Maximum curves and isolated points of entire functions

Given M(r; f) =maxjzj=r (jf(z)j) , curves belonging to the set of points M = fz : jf(z)j = M(jzj; f)g were de�ned by Hardy to be maximum curves. Clunie asked the question as to whether the set M could also contain isolated points. This paper shows that maximum curves consist of analytic arcs and determines a necessary condition for such curves to intersect. Given two entire functions f1(z) and f2(z), if the maximum curve of f1(z) is the real axis, conditions are found so that the real axis is also a maximum curve for the product function f1(z)f2(z). By means of these results an entire function of in�nite order is constructed for which the set M has an in�nite number of isolated points. A polynomial is also constructed with an isolated point.

Finance for water and sanitation as a public service

Drawing on empirical evidence gathered through the PSIRU database, this contribution aims at addressing the potential of public finance to enhance the provision of water supply and sanitation as a public service. It highlights the problems associated with (and the disappointing results obtained from) resort to Private Sector Participation and private finance, both historically and in the last 15-20 years, in developed and developing countries. It also addresses the advantages of using public finance as a more cost-effective and equitable instrument to achieve developmental objectives such as the expansion of service coverage and development of water and sanitation infrastructure. The potential of public operations in maximising developmental impact from the social, economic and environmental points of view is then explored referring to specific examples from a variety of countries and regions. These include the in-house restructuring of public operations to enhance transparency, accountability and effectiveness, as well as the use of Public-Public Partnerships (PUPs) to build capacity. Attention is devoted to the specific financial requirements of expanding sewerage services at global level to achieve MDGs or broader developmental goals. These requirements are revisited in light of a regional breakdown of coverage gaps, available resources and development aid flows. These findings challenge the established view among international and bilateral agencies that expanding sewerage services in developing countries is excessively costly and should be abandoned as a priority because unaffordable. This contribution draws on a number of PSIRU Reports, and particularly the following. - http://www.psiru.org/reports/2008-03-W-sewers.pdf - http://boell-latinoamerica.org/download_es/agua08_privatizacion_LA_2007.pdf - http://boell-latinoamerica.org/download_es/agua08_agua_un_servicio_publico.pdf - http://www.psiru.org/reports/2006-03-W-investment.pdf All PSIRU Reports are accessible at http://www.psiru.org/publicationsindex.asp.

Analysing the evacuation procedures employed on a Thames passenger boat using the maritimeEXODUS evacuation model

On the 19 June 2001, a Thames passenger/tour boat underwent several evacuation trials. This work was conducted in order to collect data for the validation of marine-based computer models. The trials involved 111 participants who were distributed throughout the vessel. The boat had two decks and two points of exit from the lower deck placed on either side of the craft, forward and aft. The boat had a twin set of staircases towards the rear of the craft, just forward of the rear exits. maritimeEXODUS was used to simulate the full-scale evacuation trials conducted. The simulation times generated were compared against the original results and categorised according to the exit point availability. The predictions closely approximate the original results, differing by an average of 6.6% across the comparisons, with numerous qualitative similarities between the predictions and experimental results. The maritimeEXODUS evacuation model was then used to examine the evacuation procedure currently employed on the vessel. This was found to have potential to produce long evacuation times. maritimeEXODUS was used to suggest modifications to the mustering procedures. These theoretical results suggest that it is possible to significantly reduce evacuation times.

Journal citation among heterodox economists 1995-2007: Dynamics of community emergence

Purpose – This study aims to investigate the pattern among 17 heterodox economic journals over a prolonged period to provide evidence about the social dynamics among the group of researchers who publish in them and the extent to which they hold or develop a collective identity as heterodox economists. Design/methodology/approach – Traditional approaches to citation analysis are extended by the use of techniques from social network analysis. In addition to citation counts, measures of network position and clique membership are used to identify key journals and turning points in a longitudinal analysis. Findings – Important shifts in the nature of citation within the network of journals are identified in the 1998-2001 period and evidence is found of the emergence of a collective identity. Research limitations/implications – The methods prove a valuable extension of citation analysis and also focus greater consideration on the social relationships that citations represent. They are well suited to addressing the principal limitation of the study, its restriction to journals within the defined community rather than journals in general. Originality/value – This extends traditional approaches to citation analysis, provides an important new technique in identifying emergent collective identities and provides insight into the history and nature of the heterodox economic community.