulating turbulent dispersion and coalescence of droplets within a spray

Lagrangian and Eulerian modelling approaches are compared for simulating turbulent dispersion and coalescence of droplets within a spray. Both models predict similar droplet dispersion rates and shifts in droplet size distribution due to coalescence within the spray, over a wide range of droplet and gas flows, and for sprays with different droplet-size distributions at the nozzle exit. The computer time required for simulating coalescence within a steady axisymmetric spray is of a similar order of magnitude regardless of which formulation, Eulerian or Lagrangian, is adopted. However, the Lagrangian formulation is more practical in terms of the range of applicability and ease of implementation.     

Investigation into the absolute stereochemistry of the marine sponge alkaloid pyrinodemin A

The absolute configuration of the marine sponge alkaloid pyrinodemin A is established by organic synthesis.     

Labile Interactions Defined in Crystalline Metal Complexes

The problems involved in identifying and quantifying labile interactions considered to influence complex compound structures are highlighted through the assessment of four different families of metal complexes for which extensive crystallographic data are available. Modification of the charge distribution within a ligand molecule as a result of coordination is one factor with a number of ramifications. A detailed analysis of evidence for both intra- and inter-molecular attractions in dimethylsulfoxide complexes of metal perchlorates is used to provide a basis for the consideration of weak interactions between complex ions involving forces including phenyl-group attractions, hydrogen bonding and cavity inclusion.     

Fields for which the projective schur subgroup is the whole Brauer group

LetBr(K) denote the Brauer group of a fieldK andPS(K) the projective Schur subgroup. 1. LetK be a finitely generated infinite field. ThenPS(K)=Br(K) if and only ifK is a global field. 2.|LetK be a finitely generated infinite field, and letK((t)) denote the field of formal power series int overK. ThenPS(K((t)))=Br(K((t))) if and only ifK=ℚ.     

Monte Carlo determinations of the beta dose rate to tooth enamel

The results of Monte Carlo simulations of the beta dose rate to enamel are presented. The dose rates are the most comprehensive to date, incorporating the beta spectrum from 21 different radionuclides, all internal conversion and Auger electrons, the majority of the bremsstrahlung radiation, effects due to radon loss in the uranium series, and variations in the moisture content of the sediment. Applications to a new dating technique in archaeology using electron spin resonance and beta-gradient isochrons are discussed.     

Bayesian Prediction Analysis for Growth Curve Model Using Noninformative Priors

We apply a Bayesian approach to the problem of prediction in an unbalanced growth curve model using noninformative priors. Due to the complexity of the model, no analytic forms of the predictive densities are available. We propose both approximations and a prediction-oriented Metropolis-Hastings sampling algorithm for two types of prediction, namely the prediction of future observations for a new subject and the prediction of future values for a partially observed subject. They are illustrated and compared through real data and simulation studies. Two of the approximations compare favorably with the approximation in Fearn (1975, Biometrika, 62, 89–100) and are very comparable to the more accurate Rao-Blackwellization from Metropolis-Hastings sampling algorithm.     

OR and the challenge to improve the NHS: modelling for insight and improvement in in-patient flows

This paper considers efforts to improve in-patient flows, a particularly urgent issue in the National Health Service (NHS). The context is described and related to reasons why OR has been making relatively little contribution. The paper argues that large complex models may often be unnecessary and even get in the way of providing clear insight and guidance for problem owners. The importance of understanding the generic working of systems to lead to improvement, and the limitations of simply describing them, is stressed. It is demonstrated that some very simple models can be of significant practical value in understanding and managing complex systems, changing mindsets and driving collection and use of operationally valuable data. Recommendations for more effective engagement with the NHS are offered.