Stark's conjecture over complex cubic number fields

Systematic computation of Stark units over nontotally real base fields is carried out for the first time. Since the information provided by Stark's conjecture is significantly less in this situation than the information provided over totally real base fields, new techniques are required. Precomputing Stark units in relative quadratic extensions (where the conjecture is already known to hold) and coupling this information with the Fincke-Pohst algorithm applied to certain quadratic forms leads to a significant reduction in search time for finding Stark units in larger extensions (where the conjecture is still unproven). Stark's conjecture is verified in each case for these Stark units in larger extensions and explicit generating polynomials for abelian extensions over complex cubic base fields, including Hilbert class fields, are obtained from the minimal polynomials of these new Stark units.

     

Constructing orthogonal pandiagonal Latin squares and panmagic squares from modular n‐queens solutions

In this article, we show how to construct pairs of orthogonal pandiagonal Latin squares and panmagic squares from certain types of modular n‐queens solutions. We prove that when these modular n‐queens solutions are symmetric, the panmagic squares thus constructed will be associative, where for an n × n associative magic square A = (a_ij), for all i and j it holds that a_ij + an?i?1,n?j?1 = c for a fixed c. We further show how to construct orthogonal Latin squares whose modular difference diagonals are Latin from any modular n‐queens solution. As well, we analyze constructing orthogonal pandiagonal Latin squares from particular classes of non‐linear modular n‐queens solutions. These pandiagonal Latin squares are not row cyclic, giving a partial solution to a problem of Hedayat. © 2007 Wiley Periodicals, Inc. J Combin Designs 15: 221–234, 2007     

Modelling for the planning and management of bed capacities in hospitals

The internal dynamics of a hospital represent a complex non-linear structure. Planning and management of bed capacities must be evaluated within an environment of uncertainty, variability and limited resources. A common approach is to plan and manage capacities based on simple deterministic spreadsheet calculations. This paper demonstrates that these calculations typically do not provide the appropriate information and result in underestimating true bed requirements. More sophisticated, flexible and necessarily detailed capacity models are needed. The development and use of such a simulation model is presented in this paper. The modelling work, in conjunction with a major UK NHS Trust, considers various types of patient flows, at the individual patient level, and resulting bed needs over time. The consequence of changes in capacity planning policies and management of existing capacities can be readily examined. The work has highlighted the need for evaluating hospital bed capacities in light of both bed occupancies and refused admission rates. The relationship between occupancy and refusals is complex and often overlooked by hospital managers.     

Immobilization of catalase on membranes of poly(ethylene)-g-co-acrylic acid and poly(tetrafluoroethylene)-g-co-acrylic acid and their application in hydrogen peroxide electrochemical sensors

The immobilization of catalase on grafted membranes of poly(ethylene)-g-co-acrylic acid and poly(tetrafluoroethylene)-g-co-acrylic acid and their application in hydrogen peroxide electrochemical sensors is described. The introduction of carboxylic acid groups onto a hydrophobic support provides a good environment for subsequent enzyme immobilization. This single membrane, hydrogen peroxide sensor showed significant improvement with respect to the double membrane versions. The response is very rapid, the linear range being from 10 μM up to 6 mM, with a detection limit of 4.7 μM, and a lifetime of more than 4 months.     

Determination of iphosphamide and seven metabolites in blood plasma,as stable trifluoroacetyl derivatives,by electron capture chemical ionization GC-MS

A method is described for the determination of the antitumor agent iphosphamide and seven of its metabolites in the plasma of cancer patients by multiple ion monitoring (MIM) GC-MS, mainly using the electron capture chemical ionization mode, of stable methyl and/or trifluoroacetyl derivatives. The metabolites determined were 2- and 3-dechloroethyliphosphamide, 4-ketoiphosphamide, carboxyiphosphamide, iphosphamide mustard, and two previously undetected metabolites, chloroethylamine and 1,3-oxazolidine-2-one. The isolation of the acidic and neutral metabolites was performed by solid phase extraction on to C₁₈ adsorbent at pH 4. The weakly acidic iphosphamide mustard, isolated under these conditions with a yield of ca 50%, was measured as a stable methyltrifluoroacetyl derivative, in contrast to the corresponding phosphoramide mustard of the isomer cyclophosphamide which decomposes during derivatization. Chloroethylamine and 1,3-oxazolidine-2-one were isolated with high yield by liquid extraction with ethyl acetate at pH 10. Selective measurement of several metabolite derivatives with similar retention times was performed by multiple ion monitoring MS of specific ion masses, using a methyl phenyl siloxane capillary column previously employed in the study of cyclophosphamide metabolites. Quantitation of metabolites in patient plasma samples could be performed in the concentration range 3 ng to 20 μg per ml of original plasma.     

Mother-to-child transmission of HIV: a simulation-based approach for the evaluation of intervention strategies

Mother-to-child transmission (MTCT) of HIV is the most significant source of HIV infection in children below the age of 15 years. In 2000 alone, about 600 000 new infections occurred, the vast majority from mothers living in developing countries who were not aware of their HIV-positive status. To date, at least 4.3 million children have died from AIDS. In this paper, we discuss the development of an operational model that can be used to evaluate intervention options for the prevention of MTCT of HIV. The problem was approached by defining suitable pregnancy risk groups, prevention options and the required model outputs to evaluate different intervention strategies. The method chosen to approach the problem was a discrete-event, three-phase simulation, built in Visual Basic, with a stochastic semi-Markov structure. The developed model takes individual pregnant women through each stage of their pregnancy, labour and birth. Different intervention strategies may be modelled at any time, including short-course antiretroviral drugs and cessation of breastfeeding. The model is demonstrated with data from Botswana, which has one of the highest HIV-infection rates in the world.     

On the challenges of healthcare modelling and a proposed project life cycle for successful implementation

OR methods and tools are being increasingly applied within the health services domain to support objective decision-making for the effective and efficient provision of resources. Healthcare modelling, however, is beset with many challenges and this paper examines a number of issues that define the primary challenges faced by the modeller in this field. It is fair to say that their resolution determines the likely success or failure of healthcare modelling in general. Working with a number of participating health service organizations, a proposed framework towards successful implementation has evolved and is presented in this paper