Application of real and functional analysis to solve boundary value problems

This thesis is about using appropriate tools in functional analysis arid classical analysis to tackle the problem of existence and uniqueness of nonlinear partial differential equations. There being no unified strategy to deal with these equations, one approaches each equation with an appropriate method, depending on the characteristics of the equation. The correct setting of the problem in appropriate function spaces is the first important part on the road to the solution. Here, we choose the setting of Sobolev spaces. The second essential part is to choose the correct tool for each equation. In the first part of this thesis (Chapters 3 and 4) we consider a variety of nonlinear hyperbolic partial differential equations with mixed boundary and initial conditions. The methods of compactness and monotonicity are used to prove existence and uniqueness of the solution (Chapter 3). Finding a priori estimates is the main task in this analysis. For some types of nonlinearity, these estimates cannot be easily obtained, arid so these two methods cannot be applied directly. In this case, we first linearise the equation, using linear recurrence (Chapter 4). In the second part of the thesis (Chapter 5), by using an appropriate tool in functional analysis (the Sobolev Imbedding Theorem), we are able to improve previous results on a posteriori error estimates for the finite element method of lines applied to nonlinear parabolic equations. These estimates are crucial in the design of adaptive algorithms for the method, and previous analysis relies on, what we show to be, unnecessary assumptions which limit the application of the algorithms. Our analysis does not require these assumptions. In the last part of the thesis (Chapter 6), staying with the theme of choosing the most suitable tools, we show that using classical analysis in a proper way is in some cases sufficient to obtain considerable results. We study in this chapter nonexistence of positive solutions to Laplace's equation with nonlinear Neumann boundary condition. This problem arises when one wants to study the blow-up at finite time of the solution of the corresponding parabolic problem, which models the heating of a substance by radiation. We generalise known results which were obtained by using more abstract methods.

Dasyurid dilemmas: problems and solutions for conserving Australia's small carnivorous marsupials

Dasyurid marsupials are distributed throughout the major terrestrial environments of Australia but since European settlement have suffered local and regional extinctions, range reductions and population declines. In this paper we examine the conservation status of small dasyurids (<500 g) and the threats they face. We also evaluate recovery procedures for threatened taxa and assess their success. Twenty-four percent of smaller dasyurids are classified as vulnerable, endangered or data deficient. Large body size and occupancy of one or two habitat types are correlated strongly with  endangerment species currently considered as 'low risk, near threatened' group closely with vulnerable and endangered species, indicating a risk of further declines. The processes contributing most to declines include habitat loss and fragmentation, altered fire regimes and predation. As of April 200 I, no Recovery Plans had been adopted by the Commonwealth Govemment for any small dasyund species. There is much information on the reproduction and development of smaller dasyurids, making them suitable for captive breeding. However, captive breeding programs have been limited. the  dibbler Paranrechinus apicalis being the only species bred systematically for reintroductions. There is a need for integration between captive breeding programs and recovery planning. as well as for more information on the population viability and metapopulation structures of small dasyurids genetic diversity of populations and inbreeding depression. We suggest a program of survey. research. management and education to Improve conservation outcomes for all small dasyurids.

Problems and solutions on land reservation system of small and medium-sized cities in China

Based on the analysis of the basic principal of land reservation system of small and medium-sized cities, this paper gives detailed discuss on many problems which exist during the process of land reservation system, such as unclear function position of land reservation organization, single capital resource, unfair land compensation standard and incomplete urban design. It also submits the proposal—choosing one scientific model, establishing suitable organization, opening more channels for raising funds, and setting up reasonable land compensation standard to unify the land reservation in small and medium-sized cities, improve the efficacy of reserve departments, adjust and standardize the land market in order to promote the healthy development of small and medium-sized cities in the long term.

Framework to improve the application of theory in ecology and conservation

Ecological theory often fails applied ecologists in three ways: (1) Theory has little predictive value but is nevertheless applied in conservation with a risk of perverse outcomes, (2) individual theories have limited heuristic value for planning and framing research because they are narrowly focused, and (3) theory can lead to poor communication among scientists and hinder scientific progress through inconsistent use of terms and widespread redundancy. New approaches are therefore needed that improve the distillation, communication, and application of ecological theory. We advocate three approaches to resolve these problems: (1) improve prediction by reviewing theory across case studies to develop contingent theory where possible, (2) plan new research using a checklist of phenomena to avoid the narrow heuristic value of individual theories, and (3) improve communication among scientists by rationalizing theory associated with particular phenomena to purge redundancy and by developing definitions for key terms. We explored the extent to which these problems and solutions have been featured in two case studies of long-term ecological research programs in forests and plantations of southeastern Australia. We found that our main contentions were supported regarding the prediction, planning, and communication limitations of ecological theory. We illustrate how inappropriate application of theory can be overcome or avoided by investment in boundary-spanning actions. The case studies also demonstrate how some of our proposed solutions could work, particularly the use of theory in secondary case studies after developing primary case studies without theory. When properly coordinated and implemented through a widely agreed upon and broadly respected international collaboration, the framework that we present will help to speed the progress of ecological research and lead to better conservation decisions.

A celebrity chef goes global : the business of eating

Purpose – This paper examines the internationalization strategy of Gordon Ramsay Holdings Ltd (GRH) from its base in London. While a substantial body of research on the strategic prerequisites for successful internationalization already exists, little attention has been given within this literature to the international growth of small, informally organized and entrepreneurially-driven firms. The discussion also identifies the challenges facing GRH as it strives to continue its international expansion.

Design/methodology/approach – The paper utilizes various published sources from the general press, business press and trade journals to examine the international expansion of GRH on the back of the personal brand the charismatic Gordon Ramsay has achieved in culinary and media circles. The growth of the GRH organization is interpreted through a theoretical framework of strategic capabilities and relationships.

Findings – The analysis illustrates how critical resources and capabilities, branded reputation, and strategic relationships established in GRH's home market have been leveraged effectively overseas. The most fundamental challenge facing GRH going forward is balancing the opportunities and pressures for growth against the need to maintain the highest levels of quality in existing establishments. This “balancing act” has to unfold within an empire in which the entrepreneur-emperor (Ramsay) has less and less time to devote to any particular activity or establishment.

Originality/value – The case illustrates the importance of developing and leveraging strategic capabilities and relationships in support of successful international expansion. Some of the unique challenges associated with the internationalization of small, informally organized and entrepreneurially-driven (and branded) firms are addressed in terms of both problems and solutions.

An efficient algorithm for partitioning and authenticating problem-solutions of elearning contents

Content authenticity and correctness is one of the important challenges in eLearning as there can be many solutions to one specific problem in cyber space. Therefore, the authors feel it is necessary to map problems to solutions using graph partition and weighted bipartite matching. This article proposes an efficient algorithm to partition question-answer (QA) space and explores the best possible solution to a particular problem. The approach described can be efficiently applied to social eLearning space where there are one-to-many and many-to-many relationships with a level of bonding. The main advantage of this approach is that it uses QA ranking by adjusted edge weights provided by subject-matter experts or the authors' expert database.

Feature nodes : an interaction construct for sharing initiative in design exploration

Exploration with formal design systems comprises an iterative process of specifying problems, finding plausible and alternative solutions, judging the validity of solutions relative to problems and reformulating problems and solutions. Recent advances in formal generative design have developed the mathematics and algorithms to describe and perform conceptual design tasks. However, design remains a human enterprise: formalisms are part of a larger equation comprising human computer interaction. To support the user in designing with formal systems, shared representations that interleave initiative of the designer and the design formalism are necessary. The problem of devising representational structures in which initiative is sometimes taken by the designer and sometimes by a computer in working on a shared design task is reported in this paper. To address this problem, the requirements, representation and
implementation of a shared interaction construct, the feature node, is
described. The feature node facilitates the sharing of initiative in formulating and reformulating problems, generating solutions, making
choices and navigating the history of exploration.

The domain layer for mixed-initiative interaction in generative design

The design space exploration formalism has developed data structures and algorithms of sufficient complexity and scope to support conceptual layout, massing, and enclosure configurations. However, design remains a human enterprise. To support the user in designing with the formalism, we have developed an interaction model that addresses the interleaving of user actions with the formal operations of design space exploration. The central feature of our interaction model is the modeling of control based on mixed-initiative. Initiative is sometimes taken by the designer and sometimes by the formalism in working on a shared design task. The model comprises three layers, domain, task, and dialogue. In this paper we describe the formulation of the domain layer of our mixed-initiative interaction model for design space exploration. We present the view of the domain as understood in the formalism in terms of the three abstract concepts of state, move, and structure. In order to support mixed initiative, it is necessary to develop a shared view of the domain. The domain layer addresses this problem by mapping the designer's view onto the symbol substrate. First, we present the designer's view of the domain in terms of problems, solutions, choices, and history. Second, we show how this view is interleaved with the symbol-substrate through four domain layer constructs, problem state, solution state, choice, and exploration history. The domain layer presents a suitable foundation for integrating the role of the designer with a description formalism. It enables the designer to maintain exploration freedom in terms of formulating and reformulating problems, generating solutions, making choices, and navigating the history of exploration.

A case for an international consortium on system-of-systems engineering

A system-of-systems (SoS) conceptualization is essential in resolving issues involving heterogeneous independently operable systems to achieve a unique purpose. Successful operation as an SoS requires communication among appropriate individuals and groups across enterprises through an effective protocol. This paper presents a position on the creation of a consortium of concerned system engineers and scientists worldwide to examine the problems and solutions strategies associated with SoS. The consortium could lead efforts in clarifying ambiguities and in seeking remedies to numerous open questions with respect to SoS analysis, SoS engineering (SoSE), as well as differences between systems engineering (SE) and SoSE. The mission of this consortium is envisioned to: 1) act as a neutral party; 2) provide a forum to put forth Calls to Action; and 3) establish a community of interest to recommend a set of solutions.

Sudden drawdown and drainage of a horizontal aquifer

Drainage of a saturated horizontal aquifer following a sudden drawdown is reanalyzed using the Boussinesq equation. The effect of the finite length of the aquifer is considered in detail. An analytical approximation based on a superposition principle yields a very good estimate of the outflow when compared to accurate numerical solutions. An illustration of the new analytical approach to analyze basin-scale field data is used to demonstrate possible field applications of the new solution.

Using spreadsheets in chemical education to avoid symbolic mathematics.

Traditionally, quantum theory has traditionally relied heavily on the use of  mathematics. However, there is a significant cohort of students who are  weak in mathematics, for example, students who are majoring in   biochemistry, biological sciences, etc. This paper reports on the use of  spreadsheets to generate approximate numerical solutions and visual  (graphical) descriptions as a method of avoiding or minimizing symbolic  manipulations, mathematical derivations and numerical computation. A  specific example from quantum theory is provided. Some aspects of  educational pedagogy of spreadsheet usage are discussed.

Lie symmetries of partial differential equations using symbolic computing

This study presents a theoretical basis for and outlines the method of finding the Lie point symmetries of systems of partial differential equations. It seeks to determine which of five computer algebra packages is best at finding these symmetries. The chosen packages are LIEPDE and DIMSYM for REDUCE, LIE and BIGLIE for MUMATH, DESOLV for MAPLE, and MATHLIE for MATHEMATICA. This work concludes that while all of the computer packages are useful, DESOLV appears to be the most successful system at determining the complete set of Lie symmetries. Also, the study describes REDUCEVAR, a new package for MAPLE, that reduces the number of independent variables in systems of partial differential equations, using particular Lie point symmetries. It outlines the results of some testing carried out on this package. It concludes that REDUCEVAR is a very useful tool in performing the reduction of independent variables according to Lie's theory and is highly accurate in identifying cases where the symmetries are not suitable for finding S/G equations.

A state space based approach in non-linear hemodynamic response modeling with fMRI data

In this paper we use the modified and integrated version of the balloon model in the analysis of fMRI data. We propose a new state space model realization for this balloon model and represent it with the standard A,B,C and D matrices widely used in system theory. A second order Padé approximation with equal numerator and denominator degree is used for the time delay approximation in the modeling of the cerebral blood flow. The results obtained through numerical solutions showed that the new state space model realization is in close agreement to the actual modified and integrated version of the balloon model. This new system theoretic formulation is likely to open doors to a novel way of analyzing fMRI data with real time robust estimators. With further development and validation, the new model has the potential to devise a generalized measure to make a significant contribution to improve the diagnosis and treatment of clinical scenarios where the brain functioning get altered. Concepts from system theory can readily be used in the analysis of fMRI data and the subsequent synthesis of filters and estimators.

Measuring the social inclusion of people with a disability in Australia : the first national 1-in-4 poll

 Measuring social inclusion of people with a disability in Australia: the first national 1-in-4 poll. Moore, M; Hagiliassis, N; McGillivray, J; Wilson, E; Campain, R; Graffam, J. & Bink, M. The ‘1-in-4 poll’ is a regular survey of people with a disability in Australia, beginning in 2010. Each survey will deal with a different topic with the first survey focusing on social inclusion. Social inclusion means being included in a society where we feel valued, and can participate in work, social and cultural activities. This conference paper explains how the first survey was developed. This involved looking at information from other research about the social inclusion of people with disability in Australia compared with the general population. Most surveys to date lack information about people with a disability. Our survey draws on questions asked in other surveys and will enable a better understanding of social inclusion for people with disability in Australia. This conference paper will also report on the problems and solutions of developing a survey that is easy to use and meaningful to a large population of people with a disability including people with an intellectual disability. This survey instrument will enable people with a disability to have a say about their social inclusion. There are three versions of the survey including an on-line version that works with a range of assistive technologies, an Easy English version with pictures, and a standard print version. Results from the survey will be shared with government with the aim of improving social inclusion for people with disability The conference paper shows how we have designed a survey that enables a very wide range of people with a disability to give information about their participation in society.