Optimal Alphabetic Ternary Trees

We give a new algorithm to construct optimal alphabetic ternary trees, where every internal node has at most three children. This algorithm generalizes the classic Hu-Tucker algorithm, though the overall computational complexity has yet to be determined

Impact of European Water Framework Directive Article 7 on Drinking Water Directive compliance for pesticides: challenges of a prevention-led approach

Article 7 of the European Water Framework Directive (WFD) promotes a prevention-led approach to European Drinking Water Directive (DWD) compliance for those parameters that derive from anthropogenic influences on raw water quality. However, the efficacy of pollution prevention interventions is currently uncertain and likely to be variable, which makes absolute compliance with the drinking water standard a significant challenge. Member State governments, the WFD competent authority, the DWD competent authority, water suppliers and agriculture are all affected by and have a different perspective on the nature of this challenge. This paper presents a discussion of these perspectives applicable to stakeholders in all European Member States; the analysis is supported with examples from England and Wales. Improved understanding of the challenges faced by each group is needed if these groups are to achieve the shared goals of WFD Article 7 compliance and DWD compliance without a disproportionately negative impact on agricultural productivity. In addition, the European Commission needs to be aware of and address a potential incompatibility between WFD Article 7 and the DWD. With this in mind, targeted recommendations for action are presented for each stakeholder group

A Two-Dimensional Carbon Semiconductor

We show that patterned defects can be used to disrupt the sub-lattice symmetry of graphene so as to open up a band gap. This way of modifying graphene's electronic structure does not rely on external agencies, the addition of new elements or special boundaries. The method is used to predict a planar, low energy, graphene allotrope with a band gap of 1.2 eV. This defect engineering also allows semiconducting ribbons of carbon to be fabricated within graphene. Linear arrangements of defects lead to naturally embedded ribbons of the semiconducting material in graphene, offering the prospect of two-dimensional circuit logic composed entirely of carbon.Comment: 4 pages, 5 figure