2 resultados para Cournot competition and welfare

em Nottingham eTheses


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This chapter will start by providing an overview of current knowledge about young people with learning disabilities who sexually abuse. Research cited will, unless otherwise indicated, be limited to UK studies since international variations in the definitions of both learning disability and sexual abuse make the use of a wider literature base problematic – particularly that relating to prevalence and incidence. It will then go on to report key findings from a recent study (Fyson et al, 2003; Fyson, 2005) which examined how special schools and statutory child protection and youth offending services in four English local authorities responded to sexually inappropriate or abusive behaviours exhibited by young people with learning disabilities. It will conclude by highlighting areas of current practice which give cause for concern, and suggest some pointers for future best practice.

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We investigate the Becker-Döring model of nucleation with three generalisations; an input of monomer, an input of inhibitor and finally, we allow the monomers to form two morphologies of cluster. We assume size-independent aggregation and fragmentation rates. Initially we consider the problem of constant monomer input and determine the steady-state solution approached in the large-time limit, and the manner in which it is approached. Secondly, in addition to a constant input of monomer we allow a constant input of inhibitor, which prevents clusters growing any larger and this removes them from the kinetics of the process; the inhibitor is consumed in the action of poisoning a cluster. We determine a critical ratio of poison to monomer input below which the cluster concentrations tend to a non-zero steady-state solution and the poison concentration tends to a finite value. Above the critical input ratio, the concentrations of all cluster sizes tend to zero and the poison concentration grows without limit. In both cases the solution in the large-time limit is determined. Finally we consider a model where monomers form two morphologies, but the inhibitor only acts on one morphology. Four cases are identified, depending on the relative poison to monomer input rates and the relative thermodynamic stability. In each case we determine the final cluster distribution and poison concentration. We find that poisoning the less stable cluster type can have a significant impact on the structure of the more stable cluster distribution; a counter-intuitive result. All results are shown to agree with numerical simulation.