A titration model: an analysis and solution

The Newton‐Raphson method is proposed for the solution of the nonlinear equation arising from a theoretical model of an acid/base titration. It is shown that it is necessary to modify the form of the equation in order that the iteration is guaranteed to converge. A particular example is considered to illustrate the analysis and method, and a BASIC program is included that can be used to predict the pH of any weak acid/weak base titration.

Social networks, migration, and care in Tanzania

This paper explores the impacts of the HIV/AIDS epidemic on children and families in northern Tanzania using the concept of social resilience.1 The study is based on the findings of childfocused research with street children and children and families from HIV/AIDS-affected households. The paper illustrates the coping strategies that children and young people, and parents and caregivers adopt at the household level. In particular, it examines how the burden of care affects different generations of women and highlights their resilience, together with the importance of social networks and the fluidity of movement between rural and urban areas. The research suggests that migrating to urban areas to seek a living in the informal sector represents a survival strategy adopted by some children and young people orphaned by AIDS when their families and communities are unable or unwilling to support them. The paper concludes by exploring parents’, caregivers’, children’s, and young people’s views on the forms of social support that would promote their resilience and thereby help to mitigate the impacts of the epidemic at the household level.

Advanced global optimisation for mission analysis and design

This report describes the analysis and development of novel tools for the global optimisation of relevant mission design problems. A taxonomy was created for mission design problems, and an empirical analysis of their optimisational complexity performed - it was demonstrated that the use of global optimisation was necessary on most classes and informed the selection of appropriate global algorithms. The selected algorithms were then applied to the di®erent problem classes: Di®erential Evolution was found to be the most e±cient. Considering the speci¯c problem of multiple gravity assist trajectory design, a search space pruning algorithm was developed that displays both polynomial time and space complexity. Empirically, this was shown to typically achieve search space reductions of greater than six orders of magnitude, thus reducing signi¯cantly the complexity of the subsequent optimisation. The algorithm was fully implemented in a software package that allows simple visualisation of high-dimensional search spaces, and e®ective optimisation over the reduced search bounds.

Evolving social networks, attitudes and beliefs and counter terrorism

'The Princeton Companion to Applied Mathematics' is an introduction to applied mathematics for students, teachers, and professionals. This article is for the "Application Areas" part of the book, which comprises articles on connections between applied mathematics and other disciplines.