Scale-invariant moving finite elements for nonlinear partial differential equations in two dimensions

A scale-invariant moving finite element method is proposed for the adaptive solution of nonlinear partial differential equations. The mesh movement is based on a finite element discretisation of a scale-invariant conservation principle incorporating a monitor function, while the time discretisation of the resulting system of ordinary differential equations is carried out using a scale-invariant time-stepping which yields uniform local accuracy in time. The accuracy and reliability of the algorithm are successfully tested against exact self-similar solutions where available, and otherwise against a state-of-the-art h-refinement scheme for solutions of a two-dimensional porous medium equation problem with a moving boundary. The monitor functions used are the dependent variable and a monitor related to the surface area of the solution manifold. (c) 2005 IMACS. Published by Elsevier B.V. All rights reserved.

Moving boundary value problems for the wave equation

We study certain boundary value problems for the one-dimensional wave equation posed in a time-dependent domain. The approach we propose is based on a general transform method for solving boundary value problems for integrable nonlinear PDE in two variables, that has been applied extensively to the study of linear parabolic and elliptic equations. Here we analyse the wave equation as a simple illustrative example to discuss the particular features of this method in the context of linear hyperbolic PDEs, which have not been studied before in this framework.

Intentions of UK farmers toward biofuel crop production: Implications for policy targets and land use change

The United States and the European Union have set targets for biofuel production to decrease reliance on fossil fuels and to reduce fossil carbon emissions. Attainment of biofuel targets d6pends upon policy and infrastructure development but also on production of suitable raw materials. Production of relevant crops relies on the decisions that farmers make in their economic and political environment. We need to identify any farmer-related barriers to biofuel production and to determine whether novel policy and technology are required to meet targets. These aspects of the emerging biofuel industry are relevant across international barriers and have notyet been addressed quantitatively. We describe a case study from the UK of farmers' intentions toward producing two biofuel crops for which refining capacity either exists or is under construction. Given farmers' intentions, current land use, and conversion efficiency, we estimate potential biofuel production. These estimates indicate that EU targets are not achievable using domestically grown raw materials without policy intervention, use of alternative feedstocks, and either significant improvements in processing efficiency or largescale changes in land use.

Are class II phosphoinositide 3-kinases potential targets for anticancer therapies?

Of the three classes of true phosphoinositide (PI) 3-kinases, the class II subdivision, which consists of three isoforms, PI3K-C2alpha, PI3K-C2beta and PI3K-C2gamma, is the least well understood. There are a number of reasons for this. This class of PI 3-kinase was identified exclusively by PCR and homology cloning approaches and not on the basis of cellular function. Like class I PI 3-kinases, class II PI 3-kinases are activated by diverse receptor types. To complicate the elucidation of class II PI 3-kinase function further, their in vitro substrate specificity is intermediate between the receptor activated class I PI 3-kinases and the housekeeping class III PI 3-kinase. The class II PI 3-kinases are inhibited by the two commonly used PI 3-kinase family selective inhibitors, wortmannin and LY294002, and there are no widely available, specific inhibitors for the individual classes or isoforms. Here the current state of understanding of class II PI 3-kinase function is reviewed, followed by an appraisal as to whether there is enough evidence to suggest that pharmaceutical companies, who are currently targeting the class I PI 3-kinases in an attempt to generate anticancer agents, should also consider targeting the class II PI 3-kinases.

Hitting emissions targets with (statistical) confidence in multi-instrument Emissions Trading Schemes

A means of assessing, monitoring and controlling aggregate emissions from multi-instrument Emissions Trading Schemes is proposed. The approach allows contributions from different instruments with different forms of emissions targets to be integrated. Where Emissions Trading Schemes are helping meet specific national targets, the approach allows the entry requirements of new participants to be calculated and set at a level that will achieve these targets. The approach is multi-levelled, and may be extended downwards to support pooling of participants within instruments, or upwards to embed Emissions Trading Schemes within a wider suite of policies and measures with hard and soft targets. Aggregate emissions from each instrument are treated stochastically. Emissions from the scheme as a whole are then the joint probability distribution formed by integrating the emissions from its instruments. Because a Bayesian approach is adopted, qualitative and semi-qualitative data from expert opinion can be used where quantitative data is not currently available, or is incomplete. This approach helps government retain sufficient control over emissions trading scheme targets to allow them to meet their emissions reduction obligations, while minimising the need for retrospectively adjusting existing participants’ conditions of entry. This maintains participant confidence, while providing the necessary policy levers for good governance.

Moving on: the challenges for foreign language learning on transition from primary to secondary school

Europe's commitment to language learning has resulted in higher percentages of pupils studying foreign languages during primary education. In England, recent policy decisions to expand foreign language learning at primary level by 2010 create major implications for transition to secondary. This paper presents findings on transition issues from case studies of a DfES-funded project evaluating 19 local authority Pathfinders piloting the introduction of foreign language learning at primary level. Research on transition in other countries sets these findings in context. Finally, it investigates the challenges England faces for transition in the light of this expansion and discusses future implications.

Student perceptions of their IEP targets

The 2001 Code of Practice for Special Educational Needs (DfES, 2001) explicitly states that students with IEPs should have an active role in the writing and implementing of them. A research project was conducted in which 19 Year 8 students in three schools were interviewed, with the findings cross-referenced against an examination of their individual education plans (IEPs) and interviews with the SENCos. Very few students were able to communicate a clear understanding of IEPs. Students' stated targets mostly reflected mainstream target-setting: very few stated targets matched with those in their IEPs. Consistent with these findings is literature which argues that meaningfully involving students in the IEP process takes considerable time and effort, which would appear to imply that the number of students with IEPs in any one school must be limited. Against this are pressures, particularly from OFSTED but also from examination boards, to have IEPs available as evidence that students' needs are being met. The article concludes by suggesting that SENCos look to limit the number of IEPs issued, alongside a robust defence of the school's special educational needs policy within the school evaluation form to ensure that students' needs are met and also are seen to be met.