Tau-functions and dressing transformations for zero-curvature affine integrable equations

The solutions of a large class of hierarchies of zero-curvature equations that includes Toda- and KdV-type hierarchies are investigated. All these hierarchies are constructed from affine (twisted or untwisted) Kac-Moody algebras g. Their common feature is that they have some special vacuum solutions corresponding to Lax operators lying in some Abelian (up to the central term) subalgebra of g; in some interesting cases such subalgebras are of the Heisenberg type. Using the dressing transformation method, the solutions in the orbit of those vacuum solutions are constructed in a uniform way. Then, the generalized tau-functions for those hierarchies are defined as an alternative set of variables corresponding to certain matrix elements evaluated in the integrable highest-weight representations of g. Such definition of tau-functions applies for any level of the representation, and it is independent of its realization (vertex operator or not). The particular important cases of generalized mKdV and KdV hierarchies as well as the Abelian and non-Abelian affine Toda theories are discussed in detail. © 1997 American Institute of Physics.

Solitons from dressing in an algebraic approach to the constrained KP hierarchy

The algebraic matrix hierarchy approach based on affine Lie sl(n) algebras leads to a variety of 1 + 1 soliton equations. By varying the rank of the underlying sl(n) algebra as well as its gradation in the affine setting, one encompasses the set of the soliton equations of the constrained KP hierarchy.The soliton solutions are then obtained as elements of the orbits of the dressing transformations constructed in terms of representations of the vertex operators of the affine sl(n) algebras realized in the unconventional gradations. Such soliton solutions exhibit non-trivial dependence on the KdV (odd) time flows and KP (odd and even) time Bows which distinguishes them From the conventional structure of the Darboux-Backlund-Wronskian solutions of the constrained KP hierarchy.

The Bullough-Dodd model coupled to matter fields

The Bullough-Dodd model is an important two-dimensional integrable field theory which finds applications in physics and geometry. We consider a conformally invariant extension of it, and study its integrability properties using a zero curvature condition based on the twisted Kac-Moody algebra A(2)((2)). The one- and two-soliton solutions as well as the breathers are constructed explicitly. We also consider integrable extensions of the Bullough-Dodd model by the introduction of spinor (matter) fields. The resulting theories are conformally invariant and present local internal symmetries. All the one-soliton solutions, for two examples of those models, are constructed using a hybrid of the dressing and Hirota methods. One model is of particular interest because it presents a confinement mechanism for a given conserved charge inside the solitons. (C) 2008 Elsevier B.V. All rights reserved.

Solitons, τ-functions and hamiltonian reduction for non-Abelian conformal affine Toda theories

We consider the Hamiltonian reduction of the two-loop Wess-Zumino-Novikov-Witten model (WZNW) based on an untwisted affine Kac-Moody algebra script Ĝ. The resulting reduced models, called Generalized Non-Abelian Conformal Affine Toda (G-CAT), are conformally invariant and a wide class of them possesses soliton solutions; these models constitute non-Abelian generalizations of the conformal affine Toda models. Their general solution is constructed by the Leznov-Saveliev method. Moreover, the dressing transformations leading to the solutions in the orbit of the vacuum are considered in detail, as well as the τ-functions, which are defined for any integrable highest weight representation of script Ĝ, irrespectively of its particular realization. When the conformal symmetry is spontaneously broken, the G-CAT model becomes a generalized affine Toda model, whose soliton solutions are constructed. Their masses are obtained exploring the spontaneous breakdown of the conformal symmetry, and their relation to the fundamental particle masses is discussed. We also introduce what we call the two-loop Virasoro algebra, describing extended symmetries of the two-loop WZNW models.

Local agenda 21 and planning practice: structural transformation or window dressing?

Local Agenda 21 seeks the meaningful involvement of a wide range of local groups and stakeholders in the formulation and implementation of public policy and a free flow of communication and discussion between them and their respective local authorities (and other areas and levels of decision-making). This paper explores the reality of this process using case study evidence from local planning practice in Liverpool (in the north of England) and Reading (in the south of the country). It concentrates on the interaction between LA21 groups and local planning authorities around the preparation of local land use plans and other policy initiatives and the day-to-day regulation of development permits. The paper builds on ‘New Institutionalist’ theory to explore the constraints and opportunities for significant transformations in social, political and economic ‘structures’ or ‘ways of doing things’ through the LA21 process. It concludes that the two cases provide evidence of mixed success in achieving such changes in established planning practices.

Practical Transformations and Transformational Practices : Globalization, Postmodernism, and Early Childhood Education : Advances in Early Education and Day Care

Both traditional and progressive curricula are inadequate for the task of responding to the economic, political, social, and cultural changes that have occurred as a result of globalization. This book documents some of the ongoing work occurring in early childhood settings that is aimed at improving, and ultimately transforming, early childhood practice in these changed and changing times. The authors do not simply critique developmental approaches or the increasing standardization of the field. Instead, they describe how they are playing around with postmodern ideas in practice and developing unique approaches to the diverse educational circumstances that confront early childhood educators. Whether it is preparing teachers, using materials, or developing policies, each chapter provides readers with possibilities for enacting pedagogies that are responsive to the contemporary circumstances shaping the lives of young children.

The efficacy of an augmented virtual reality system to alleviate pain in children undergoing burns dressing changes : a randomised controlled trial

In children, the pain and anxiety associated with acute burn dressing changes can be severe, with drug treatment alone frequently proving to be inadequate. Virtual reality (VR) systems have been successfully trialled in limited numbers of adult and paediatric burn patients. Augmented reality (AR) differs from VR in that it overlays virtual images onto the physical world, instead of creating a complete virtual world. This prospective randomised controlled trial investigated the use of AR as an adjunct to analgesia and sedation in children with acute burns. Forty-two children (30 male and 12 female), with an age range of 3–14 years (median age 9 years) and a total burn surface area ranging from 1 to 16% were randomised into a treatment (AR) arm and a control (basic cognitive therapy) arm after administration of analgesia and/or sedation. Pain scores, pulse rates (PR), respiratory rates (RR) and oxygen saturations (SaO2) were recorded pre-procedurally, at 10 min intervals and post-procedurally. Parents were also asked to grade their child's overall pain score for the dressing change. Mean pain scores were significantly lower (p = 0.0060) in the AR group compared to the control group, as were parental pain assessment scores (p = 0.015). Respiratory and pulse rates showed significant changes over time within groups, however, these were not significantly different between the two study groups. Oxygen saturation did not differ significantly over time or between the two study groups. This trial shows that augmented reality is a useful adjunct to pharmacological analgesia.

Nitrogen and phosphorus transformations in fixed-film biofilters subjected to aeration/no-aeration cycles

Despite recent developments in fixed-film combined biological nutrients removal (BNR) technology; fixed-film systems (i.e., biofilters), are still at the early stages of development and their application has been limited to a few laboratory-scale experiments. Achieving enhanced biological phosphorus removal in fixed-film systems requires exposing the micro-organisms and the waste stream to alternating anaerobic/aerobic or anaerobic/anoxic conditions in cycles. The concept of cycle duration (CD) as a process control parameter is unique to fixed-film BNR systems, has not been previously investigated, and can be used to optimise the performance of such systems. The CD refers to the elapsed time before the biomass is re-exposed to the same environmental conditions in cycles. Fixed-film systems offer many advantages over suspended growth systems such as reduced operating costs, simplicity of operation, absence of sludge recycling problems, and compactness. The control of nutrient discharges to water bodies, improves water quality, fish production, and allow water reuse. The main objective of this study was to develop a fundamental understanding of the effect of CD on the transformations of nutrients in fixed-film biofilter systems subjected to alternating aeration I no-aeration cycles A fixed-film biofilter system consisting of three up-flow biofilters connected in series was developed and tested. The first and third biofilters were operated in a cyclic mode in which the biomass was subjected to aeration/no-aeration cycles. The influent wastewater was simulated aquaculture whose composition was based on actual water quality parameters of aquacuture wastewater from a prawn grow-out facility. The influent contained 8.5 - 9:3 mg!L a111monia-N, 8.5- 8.7 mg/L phosphate-P, and 45- 50 mg!L acetate. Two independent studies were conducted at two biofiltration rates to evaluate and confirm the effect of CD on nutrient transformations in the biofilter system for application in aquaculture: A third study was conducted to enhance denitrification in the system using an external carbon- source at a rate varying from 0-24 ml/min. The CD was varied in the range of0.25- 120 hours for the first two studies and fixed at 12 hours for the third study. This study identified the CD as an important process control parameter that can be used to optimise the performance of full-scale fixed-film systems for BNR which represents a novel contribution in this field of research. The CD resulted in environmental conditions that inhibited or enhanced nutrient transformations. The effect of CD on BNR in fixed-film systems in terms of phosphorus biomass saturation and depletion has been established. Short CDs did not permit the establishment of anaerobic activity in the un-aerated biofilter and, thus, inhibited phosphorus release. Long CDs resulted in extended anaerobic activity and, thus, resulted in active phosphorus release. Long CDs, however, resulted in depleting the biomass phosphorus reservoir in the releasing biofilter and saturating the biomass phosphorus reservoir in the up-taking biofilter in the cycle. This phosphorus biomass saturation/depletion phenomenon imposes a practical limit on how short or long the CD can be. The length of the CD should be somewhere just before saturation or depletion occur and for the system tested, the optimal CD was 12 hours for the biofiltration rates tested. The system achieved limited net phosphorus removal due to the limited sludge wasting and lack of external carbon supply during phosphorus uptake. The phosphorus saturation and depletion reflected the need to extract phosphorus from the phosphorus-rich micro-organisms, for example, through back-washing. The major challenges of achieving phosphorus removal in the system included: (I) overcoming the deterioration in the performance of the system during the transition period following the start of each new cycle; and (2) wasting excess phosphorus-saturated biomass following the aeration cycle. Denitrification occurred in poorly aerated sections of the third biofilter and generally declined as the CD increased and as the time progressed in the individual cycle. Denitrification and phosphorus uptake were supplied by an internal organic carbon source, and the addition of an external carbon source (acetate) to the third biofilter resulted in improved denitrification efficiency in the system from 18.4 without supplemental carbon to 88.7% when the carbon dose reached 24 mL/min The removal of TOC and nitrification improved as the CD increased, as a result of the reduction in the frequency of transition periods between the cycles. A conceptual design of an effective fixed-film BNR biofilter system for the treatment of the influent simulated aquaculture wastewater was proposed based on the findings of the study.

"Surviving" adolescence : apocalyptic and post-apocalyptic transformations in young adult fiction

This study, entitled "Surviving" Adolescence: Apocalyptic and post-apocalyptic transformations in young adult fiction‖, analyses how discourses surrounding the apocalyptic and post-apocalyptic are represented in selected young adult fiction published between 1997 and 2009. The term ―apocalypse‖ is used by current theorists to refer to an uncovering or disclosure (most often a truth), and ―post-apocalypse‖ means to be after a disclosure, after a revelation, or after catastrophe. This study offers a double reading of apocalyptic and post-apocalyptic discourses, and the dialectical tensions that are inherent in, and arise from, these discourses. Drawing on the current scholarship of children‘s and young adult literature this thesis uses post-structural theoretical perspectives to develop a framework and methodology for conducting a close textual analysis of exclusion, ‗un‘differentiation, prophecy, and simulacra of death. The combined theoretical perspectives and methodology offer new contributions to young adult fiction scholarship. This thesis finds that rather than conceiving adolescence as the endurance of a passing phase of a young person‘s life, there is a new trend emerging in young adult fiction that treats adolescence as a space of transformation essential to the survival of the young adult, and his/her community.

In vivo evaluation of an ultra-thin polycaprolactone film as a wound dressing

The use of ultra-thin films as dressings for cutaneous wounds could prove advantageous in terms of better conformity to wound topography and improved vapour transmission. For this purpose, ultra-thin poly(epsilon-caprolactone) (PCL) films of 5-15 microm thickness were fabricated via a biaxial stretching technique. To evaluate their in vivo biocompatibility and feasibility as an external wound dressing, PCL films were applied over full and partial-thickness wounds in rat and pig models. Different groups of PCL films were used: untreated, NaOH-treated, untreated with fibrin, NaOH-treated with perforations, and NaOH-treated with fibrin and S-nitrosoglutathione. Wounds with no external dressings were used as controls. Wound contraction rate, histology and biomechanical analyses were carried out. Wounds re-epithelialized completely at a comparable rate. Formation of a neo-dermal layer and re-epithelialization were observed in all the wounds. A lower level of fibrosis was observed when PCL films were used, compared to the control wounds. Ultimate tensile strength of the regenerated tissue in rats reached 50-60% of that in native rat skin. Results indicated that biaxially-stretched PCL films did not induce inflammatory reactions when used in vivo as a wound dressing and supported the normal wound healing process in full and partial-thickness wounds.

Strategising knowledge-based urban development : knowledge city transformations of Brisbane, Australia

In the global knowledge economy, knowledge-intensive industries and knowledge workers are extensively seen as the primary factors to improve the welfare and competitiveness of cities. To attract and retain such industries and workers, cities produce knowledge-based urban development strategies, and therefore such strategising has become an important development mechanism for cities and their economies. The paper discusses the critical connections between knowledge city foundations and integrated knowledge-based urban development mechanisms in both the local and regional level. In particular, the paper investigates Brisbane’s knowledge-based urban development strategies that support gentrification, attraction, and retention of investment and talent. Furthermore, the paper develops a knowledge-based urban development assessment framework to provide a clearer understanding of the local and regional policy frameworks, and relevant applications of Brisbane’s knowledge-based urban development experience, in becoming a prosperous knowledge city. The paper, with its knowledge-based urban development assessment framework, scrutinises Brisbane’s four development domains in detail: economy; society; institutional; built and natural environments. As part of the discussion of the case study findings, the paper describes the global orientation of Brisbane within the frame of regional and local level knowledge-based urban development strategies performing well. Although several good practices from Brisbane have already been internationally acknowledged, the research reveals that Brisbane is still in the early stages of its knowledge-based urban development implementation. Consequently, the development of a monitoring system for all knowledge-based urban development at all levels is highly crucial in accurately measuring the success and failure of specific knowledge-based urban development policies, and Brisbane’s progress towards a knowledge city transformation.

Linear models for endocytic transformations from live cell imaging

Endocytosis is the process by which cells internalise molecules including nutrient proteins from the extracellular media. In one form, macropinocytosis, the membrane at the cell surface ruffles and folds over to give rise to an internalised vesicle. Negatively charged phospholipids within the membrane called phosphoinositides then undergo a series of transformations that are critical for the correct trafficking of the vesicle within the cell, and which are often pirated by pathogens such as Salmonella. Advanced fluorescent video microscopy imaging now allows the detailed observation and quantification of these events in live cells over time. Here we use these observations as a basis for building differential equation models of the transformations. An initial investigation of these interactions was modelled with reaction rates proportional to the sum of the concentrations of the individual constituents. A first order linear system for the concentrations results. The structure of the system enables analytical expressions to be obtained and the problem becomes one of determining the reaction rates which generate the observed data plots. We present results with reaction rates which capture the general behaviour of the reactions so that we now have a complete mathematical model of phosphoinositide transformations that fits the experimental observations. Some excellent fits are obtained with modulated exponential functions; however, these are not solutions of the linear system. The question arises as to how the model may be modified to obtain a system whose solution provides a more accurate fit.

Stories of cross-dressing and the body : family memories in fiction

Ruth Finnegan (2006, 179) describes how family myths have the power to provoke images that recur throughout generations. This paper will document my own encounter with such persistent images in the stories of a mother and daughter. Both mother and daughter told stories about encountering cross-dressing men in the streets of Brisbane, and both showed similar anxiety over their own body size. As a creative writer working with oral histories, I found these stories of the disguised body compelling. By drawing on the storytelling strategies and preoccupations present in the interview, I used imagination and fictional techniques to investigate the possibility of symbolic resonance of memories across generations. In her novel Beloved, Toni Morrison (1987) uses the notion of ‘rememory’ to describe how characters actively make and suppress meanings in their recollections. Like Morrison, my writing speaks to notions around the way stories are remembered and told.