An Integro-Differential Equation Arising from an Electrochemistry Model

In this paper, we prove the existence and uniqueness of steady-state solutions for a system of equations arising from a model in electrochemistry. The same result was established by the authors in an earlier paper under the additional assumptions that the space-dimension N = 2 and the concentrations of the charged ions satisfy an electro-neutrality condition

Global Spatio-temporal Patterns of Influenza in the Post-pandemic Era

We study the global spatio-temporal patterns of influenza dynamics. This is achieved by analysing and modelling weekly laboratory confirmed cases of influenza A and B from 138 countries between January 2006 and May 2014. The data were obtained from FluNet, the surveillance network compiled by the the World Health Organization. We report a pattern of {\it skip-and-resurgence} behavior between the years 2011 and 2013 for influenza H1N1/09, the strain responsible for the 2009 pandemic, in Europe and Eastern Asia. In particular, the expected H1N1/09 epidemic outbreak in 2011 failed to occur (or"skipped") in many countries across the globe, although an outbreak occurred in the following year. We also report a pattern of {\it well-synchronized} 2010 winter wave of H1N1/09 in the Northern Hemisphere countries, and a pattern of replacement of strain H1N1/77 by H1N1/09 between the 2009 and 2012 influenza seasons. Using both a statistical and a mechanistic mathematical model, and through fitting the data of 108 countries (108 countries in a statistical model and 10 large populations with a mechanistic model), we discuss the mechanisms that are likely to generate these events taking into account the role of multi-strain dynamics. A basic understanding of these patterns has important public health implications and scientific significance

Learning together through international collaboration in teacher education in Malaysia. Report of a project to develop a Bachelor of Education (Honours) in Primary Mathematics

Copyright University of Hertfordshire, School of Education 2011Learning together through international collaboration in teacher education in Malaysia is the report of an enterprising partnership between the University of Hertfordshire, UK, the Ministry of Education Malaysia and two Institutes of Teacher Education in Malaysia. Working collaboratively with colleagues in Malaysia, the University of Hertfordshire School of Education designed, validated, supported and quality assured a Bachelor of Education (Honours) degree programme for initial teacher training for a single cohort of 120 students over four years. All the students graduated in 2010. Learning together through international collaboration in teacher education in Malaysia provides a record of the project itself. It also documents in-depth insights from contributors to the project in two main areas: the collaborative approach to working together and issues relating to learning and teaching, including the Action – Reflection – Modelling (ARM) pedagogical approach, which underpinned the degree programme. Senior managers, teacher educators and lecturers share some of their learning from working together to develop and implement the new degree programme. Student teachers voice some experiences from their school placements. They describe how they used ARM; highlight some of the benefits of the approach and identify some of the challenges associated with introducing a different pedagogy in schools as they were 'learning to teach'. There are glimpses of 'lively and attractive' classes in which 'pupils enjoy and feel comfortable to learn' and 'are eager to answer my questions'. School mentors provide additional insights into the student teachers' learning and teaching practice. The richness of the contributions is reflected in the many quotations included in the report. The successful completion of this project was due to the dedication and expertise of many contributors. The findings documented in this report are relevant for all those engaged in international collaboration and teacher education.Final Published versio

On the size-dependent fatigue behaviour of laser powder bed fusion Ti-6Al-4V

A sample size effect which influences the fatigue behaviour of laser powder bed fusion Ti-6Al-4V is identified and quantified. Two cylindrical samples are considered: ∅ 1.3 mm and ∅ 2.0 mm. The larger specimen demonstrates better fatigue resistance particularly in the high-cycle regime, with the differing surface roughness contributing to this effect. It is also confirmed that processing-induced porosity can compromise the fatigue performance even when the initiation sites are surface defects. The larger contribution of porosity to the fatigue fracture process of the larger specimen results in a higher scatter in the fatigue life. Differences in microstructure do not seem to contribute strongly to the variation in fatigue properties of the two specimens, but we present some evidence that the coarser microstructure of the larger specimen promotes a stronger tolerance to defects and induces more tortuous crack paths which hinders fatigue crack growth