Mathematical notation: help or hindrance?

In this article Geoff Tennant puts forward a range of reasons for using mathematical notation, emphasising the need to allow children learning it time and space to come to terms with it. Examples are given in furthering the argument that the time to introduce notation is after the concept is already fully understood.

Integration of chaos theory and mathematical models in building simulation: Part I: Literature review

Current mathematical models in building research have been limited in most studies to linear dynamics systems. A literature review of past studies investigating chaos theory approaches in building simulation models suggests that as a basis chaos model is valid and can handle the increasingly complexity of building systems that have dynamic interactions among all the distributed and hierarchical systems on the one hand, and the environment and occupants on the other. The review also identifies the paucity of literature and the need for a suitable methodology of linking chaos theory to mathematical models in building design and management studies. This study is broadly divided into two parts and presented in two companion papers. Part (I) reviews the current state of the chaos theory models as a starting point for establishing theories that can be effectively applied to building simulation models. Part (II) develops conceptual frameworks that approach current model methodologies from the theoretical perspective provided by chaos theory, with a focus on the key concepts and their potential to help to better understand the nonlinear dynamic nature of built environment systems. Case studies are also presented which demonstrate the potential usefulness of chaos theory driven models in a wide variety of leading areas of building research. This study distills the fundamental properties and the most relevant characteristics of chaos theory essential to building simulation scientists, initiates a dialogue and builds bridges between scientists and engineers, and stimulates future research about a wide range of issues on building environmental systems.

Integration of chaos theory and mathematical models in building simulation: Part II: Conceptual frameworks

Current mathematical models in building research have been limited in most studies to linear dynamics systems. A literature review of past studies investigating chaos theory approaches in building simulation models suggests that as a basis chaos model is valid and can handle the increasing complexity of building systems that have dynamic interactions among all the distributed and hierarchical systems on the one hand, and the environment and occupants on the other. The review also identifies the paucity of literature and the need for a suitable methodology of linking chaos theory to mathematical models in building design and management studies. This study is broadly divided into two parts and presented in two companion papers. Part (I), published in the previous issue, reviews the current state of the chaos theory models as a starting point for establishing theories that can be effectively applied to building simulation models. Part (II) develop conceptual frameworks that approach current model methodologies from the theoretical perspective provided by chaos theory, with a focus on the key concepts and their potential to help to better understand the nonlinear dynamic nature of built environment systems. Case studies are also presented which demonstrate the potential usefulness of chaos theory driven models in a wide variety of leading areas of building research. This study distills the fundamental properties and the most relevant characteristics of chaos theory essential to (1) building simulation scientists and designers (2) initiating a dialogue between scientists and engineers, and (3) stimulating future research on a wide range of issues involved in designing and managing building environmental systems.

A simplified mathematical model for urban microclimate simulation

Techniques for modelling urban microclimates and urban block surfaces temperatures are desired by urban planners and architects for strategic urban designs at the early design stages. This paper introduces a simplified mathematical model for urban simulations (UMsim) including urban surfaces temperatures and microclimates. The nodal network model has been developed by integrating coupled thermal and airflow model. Direct solar radiation, diffuse radiation, reflected radiation, long-wave radiation, heat convection in air and heat transfer in the exterior walls and ground within the complex have been taken into account. The relevant equations have been solved using the finite difference method under the Matlab platform. Comparisons have been conducted between the data produced from the simulation and that from an urban experimental study carried out in a real architectural complex on the campus of Chongqing University, China in July 2005 and January 2006. The results show a satisfactory agreement between the two sets of data. The UMsim can be used to simulate the microclimates, in particular the surface temperatures of urban blocks, therefore it can be used to assess the impact of urban surfaces properties on urban microclimates. The UMsim will be able to produce robust data and images of urban environments for sustainable urban design.

Role of rpoS in the Development of Cell Envelope Resilience and Pressure Resistance in Stationary-Phase Escherichia coli

This work investigated the role of rpoS in the development of increased cell envelope resilience and enhanced pressure resistance in stationary phase cells of Escherichia coli. Loss of both colony-forming ability and membrane integrity, measured as uptake of propidium iodide (PI), occurred at lower pressures in E. coli BW3709 (rpoS) than in the parental strain (BW2952). The rpoS mutant also released much higher concentrations of protein under pressure than the parent. We propose that RpoS-regulated functions are responsible for the increase in membrane resilience as cells enter stationary phase and that this plays a major role in the development of pressure resistance. Strains from the Keio collection with mutations in two RpoS-regulated genes, cfa (cyclopropane fatty acyl phospholipid synthase) and osmB (outer membrane lipoprotein), were significantly more pressure-sensitive and took up more PI than the parent strains with cfa having the greatest effect. Mutations in the bolA morphogene and other RpoS-regulated lipoprotein genes (osmC, osmE, osmY and ybaY) had no effect on pressure resistance. The cytoplasmic membranes of the rpoS mutant failed to reseal after pressure treatment and strains with mutations in osmB and nlpI (new lipoprotein) were also somewhat impaired in the ability to reseal their membranes. The cfa mutant, though pressure-sensitive, was unaffected in membrane resealing implying that the initial transient permeabilization event is critical for loss of viability rather than the failure to reseal. The enhanced pressure sensitivity of polA, recA and xthA mutants suggested that DNA may be a target of oxidative stress in pressure-treated cells.

Asynchronous flowering and within-plant flowering diversity in wheat and the implications for crop resilience to heat

Self-pollination dominates in wheat , with a small level of out-crossing due to flowering asynchrony and male sterility. However, the timing and synchrony of male and female flowering in wheat is a crucial determinant of seed set and may be an important factor affecting gene flow and resilience to climate change. Here, a methodology is presented for assessing the timing and synchrony of flowering in wheat. From the onset of flowering until the end of anthesis, the anther and stigma activity of each floret was assessed on the first five developing ears in potted plants grown under ambient conditions and originating from cv Paragon or cvs Spark-Rialto backgrounds. At harvest maturity, seed presence, size and weight was recorded for each floret scored. The synchrony between pollen dehiscence and stigma collapse within a flower was dependent on its relative position in a spike and within a floret. Determined on the basis of synchrony within each flower, the level of pollination by pollen originating from other flowers reached approximately 30% and did not change throughout the duration of flowering. A modelling exercise parameterised by flowering observations indicated that the temporal and spatial variability of anther activity within and between spikes may influence the relative resilience of wheat to sudden, extreme climatic events which has direct relevance to predicted future climate scenarios in the UK.

Resilience planning, economic change and the politics of post-recession development in London and Hong Kong

For much of the 1990s and 2000s, the emphasis of urban policy in many global cities was on managing and mitigating the social and environmental effects of rapid economic growth. The credit crunch of 2008 and the subsequent recession have undermined some of the core assumptions on which such policies were based. It is in this context that the concept of resilience planning has taken on a new significance. Drawing on contemporary research in London and Hong Kong, the paper shows how resilience and recovery planning has become a key area of political debate. It examines what is meant by conservative and radical interpretations of resilience and how conservative views have come to dominate ‘recovery’ thinking, with élite groups unwilling to accept the limits to the neo-liberal orthodoxies that helped to precipitate the economic crisis. The paper explores the implications of such thinking for the politics of urban development.

Safeguarding inheritance and enhancing the resilience of orphaned young people living in child- and youth-headed households in Tanzania and Uganda

This paper explores the resilience of orphaned young people in safeguarding the physical assets (land and property) that they inherited from their parents and in sustaining their households without a co-resident adult relative. Drawing on the concept of resilience and the sustainable livelihoods framework, this paper analyses the findings of an exploratory study conducted with 15 orphaned young people heading households,18 of their siblings and 39 NGO workers and community members in Tanzania and Uganda. The research suggests that inherited land and property represent key determining factors in the formation and viability of child- and youth-headed households in both rural and urban areas. Despite experiences of stigma and marginalisation in the community, social networks were crucial in enabling young people to protect themselves and their property, in providing access to material and emotional resources and in enhancing their skills and capabilities to develop sustainable livelihoods. Support for child- and youth-headed households needs to recognise young people's agency and adopt a holistic approach to their lives that analyses the physical assets, material resources, human and social capital available to the household, as well as individual young people's wellbeing, outlook and aspirations. Alongside cash transfers and material support, youth-led collective mobilisation that is sustained over time may also help to build resilience and foster more supportive social environments that challenge property grabbing and the stigmatisation of child- and youth-headed households.

Community-based climate change adaptation strategies for integrated prawn-fish-rice farming in Bangladesh to promote social-ecological resilience

Farming freshwater prawns with fish in rice fields is widespread in coastal regions of southwest Bangladesh because of favourable resources and ecological conditions. This article provides an overview of an ecosystem-based approach to integrated prawn-fish-rice farming in southwest Bangladesh. The practice of prawn and fish farming in rice fields is a form of integrated aquaculture-agriculture, which provides a wide range of social, economic and environmental benefits. Integrated prawn-fish-rice farming plays an important role in the economy of Bangladesh, earning foreign exchange and increasing food production. However, this unique farming system in coastal Bangladesh is particularly vulnerable to climatechange. We suggest that community-based adaptation strategies must be developed to cope with the challenges. We propose that integrated prawn-fish-rice farming could be relocated from the coastal region to less vulnerable upland areas, but caution that this will require appropriate adaptation strategies and an enabling institutional environment.

A mathematical approach to chemical equilibrium theory for gaseous systems—I: theory

Equilibrium theory occupies an important position in chemistry and it is traditionally based on thermodynamics. A novel mathematical approach to chemical equilibrium theory for gaseous systems at constant temperature and pressure is developed. Six theorems are presented logically which illustrate the power of mathematics to explain chemical observations and these are combined logically to create a coherent system. This mathematical treatment provides more insight into chemical equilibrium and creates more tools that can be used to investigate complex situations. Although some of the issues covered have previously been given in the literature, new mathematical representations are provided. Compared to traditional treatments, the new approach relies on straightforward mathematics and less on thermodynamics, thus, giving a new and complementary perspective on equilibrium theory. It provides a new theoretical basis for a thorough and deep presentation of traditional chemical equilibrium. This work demonstrates that new research in a traditional field such as equilibrium theory, generally thought to have been completed many years ago, can still offer new insights and that more efficient ways to present the contents can be established. The work presented here can be considered appropriate as part of a mathematical chemistry course at University level.