A Simple Geometric Representative for μ\mu of a Point

For $SU(2)$ (or $SO(3)$) Donaldson theory on a 4-manifold $X$, we construct a simple geometric representative for $\mu$ of a point. Let $p$ be a generic point in $X$. Then the set $\{ [A] | F_A^-(p)$ is reducible $\}$, with coefficient -1/4 and appropriate orientation, is our desired geometric representative.Comment: Updated 2018 to published version. 8 pages, AmS-TeX, no figure

The relationship between eddy-transport and second-order closure models for stratified media and for vortices

The question is considered of how complex a model should be used for the calculation of turbulent shear flows. At the present time there are models varying in complexity from very simple eddy-transport models to models in which all the equations for the nonzero second-order correlations are solved simultaneously with the equations for the mean variables. A discussion is presented of the relationship between these two models of turbulent shear flow. Two types of motion are discussed: first, turbulent shear flow in a stratified medium and, second, the motion in a turbulent line vortex. These two cases are instructive because in the first example eddy-transport methods have proven reasonably effective, whereas in the second, they have led to erroneous conclusions. It is not generally appreciated that the simplest form of eddy-transport theory can be derived from second-order closure models of turbulent flow by a suitably limiting process. This limiting process and the suitability of eddy-transport modeling for stratified media and line vortices are discussed

Use of programme budgeting and marginal analysis to set priorities for local NHS dental services: learning from the north east of England

Background - Priority setting is necessary where competing demands exceed the finite resources available. The aim of the study was to develop and test a prioritization framework based upon programme budgeting and marginal analysis (PBMA) as a tool to assist National Health Service (NHS) commissioners in their management of resources for local NHS dental services. Methods - Twenty-seven stakeholders (5 dentists, 8 commissioners and 14 patients) participated in a case-study based in a former NHS commissioning organization in the north of England. Stakeholders modified local decision-making criteria and applied them to a number of different scenarios. Results - The majority of financial resources for NHS dental services in the commissioning organization studied were allocated to primary care dental practitioners’ contracts in perpetuity, potentially constraining commissioners’ abilities to shift resources. Compiling the programme budget was successful, but organizational flux and difficulties engaging local NHS commissioners significantly impacted upon the marginal analysis phase. Conclusions - NHS dental practitioners’ contracts resemble budget-silos which do not facilitate local resource reallocation. ‘Context-specific’ factors significantly challenged the successful implementation and impact of PBMA. A local PBMA champion embedded within commissioning organizations should be considered. Participants found visual depiction of the cost-value ratio helpful during their initial priority setting deliberations

Development of a second order closure model for computation of turbulent diffusion flames

A typical eddy box model for the second-order closure of turbulent, multispecies, reacting flows developed. The model structure was quite general and was valid for an arbitrary number of species. For the case of a reaction involving three species, the nine model parameters were determined from equations for nine independent first- and second-order correlations. The model enabled calculation of any higher-order correlation involving mass fractions, temperatures, and reaction rates in terms of first- and second-order correlations. Model predictions for the reaction rate were in very good agreement with exact solutions of the reaction rate equations for a number of assumed flow distributions

In Defense of Welfarism

This paper characterizes welfarist social evaluation in a multi-profile setting where, in addition to multiple utility profiles, it is assumed that there are several profiles of non-welfare information. We prove new versions of the welfarism theorems in this alternative framework, and we illustrate that a very plausible and weak anonymity property is sufficient to generate anonymous social-evaluation orderings.Welfarism, multiple-profile social choice

Computing dispersal of atmospheric pollutants near airports

Computing dispersal of atmospheric pollutants near airports by use of mean wind and temperature profile

An invariant second-order closure model of the compressible turbulent boundary layer on a flat plate

The development of an invariant model designed expressly for the computation of shear flows is discussed. The model for incompressible layers seeks a second-order closure of the equations for the mean and fluctuating fields. The development of a method for computing the behavior of shear layers in compressible forces is described. The complexity of the analysis is restrained by limiting the consideration to a flat plate boundary layer where the mean pressure can be taken to be constant

Central precocious puberty in a 3 year-old girl with Phenylketonuria: a rare association?

Background Central precocious puberty (CPP) and phenylketonuria (PKU) are two rare conditions, the latter being the rarer. To date, only one case featuring both these conditions has been reported, and hyperphenylalaninemia was assumed triggering CPP. Case presentation We present a 3.2 years old girl referred with a 12 months history of breast and pubic hair development, and vaginal discharge. Hyperphenylalaninemia had been identified by newborn screening and PKU subsequently confirmed by plasma amino acid and genetic analysis. Early dietary control of plasma phenylalanine had been excellent afterwards, resulting in phenylalanine concentrations consistently within the recommended range. Clinical scenario, hormonal assessment and imaging were in keeping with true idiopathic central precocious puberty. Treatment with long lasting gonadotropin-releasing hormone analogue led to regression of secondary sexual characteristics. Conclusion We describe for the first time CPP in a girl affected with PKU but with persistently well controlled blood phenylalanine concentrations. This finding is in contrast to a previous report which suggested persistently high phenylalaninemia levels as potential trigger for CPP in PKU patients. Our report, together with the lack of evidence in published cohort studies of children with PKU, strongly suggests this rare association is coincidental and independent of the presence of severe hyperphenylalaninemia.</p

Constitutive Models for Tumour Classification

The aim of this paper is to formulate new mathematical models that will be able to differentiate not only between normal and abnormal tissues, but, more importantly, between benign and malignant tumours. We present preliminary results of a tri-phasic model and numerical simulations of the effect of cellular adhesion forces on the mechanical properties of biological tissues. We pursued the following three approaches: (i) the simulation of the time-harmonic linear elastic models to examine coarse scale effects and adhesion properties, (ii) the investigation of a tri-phasic model, with the intent of upscaling this model to determine effects of electro-mechanical coupling between cells, and (iii) the upscaling of a simple cell model as a framework for studying interface conditions at malignant cells. Each of these approaches has opened exciting new directions of research that we plan to study in the future

The pale evidence for treatment of iron-deficiency anaemia in older people

Funding The authors have received funding to carry out a pilot RCT on management of IDA in older people from the Chief Scientist Office, Scotland.Peer reviewedPostprin