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.     

Recent changes in A-level Mathematics: is the availability and uptake of mechanics declining yet more?

In the past 6 years changes have occurred in GCE A-levels. Inparticular, there have been several major changes in A-levelMathematics courses. As engineering students are usually requiredto have studied A-level Mathematics, or its equivalent, thesechanges have had an effect on their prior mathematical knowledge.Moreover, engineering students traditionally obtained a goodgrounding in mechanics as part of their A-level Mathematicsqualification. However, mechanics, which was once included inthe core syllabus, is now optional. This article investigatesthe current availability and uptake of mechanics modules withinA-level Mathematics courses in schools. Comparisons are drawnbetween these results and results of a survey of schools in2004 and surveys of first year engineering students conductedin 2004 and 2005. It is found that there is a decline in theavailability of mechanics modules and the uptake of more thanone mechanics module has also decreased. The implications ofthese findings for engineering educators are discussed.     

Nonvanishing cohomology and classes of Gorenstein rings

We give counterexamples to the following conjecture of Auslander: given a finitely generated module M over an Artin algebra Λ, there exists a positive integer n_M such that for all finitely generated Λ-modules N, if Ext_Λⁱ(M,N)=0 for all i?0, then Ext_Λⁱ(M,N)=0 for all i?n_M. Some of our examples moreover yield homologically defined classes of commutative local rings strictly between the class of local complete intersections and the class of local Gorenstein rings.     

Characteristics of radionuclide contamination of different zones of Semipalatinsk Nuclear Test Site “Opytnoe pole”

Data on the spatial distribution of radionuclides (²⁴¹Am, ²³⁹Pu, ¹³⁷Cs and ¹⁵²Eu) formed during nuclear explosions of different types near P2 SNTS test site are presented. Radionuclide contamination induced by the explosions varies in the concentrations of individual radionuclides, their proportions and species. Examination of the variations is a crucial task to plan remediation activities as well as those aimed at decrease of radiation risk for population and prevention of repeated contamination. Concentrations of ²⁴¹Am and ^239+240Pu that are the most toxic radionuclides in the area lie in hundred thousands of Bqkg^?1. The most contaminated areas are classified by the radionuclide concentration, ratio and form present in soil.     

Mathematical Model of a Social Insurance Fund with Random Expenditures for Social Programs (the Diffusion Approximation)

In the present work, the diffusion approximation of the capital is constructed for the mathematical model of a social insurance fund with random expenditures for social programs. The discontinuous hysteresis control of the fund capital is considered.     

Statistical hadronization and hadronic microcanonical ensemble I

We present a full treatment of the microcanonical ensemble of the ideal hadron-resonance gas starting from a quantum-mechanical formulation which is appropriate for the statistical model of hadronization. By using a suitable transition operator for hadronization we are able to recover the results of the statistical theory, particularly the expressions of the rates of different channels. Explicit formulae are obtained for the phase space volume or density of states of the ideal relativistic gas in quantum statistics as a cluster decomposition, generalizing previous ones in the literature. The problem of the computation of averages in the hadron gas microcanonical ensemble and the comparison with canonical ones will be the main subject of a forthcoming second paper.Received: 8 July 2003, Revised: 17 October 2003, Published online: 5 May 2004     

Diffraction of the Electromagnetic Wave on a Small Obstacle of Elliptic Form in a Layer

The problem on the diffraction of the electromagnetic plane wave on a small obstacle included in a layer is investigated. The obstacle is assumed to be an elliptic cylinder whose diameter and focal distance are small in comparison with the length of the incident wave. It is proved that the small obstacle radiates as a point source, and its amplitude is proportional to the area of the cross-section and the jumps of the dielectric and magnetic constants on the interfaces. Bibliography: 5 titles.     

Pyroelectric effect in lead-magnoniobate-based solid solutions

A coordinated study of the dielectric, electrostriction, and pyroelectric properties of the lead-magnoniobate-based ceramic solid solutions 0.9PbMg_1/3Nb_2/3O₃-0.1PbTiO₃ and 0.55PbMg_1/3Nb_2/3O₃-0.45PbSc_1/2Nb_1/2O₃ conducted at the relaxor transition temperatures is reported. Electromechanical coupling stimulated by the giant electrostriction effect is shown to play an essential part in the pyroelectric effect.