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.

Exempt treatment of financial intermediation services under a value-added tax: an assessment of alternatives

Most countries with a value-added tax (VAT) exempt financial intermediation services from the tax. While exemption is generally perceived to be undesirable, it is also widely regarded as unavoidable because of technical difficulties in applying VAT to these services. This article reviews the standard rationale for exempt treatment and then considers the relative merits of two recent challenges raised in the tax literature. The first challenge involves the application of cash flow taxation to financial intermediation services in a manner that is consistent with an invoice/credit VAT (which is the dominant form). The second challenge proposes a comprehensive system of zero-rating of financial intermediation services, which is supported by a characterization of the household consumption of such services as non-taxable. The author argues that each of these alternatives to an exemption system suffers from both theoretical and practical implementation difficulties that make maintenance of exempt treatment the preferred approach, at least in the short term. There is, however, a simpler alternative to these fundamental reform options, involving modification of just one aspect of an exemption system to relieve some of its more problematic aspects. Many of the interpretative problems and associated inefficiencies that plague an exemption system arise from the need to distinguish between taxable and exempt financial services. The author argues that these difficulties can be eliminated, to a large extent, by basing the distinction on the form of prices. In support of this approach, he points out that it is consistent with the underlying reasons for the application of exempt treatment. The author considers a number of other possible modifications, but these are either rejected outright or viewed with a healthy skepticism. For example, the author is critical of the apparent rationale for the application of cash flow taxation to property and casualty insurers. He also rejects proposals that accept some looseness in the formulaic allocation by financial intermediaries of the costs of business inputs between exempt and taxable services for input credit purposes. In his view, an explicit reliance on pricing structures to draw the boundary between exempt and taxable services is preferable to the provision of relief for blocked input tax credits of financial intermediaries. Finally, the author is skeptical of the case for a policy response intended to address the tax bias under an exemption system for financial intermediaries to insource supplies.

Accounting problems and issues in cases of municipal boundary changes

Analyses the methodologies and accounting treatments used for the transfer of assets, liabilities, revenues and expenses resulting from municipal restructuring in Victoria during the early 1990s. It was found that most municipalities adopted simple or pragmatic methods, whereby fixed assets and associated liabilities were allocated physically avoiding the need for financial valuations.

Simulation of condensation problems in a roller-skating centre

A commercial roller-skating centre in southern Australia had condensation problems on both the roof and floor. The building is a typical warehouse-type structure with a high level of natural ventilation due to poor construction and permanently open vents. A computer model of the building, using the thermal simulation software TRNSYS, was calibrated from a sensitivity analysis of three key parameters, namely air exchange rate, roof surface heat transfer coefficient and deep ground temperature. The predicted times of condensation on the roof were compared with site observations. The time of year was predicted with acceptable accuracy, although earlier in the morning than had been observed. The effect of installing foil insulation in the roof was simulated. Under normal winter conditions, this modification was enough to stop the condensation. However, in unusually cold and humid conditions, condensation still occurred on both surfaces. This was overcome by heating the floor (15 W/m 2 ) for approximately eight hours. Subsequent modifications have demonstrated the value of the simulations.

Analysis of the potential and problems of new institutional economics for third world development

Purpose – The aim of this paper is to provide a critical evaluation of the potential of new institutional economics (NIE) in third world development.

Design/methodology/approach – The paper reviews various theories under NIE from both conceptual and empirical perspectives. It then reviews the various definitions of institutions and show that institutions are essential to overcome problems of information and uncertainty.

Findings – The review finds that weak institutions can undermine development and hence governments in developing countries should strengthen their institutions to provide greater scope for efficient functioning of markets. Where the market does not work owing to high transactions costs, traditional institutions of collective action and group decision making can work and hence need to be recognised.

Research limitations/implications – The major implications of the paper is that in developing countries, a clear understanding of various institutions such as user groups, inter-linked credit markets, rotational irrigation etc. is needed before they are replaced or modified by other institutions. The main limitations of NIE are that there can be capture by elites of various institutional innovations in rural areas, and that it does not explicitly consider income distribution and uncertainty which are glossed over and hence remain areas for future research.

Originality/value – This paper critically reviews the various institutional environments that developing countries face in addressing development issues.

Council amalgamations and restructuring in Victoria: how did we value the assets and liabilities?

This study aimed to identify and critically analyse the methodologies and accounting treatments adopted in the transfer of assets, liabilities, revenues and expenses resultingfrom municipal boundary changes associated with municipal restructuring (amalgamations) in Victoria during the early 1990s. In involved the collection and use of oral evidence obtained from officers of a sample of entities engaged in the process and focused on identifying and examining the methodologies used by municipalities. It has also been shown that local government is different from the commercial domain and the accounting profession has not adequately addressed some of these differences.

Accounting for local government boundary changes in South Australia : valuing assets and liabilities or valuing revenue streams

This paper examines the methodologies adopted in the transfer of assets, liabilities, revenues and expenses resulting from boundary changes associated with municipal amalgamations in South Australia during the late 1990s. It investigates the methods employed for apportioning these financial elements, valuations used and financial settlements required. Significant transfers occurred in only three cases. In two cases, councils used simple, pragmatic methods to apportion assets and liabilities, similar to those used previously in Victoria. In the third case a transfer price was calculated based on the net present value of revenues. This method is quite different from previous methods examined and is appropriate where one council will make significant future gains at another council's loss because of net revenue transfers.

Are youth mentoring programs good value-for-money? An evaluation of the Big Brothers Big Sisters Melbourne program

Background : The Big Brothers Big Sisters (BBBS) program matches vulnerable young people with a trained, supervised adult volunteer as mentor. The young people are typically seriously disadvantaged, with multiple psychosocial problems.

Methods : Threshold analysis was undertaken to determine whether investment in the program was a worthwhile use of limited public funds. The potential cost savings were based on US estimates of life-time costs associated with high-risk youth who drop out-of-school and become adult criminals. The intervention was modelled for children aged 10–14 years residing in Melbourne in 2004.

Results : If the program serviced 2,208 of the most vulnerable young people, it would cost AUD 39.5 M. Assuming 50% were high-risk, the associated costs of their adult criminality would be AUD 3.3 billion. To break even, the program would need to avert high-risk behaviours in only 1.3% (14/1,104) of participants.

Conclusion : This indicative evaluation suggests that the BBBS program represents excellent 'value for money'.

An agent-based approach to value theory and wealth distribution in economics

Any attempt to model an economy requires foundational assumptions about the relations between prices, values and the distribution of wealth. These assumptions exert a profound influence over the results of any model. Unfortunately, there are few areas in economics as vexed as the theory of value. I argue in this paper that the fundamental problem with past theories of value is that it is simply not possible to model the determination of value, the formation of prices and the distribution of income in a real economy with analytic mathematical models. All such attempts leave out crucial processes or make unrealistic assumptions which significantly affect the results. There have been two primary approaches to the theory of value. The first, associated with classical economists such as Ricardo and Marx were substance theories of value, which view value as a substance inherent in an object and which is conserved in exchange. For Marxists, the value of a commodity derives solely from the value of the labour power used to produce it - and therefore any profit is due to the exploitation of the workers. The labour theory of value has been discredited because of its assumption that labour was the only ‘factor’ that contributed to the creation of value, and because of its fundamentally circular argument. Neoclassical theorists argued that price was identical with value and was determined purely by the interaction of supply and demand. Value then, was completely subjective. Returns to labour (wages) and capital (profits) were determined solely by their marginal contribution to production, so that each factor received its just reward by definition. Problems with the neoclassical approach include assumptions concerning representative agents, perfect competition, perfect and costless information and contract enforcement, complete markets for credit and risk, aggregate production functions and infinite, smooth substitution between factors, distribution according to marginal products, firms always on the production possibility frontier and firms’ pricing decisions, ignoring money and credit, and perfectly rational agents with infinite computational capacity. Two critical areas include firstly, the underappreciated Sonnenschein-Mantel- Debreu results which showed that the foundational assumptions of the Walrasian general-equilibrium model imply arbitrary excess demand functions and therefore arbitrary equilibrium price sets. Secondly, in real economies, there is no equilibrium, only continuous change. Equilibrium is never reached because of constant changes in preferences and tastes; technological and organisational innovations; discoveries of new resources and new markets; inaccurate and evolving expectations of businesses, consumers, governments and speculators; changing demand for credit; the entry and exit of firms; the birth, learning, and death of citizens; changes in laws and government policies; imperfect information; generalized increasing returns to scale; random acts of impulse; weather and climate events; changes in disease patterns, and so on. The problem is not the use of mathematical modelling, but the kind of mathematical modelling used. Agent-based models (ABMs), objectoriented programming and greatly increased computer power however, are opening up a new frontier. Here a dynamic bargaining ABM is outlined as a basis for an alternative theory of value. A large but finite number of heterogeneous commodities and agents with differing degrees of market power are set in a spatial network. Returns to buyers and sellers are decided at each step in the value chain, and in each factor market, through the process of bargaining. Market power and its potential abuse against the poor and vulnerable are fundamental to how the bargaining dynamics play out. Ethics therefore lie at the very heart of economic analysis, the determination of prices and the distribution of wealth. The neoclassicals are right then that price is the enumeration of value at a particular time and place, but wrong to downplay the critical roles of bargaining, power and ethics in determining those same prices.

Spinoza/space/speed/sublime: Problems of philosophy and politics in the post-colonial fiction of Gerald Murnane

This article takes account of the ‘spontaneity’ of the post-colonial fiction of Gerald Murnane within the ‘dominating space’ of the philosophy of Spinoza. My use of Paul Carter’s terms here is strategic. The compact of fiction and philosophy in Murnane corresponds with the relationship of spontaneity to the dominating organization of desire in Carter’s rendering of an Aboriginal hunter. Carter’s phrase “‘a figure at once spontaneous and wholly dominated by the space of his desire’” worries Ken Gelder and Jane M. Jacobs, who suggest that it subjugates the formation of Aboriginal desire (incorporating spontaneity) to impulses of imperialism. The captivating immanence of Spinoza’s philosophy in Murnane’s fiction, which I will demonstrate with various examples, puts pressure on the fiction to occupy the same space as the space of the philosophy. Here is a clue to why Murnane’s post-colonial thematics have been little explored by critics with an interest in post-colonial politics. The desire of Spinoza’s philosophy creates a spatial textuality within which the spontaneity of Murnane’s fiction, to the degree that it maximizes or fills the philosophy, is minimized in its political effects. That is to say, the fiction shifts politics into an external space of what Roland Barthes calls “resistance or condemnation”. However, the different speeds (or timings) of Murnane and Spinoza, within the one space, mitigate this resistance of the outside, at least in respect of certain circumstances of post-coloniality. It is especially productive, I suggest, to engage Carter’s representation of an Aboriginal hunter through the compact of coincidental spaces and differential speeds created by Murnane’s fiction in Spinoza’s philosophy. This produces a ceaseless activation of desire and domination, evidenced in Murnane’s short story ‘Land Deal’, and indexed by a post-Romantic sublime. What limits the value of Murnane’s fiction in most contexts of post-colonial politics, is precisely what makes it useful in the matter of Carter’s Aboriginal hunter.

The principle of legality as clear statement rule: significance and problems

In Australia, the common law principle of legality has hardened into a strong clear statement rule that is applied when legislation engages common law rights and freedoms. It has transformed a loose collection of rebuttable interpretive presumptions into a quasi-constitutional common law bill of rights. However, these developments are not without controversy or issue. The analysis undertaken in this article suggests that the principle of legality as clear statement rule -- as mandated by the High Court in Coco v The Queen -- can only work legitimately if Parliament has clear and prior notice of the rights and freedoms that it operates to protect. But it is problematic if what a common law right, such as freedom of speech, requires or guarantees in any given legislative context is unclear and contested, and so must be judicially divined at the point of application. In these cases, the principle operates to enforce a (post-legislative) judicial approximation of what best protects and promotes an abstract legal value or principle. It amounts to the illegitimate judicial remaking of prior legislative decisions on rights. This undercuts the normative justifications for the principle of legality as it obscures from Parliament the common law (rights) backdrop against which its legislation is enacted and interpreted.

Development and evaluation of a screening tool to identify people with diabetes at increased risk of medication problems relating to hypoglycaemia and medication non-adherence

Abstract Aims: To develop and evaluate a screening tool to identify people with diabetes at increased risk of medication problems relating to hypoglycaemia and medication non-adherence. Methods: A retrospective audit of attendances at a diabetes outpatient clinic at a public, teaching hospital over a 16-month period was conducted. Logistic regression was undertaken to examine risk factors associated with medication problems relating to hypoglycaemia and medication non-adherence and the most predictive set of factors comprise the Diabetes Medication Risk Screening Tool. Evaluating the tool involved assessing sensitivity and specificity, positive and negative predictive values, cut-off scores, inter-rater reliability, and content validity. Results: The Diabetes Medication Risk Screening Tool comprises seven predictive factors: age, living alone, English language, mental and behavioural problems, comorbidity index score, number of medications prescribed, and number of high-risk medications prescribed. The tool has 76.5% sensitivity, 59.5% specificity, and has a 65.1% positive predictive value, and a 71.8% negative predictive value. A score of 27 or more out of 62 was associated with high-risk of a medication problem. The inter-rater reliability of the tool was high (κ = 0.79, 95% CI 0.75 - 0.84) and the content validity index was 99.4%. Conclusion: The Diabetes Medication Risk Screening Tool has good psychometric properties and can proactively identify people with diabetes at greatest risk of medication problems relating to hypoglycaemia and medication non-adherence.

Problems and prospects for corporate governance in Bangladesh: Some case studies basis analysis

Bangladesh is one of the least economically developed countries in the world. A lack of corporate governance creates problem for the economic development of the country. This study has been undertaken to observe whether corporate governance is being well-executed in Bangladesh and to inform views about which approach to corporate governance will be more acceptable to the county. The study has examined six cases to see whether corporate governance is properly utilised in the country. It is suggested that monetary, fiscal and exchange rate policies should be applied with appropriate diligence by the Securities and Exchange Commission, the Bangladesh Bank and the National Board of Revenue. It is expected that value can be added through arranging primary and supportive activities. Attention to inbound and outbound logistics is likely to improve productivity, enhancing profitability, long run sustainability and creating distinct competencies for the Bangladesh economy. Ultimately this may help to improve gross domestic product and the basic needs of the population.

Investor protection, firm informational problems, big N auditors, and cost of debt around the world

This paper examines the effects of investor protection, firm informational problems (proxied by firm size, firm age, and the number of analysts following), and Big N auditors on firms' cost of debt around the world. Using data from 1994 to 2006 and over 90,000 firm-year observations, we find that the cost of debt is lower when firms are audited by Big N auditors, especially in countries with strong investor protection. Second, we find that firms with more informational problems (i.e., higher information asymmetry problems) benefit more from Big N auditors in terms of lower cost of debt only in countries with stronger investor protection.

Changes in Australian injecting drug users’ mental health problems and service uptake from 2006-2012

Purpose– The purpose of this paper is to assess changes in rates of mental health problems and service utilisation for Australian regular injecting drug users (IDUs) from 2006 to 2012. Design/methodology/approach – Data were taken from Illicit Drug Reporting System national surveys with 914 regular IDUs in 2006 and 883 in 2012. Changes in rates of self-reported mental health problems and service use were assessed. Findings – Rates of self-reported mental health problems increased from 38.3 per cent in 2006 to 43.7 per cent in 2012 – mainly due to increases in anxiety rates. Conversely, there was a decrease in mental health service use from 70.2 to 58.4 per cent by 2012. However, there was a proportional increase in the use of psychologists. These trends remained after controlling for socio-demographic and medical differences between the 2006/2012 samples. K10 scores for 2012 participants validated the use of the self-report measures. Practical implications – Reductions in stigma, improvements in mental health literacy, and modest increases in anxiety may explain increases in self-report of mental health problems. Stagnant service utilisation rates in an expanding population willing to self-report may explain decreasing service use. The introduction of key mental health reforms also may have contributed, particularly with the increase in psychologist access. This paper highlights the need for improved population monitoring of mental health in disadvantaged groups such as IDUs. Originality/value – This paper is the first to assess changes in mental health outcomes over time in Australian IDUs. This examination covered a critical era in the mental health landscape, with significant increases in public awareness campaigns and major mental health reforms.