An easy proof of Jensen's theorem on the uniqueness of infinity harmonic functions

We present a new, easy, and elementary proof of Jensen's Theorem on the uniqueness of infinity harmonic functions. The idea is to pass to a finite difference equation by taking maximums and minimums over small balls.Comment: 4 pages; comments added, proof simplifie

Development and selection of operational management strategies to achieve policy objectives

Since the reform of the EU Common Fisheries Policy in 2002, effort has been devoted to addressing the governance, scientific, social and economic issues required to introduce an ecosystem approach to fisheries management (EAFM) in Europe. Fisheries management needs to support the three pillars of sustainability (ecological, social and economic) and Fisheries Ecosystem Plans (FEPs) have been developed as a tool to assist managers considering the ecological, social and economic implications of their decision. Building upon previous studies (e.g. the FP5-funded European Fisheries Ecosystem Plan project), the core concept of the Making the European Fisheries Ecosystem Plan Operational (MEFEPO) project is to deliver operational frameworks (FEPs) for three regional seas. The project focus is on how best to make current institutional frameworks responsive to an EAFM at regional and pan-European levels in accordance with the principles of good governance. The regional seas selected for the project are the North Sea (NS), North Western Waters (NWW) and South Western Waters (SWW) RAC regions. The aim of this work package (WP5) was to develop operational objectives to achieve the ecological objectives identified for the 3 regional seas in WP2. This report describes the development and implementation of a transparent and formal process that should lead to identification of the “best” operational management strategies for an EAFM, based on sound scientific information and stakeholder involvement (e.g. regional industry groups, citizen groups, managers and other interest groups)

Implementing Groundness Analysis with Definite Boolean Functions

The domain of definite Boolean functions, Def, can be used to express the groundness of, and trace grounding dependencies between, program variables in (constraint) logic programs. In this paper, previously unexploited computational properties of Def are utilised to develop an efficient and succinct groundness analyser that can be coded in Prolog. In particular, entailment checking is used to prevent unnecessary least upper bound calculations. It is also demonstrated that join can be defined in terms of other operations, thereby eliminating code and removing the need for preprocessing formulae to a normal form. This saves space and time. Furthermore, the join can be adapted to straightforwardly implement the downward closure operator that arises in set sharing analyses. Experimental results indicate that the new Def implementation gives favourable results in comparison with BDD-based groundness analyses

β\beta-BaB2_2O4_4 deep UV monolithic walk-off compensating tandem

The generation of watt-level cw narrow-linewidth sources at specific deep UV wavelengths corresponding to atomic cooling transitions usually employs external cavity-enhanced second-harmonic generation (SHG) of moderate-power visible lasers in birefringent materials. In this work, we investigate a novel approach to cw deep-UV generation by employing the low-loss BBO in a monolithic walkoff-compensating structure [Zondy {\it{et al}}, J. Opt. Soc. Am. B {\bf{20}} (2003) 1675] to simultaneously enhance the effective nonlinear coefficient while minimizing the UV beam ellipticity under tight focusing. As a preliminary step to cavity-enhanced operation, and in order to apprehend the design difficulties stemming from the extremely low acceptance angle of BBO, we investigate and analyze the single-pass performance of a $L_c=8$mm monolithic walk-off compensating structure made of 2 optically-contacted BBO plates cut for type-I critically phase-matched SHG of a cw $\lambda=570.4$nm dye laser. As compared with a bulk crystal of identical length, a sharp UV efficiency enhancement factor of 1.65 has been evidenced with the tandem structure, but at $\sim-1$nm from the targeted fundamental wavelength, highlighting the sensitivity of this technique when applied to a highly birefringent material such as BBO. Solutions to angle cut residual errors are identified so as to match accurately more complex periodic-tandem structure performance to any target UV wavelength, opening the prospect for high-power, good beam quality deep UV cw laser sources for atom cooling and trapping.Comment: 21 pages, 8 figures, to appear in Opt. Commu

Effect of Sr substitution on superconductivity in Hg2(Ba1-ySry)2YCu2O8-d (part2): bond valence sum approach of the hole distribution

The effects of Sr substitution on superconductivity, and more particulary the changes induced in the hole doping mechanism, were investigated in Hg2(Ba1-ySry)2YCu2O8-d by a "bond valence sum" analysis with Sr content from y = 0.0 to y = 1.0. A comparison with CuBa2YCu2O7-d and Cu2Ba2YCu2O8 systems suggests a possible explanation of the Tc enhancement from 0 K for y = 0.0 to 42 K for y = 1.0. The charge distribution among atoms of the unit cell was determined from the refined structure, for y = 0.0 to 1.0. It shows a charge transfer to the superconducting CuO2 plane via two doping channels pi(1) and pi(2), i.e. through O2(apical)-Cu and Ba/Sr-O1 bonds respectively.Comment: 13 pages, 5 figures, accepted for publication in Journal of Physics: Condensed Matte

The Scottish economy [September 1995]

This section presents short and long term forecasts for the quarterly growth rates of Scottish manufacturing (Division D of the 1992 SIC) output

The Scottish economy [December 1995]

This section presents short and long term forecasts for the quarterly growth rates of Scottish manufacturing (Division D of the 1992 SIC) output

An individualized longitudinal approach to monitoring the dynamics of growth and fitness development in adolescent athletes.

This study evaluated the development of anthropometric and fitness characteristics of 3 individual adolescent junior rugby league players and compared their characteristics with a cross-sectional population matched by age and skill level. Cross-sectional anthropometric and fitness assessments were conducted on 1,172 players selected to the Rugby Football League's talent development program (i.e., the Player Performance Pathway) between 2005 and 2008. Three players of differing relative age, maturational status, and playing position were measured and tracked once per year on 3 occasions (Under 13s, 14s, 15s age categories) and compared against the cross-sectional population. Results demonstrated that the later maturing players increased height (player 1 = 9.2%; player 2 = 7.8%) and a number of fitness characteristics (e.g., 60-m speed-player 1 = -14.9%; player 2 = -9.9%) more than the earlier maturing player (player 3-Height = 2.0%, 60-m sprint = -0.7%) over the 2-year period. The variation in the development of anthropometric and fitness characteristics between the 3 players highlights the importance of longitudinally monitoring individual characteristics during adolescence to assess the dynamic changes in growth, maturation, and fitness. Findings showcase the limitations of short-term performance assessments at one-off time points within annual-age categories, instead of advocating individual development and progression tracking without deselection. Coaches should consider using an individual approach, comparing data with population averages, to assist in the prescription of appropriate training and lifestyle interventions to aid the development of junior athletes