879 resultados para Fractional powers
Resumo:
The institution the police force has been established to protect citizens and their property from harm and predatory opportunism. However, there have been occasions when the very people assigned to protect become part of the predatory force against society. Predatory policing occurs when the police use their powers to extort money in the form of bribes. While, the concept is receiving attention in Europe but there have not been any direct studies in Australia. To overcome this research deficit and determine the extent, if any, of predatory policing in Australia data is interrogated from four police corruption inquiries in the Australian states of Queensland, New South Wales, Victoria and Western Australia. In addition, it examines the role of the type of networks used by corrupt police officers. The synthesis and application of public corruption and network literatures to the predatory policing domain provides new and relevant insights to assist those responsible for the administration of our institutions of justice. The paper concludes with a framework, drawn from the first stage of the project, to assist in the conceptualisation and monitoring of this public problem.
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The accuracy of data derived from linked-segment models depends on how well the system has been represented. Previous investigations describing the gait of persons with partial foot amputation did not account for the unique anthropometry of the residuum or the inclusion of a prosthesis and footwear in the model and, as such, are likely to have underestimated the magnitude of the peak joint moments and powers. This investigation determined the effect of inaccuracies in the anthropometric input data on the kinetics of gait. Toward this end, a geometric model was developed and validated to estimate body segment parameters of various intact and partial feet. These data were then incorporated into customized linked-segment models, and the kinetic data were compared with that obtained from conventional models. Results indicate that accurate modeling increased the magnitude of the peak hip and knee joint moments and powers during terminal swing. Conventional inverse dynamic models are sufficiently accurate for research questions relating to stance phase. More accurate models that account for the anthropometry of the residuum, prosthesis, and footwear better reflect the work of the hip extensors and knee flexors to decelerate the limb during terminal swing phase.
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This thesis develops a critical realist explanatory critique of alternative schooling programs for youth at risk taking place at three case study sites. Throughout the thesis the author pursues the question, \Are alternative provisions of schooling working academically and socially for youth at risk?. The academic lens targets literacy learning and associated pedagogies. Social outcomes are posited as positive social behaviours and continued engagement in learning. A four phased analysis, drawing on critical realism, interpretive and subject specific theories is used to elicit explanations for the research question. An overall framework is a critical realist methodology as set out by Danermark, Ekstrom, Jakobsen and Karlsson (2002, p. 129). Consequently phase one describes the phenomena of alternative schooling programs taking place at three case study sites. This is reported first as staff narratives that are resolved into imaginable historical causal components of \generative events., \prior schooling structures., \models of alternative schooling., \purpose., \individual agency., and \relations with linked community organisations.. Then transcendental questions are posed about each component using retroduction to uncover structures, underlying mechanisms and powers, and individual agency. In the second phase the researcher uses modified grounded theory methodology to theoretically redescribe causal categories related to a \needed different teaching and administrative approach. that emerged from the previous critique. A transcendental question is then applied to this redescription. The research phenomena are again theoretically redescribed in the third phase, this time using three theoretically based constructs associated with literacy and literacy pedagogies; the NRS, the 4 Resources Model, and Productive Pedagogies. This redescription is again questioned in terms of its core or \necessary. components. The fourth phase makes an explanatory critique by comparing and critiquing all previous explanations, recontextualising them in a wider macro reality of alternative schooling. Through this critical realist explanatory critiquing process, a response emerges not only to whether alternative provisions of schooling are working, but also how they are working, and how they are not working, with realistically based implications for future improvement.
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This research investigated underlying issues that were critical to the success of the bifocal trial and comprised of three studies. The first study evaluated if Chinese-Canadian children were suitable subjects for the bifocal trial. The high prevalence of myopia in Chinese children suggests that genetic input plays a role in myopia development, but the rapid increase in prevalence over the last few decades indicates environmental factors are also important. Since this bifocal trial was conducted in Canada, this work aimed to determine whether Chinese children who had migrated to Canada would still have high myopia prevalence and a high rate of myopia progression. The second study determined the optimal bifocal lens power for myopia treatment and the effect of incorporating base-in prism into the bifocal. In the majority of published myopia control studies, the power of the prescribed near addition was usually predetermined in the belief that the near addition would always help to improve the near focus. In fact, the effect of near addition on the accommodative error might be quite different even for individuals in which the same magnitude of accommodation lag had been measured. Therefore, this work was necessary to guide the selection of bifocal and prism powers most suitable for the subsequent bifocal trial. The third study, the ultimate goal of this research, was to conduct a longitudinal clinical trial to determine if bifocals and prismatic bifocals could control myopia progression in children.
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Matrix function approximation is a current focus of worldwide interest and finds application in a variety of areas of applied mathematics and statistics. In this thesis we focus on the approximation of A^(-α/2)b, where A ∈ ℝ^(n×n) is a large, sparse symmetric positive definite matrix and b ∈ ℝ^n is a vector. In particular, we will focus on matrix function techniques for sampling from Gaussian Markov random fields in applied statistics and the solution of fractional-in-space partial differential equations. Gaussian Markov random fields (GMRFs) are multivariate normal random variables characterised by a sparse precision (inverse covariance) matrix. GMRFs are popular models in computational spatial statistics as the sparse structure can be exploited, typically through the use of the sparse Cholesky decomposition, to construct fast sampling methods. It is well known, however, that for sufficiently large problems, iterative methods for solving linear systems outperform direct methods. Fractional-in-space partial differential equations arise in models of processes undergoing anomalous diffusion. Unfortunately, as the fractional Laplacian is a non-local operator, numerical methods based on the direct discretisation of these equations typically requires the solution of dense linear systems, which is impractical for fine discretisations. In this thesis, novel applications of Krylov subspace approximations to matrix functions for both of these problems are investigated. Matrix functions arise when sampling from a GMRF by noting that the Cholesky decomposition A = LL^T is, essentially, a `square root' of the precision matrix A. Therefore, we can replace the usual sampling method, which forms x = L^(-T)z, with x = A^(-1/2)z, where z is a vector of independent and identically distributed standard normal random variables. Similarly, the matrix transfer technique can be used to build solutions to the fractional Poisson equation of the form ϕn = A^(-α/2)b, where A is the finite difference approximation to the Laplacian. Hence both applications require the approximation of f(A)b, where f(t) = t^(-α/2) and A is sparse. In this thesis we will compare the Lanczos approximation, the shift-and-invert Lanczos approximation, the extended Krylov subspace method, rational approximations and the restarted Lanczos approximation for approximating matrix functions of this form. A number of new and novel results are presented in this thesis. Firstly, we prove the convergence of the matrix transfer technique for the solution of the fractional Poisson equation and we give conditions by which the finite difference discretisation can be replaced by other methods for discretising the Laplacian. We then investigate a number of methods for approximating matrix functions of the form A^(-α/2)b and investigate stopping criteria for these methods. In particular, we derive a new method for restarting the Lanczos approximation to f(A)b. We then apply these techniques to the problem of sampling from a GMRF and construct a full suite of methods for sampling conditioned on linear constraints and approximating the likelihood. Finally, we consider the problem of sampling from a generalised Matern random field, which combines our techniques for solving fractional-in-space partial differential equations with our method for sampling from GMRFs.
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In this paper, we consider a modified anomalous subdiffusion equation with a nonlinear source term for describing processes that become less anomalous as time progresses by the inclusion of a second fractional time derivative acting on the diffusion term. A new implicit difference method is constructed. The stability and convergence are discussed using a new energy method. Finally, some numerical examples are given. The numerical results demonstrate the effectiveness of theoretical analysis
Resumo:
Financial processes may possess long memory and their probability densities may display heavy tails. Many models have been developed to deal with this tail behaviour, which reflects the jumps in the sample paths. On the other hand, the presence of long memory, which contradicts the efficient market hypothesis, is still an issue for further debates. These difficulties present challenges with the problems of memory detection and modelling the co-presence of long memory and heavy tails. This PhD project aims to respond to these challenges. The first part aims to detect memory in a large number of financial time series on stock prices and exchange rates using their scaling properties. Since financial time series often exhibit stochastic trends, a common form of nonstationarity, strong trends in the data can lead to false detection of memory. We will take advantage of a technique known as multifractal detrended fluctuation analysis (MF-DFA) that can systematically eliminate trends of different orders. This method is based on the identification of scaling of the q-th-order moments and is a generalisation of the standard detrended fluctuation analysis (DFA) which uses only the second moment; that is, q = 2. We also consider the rescaled range R/S analysis and the periodogram method to detect memory in financial time series and compare their results with the MF-DFA. An interesting finding is that short memory is detected for stock prices of the American Stock Exchange (AMEX) and long memory is found present in the time series of two exchange rates, namely the French franc and the Deutsche mark. Electricity price series of the five states of Australia are also found to possess long memory. For these electricity price series, heavy tails are also pronounced in their probability densities. The second part of the thesis develops models to represent short-memory and longmemory financial processes as detected in Part I. These models take the form of continuous-time AR(∞) -type equations whose kernel is the Laplace transform of a finite Borel measure. By imposing appropriate conditions on this measure, short memory or long memory in the dynamics of the solution will result. A specific form of the models, which has a good MA(∞) -type representation, is presented for the short memory case. Parameter estimation of this type of models is performed via least squares, and the models are applied to the stock prices in the AMEX, which have been established in Part I to possess short memory. By selecting the kernel in the continuous-time AR(∞) -type equations to have the form of Riemann-Liouville fractional derivative, we obtain a fractional stochastic differential equation driven by Brownian motion. This type of equations is used to represent financial processes with long memory, whose dynamics is described by the fractional derivative in the equation. These models are estimated via quasi-likelihood, namely via a continuoustime version of the Gauss-Whittle method. The models are applied to the exchange rates and the electricity prices of Part I with the aim of confirming their possible long-range dependence established by MF-DFA. The third part of the thesis provides an application of the results established in Parts I and II to characterise and classify financial markets. We will pay attention to the New York Stock Exchange (NYSE), the American Stock Exchange (AMEX), the NASDAQ Stock Exchange (NASDAQ) and the Toronto Stock Exchange (TSX). The parameters from MF-DFA and those of the short-memory AR(∞) -type models will be employed in this classification. We propose the Fisher discriminant algorithm to find a classifier in the two and three-dimensional spaces of data sets and then provide cross-validation to verify discriminant accuracies. This classification is useful for understanding and predicting the behaviour of different processes within the same market. The fourth part of the thesis investigates the heavy-tailed behaviour of financial processes which may also possess long memory. We consider fractional stochastic differential equations driven by stable noise to model financial processes such as electricity prices. The long memory of electricity prices is represented by a fractional derivative, while the stable noise input models their non-Gaussianity via the tails of their probability density. A method using the empirical densities and MF-DFA will be provided to estimate all the parameters of the model and simulate sample paths of the equation. The method is then applied to analyse daily spot prices for five states of Australia. Comparison with the results obtained from the R/S analysis, periodogram method and MF-DFA are provided. The results from fractional SDEs agree with those from MF-DFA, which are based on multifractal scaling, while those from the periodograms, which are based on the second order, seem to underestimate the long memory dynamics of the process. This highlights the need and usefulness of fractal methods in modelling non-Gaussian financial processes with long memory.
Resumo:
Researching administrative history is problematical. A trail of authoritative documents is often hard to find; and useful summaries can be difficult to organise, especially if source material is in paper formats in geographically dispersed locations. In the absence of documents, the reasons for particular decisions and the rationale underpinning particular policies can be confounded as key personnel advance in their professions and retire. The rationale for past decisions may be lost for practical purposes; and if an organisation’s memory of events is diminished, its learning through experience is also diminished. Publishing this document tries to avoid unnecessary duplication of effort by other researchers that need to venture into how policies of charging for public sector information have been justified. The author compiled this work within a somewhat limited time period and the work does not pretend to be a complete or comprehensive analysis of the issues.----- A significant part of the role of government is to provide a framework of legally-enforceable rights and obligations that can support individuals and non-government organisations in their lawful activities. Accordingly, claims that governments should be more ‘business-like’ need careful scrutiny. A significant supply of goods and services occurs as non-market activity where neither benefits nor costs are quantified within conventional accounting systems or in terms of money. Where a government decides to provide information as a service; and information from land registries is archetypical, the transactions occur as a political decision made under a direct or a clearly delegated authority of a parliament with the requisite constitutional powers. This is not a market transaction and the language of the market confuses attempts to describe a number of aspects of how governments allocate resources.----- Cost recovery can be construed as an aspect of taxation that is a sole prerogative of a parliament. The issues are fundamental to political constitutions; but they become more complicated where states cede some taxing powers to a central government as part of a federal system. Nor should the absence of markets be construed necessarily as ‘market failure’ or even ‘government failure’. The absence is often attributable to particular technical, economic and political constraints that preclude the operation of markets. Arguably, greater care is needed in distinguishing between the polity and markets in raising revenues and allocating resources; and that needs to start by removing unhelpful references to ‘business’ in the context of government decision-making.
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Compares the Chinese Securities and Regulatory Commission's guidelines for articles of association of listed companies issued in 2006 with 'replaceable' rules in the Australian Corporations Act 2001. Discusses the provisions of the Chinese guidelines and the Australian rules on corporate constitution, interpretation, a company's representative, object clauses, shareholders' powers and meetings and directors. Questions whether the Chinese guidelines facilitate effective corporate governance.
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We investigate the roles of finn and country level agency conflicts in determining corporate payout policics. Based on a large sample of 29,610 firms in 42 countries from 2001 to 2006, we show there is a form of "pecking order" in investors' ability to extract cash (whether as dividends only or share repurchases) from firms. Although investors are able to use their legal powers to extract cash from firms in high protection countries, their ability to do so can be substantially hindered when agency costs at the firm level are high. In poor protection countries, investors seem to take whatever cash they can get, even though the amount may be small, and with scant regard for investment opportunities and firm level agency conflicts. Finally, compared to repurchases, we find dividends are more likely to be the sole method of payout in high protection countries and in non insider-dominated firms.
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Ecological networks are often represented as utopian webs of green meandering through cities, across states, through regions and even across a country (Erickson, 2006, p.28; Fabos, 2004, p.326; Walmsley, 2006). While this may be an inspiring goal for some in developed countries, the reality may be somewhat different in developing countries. China, in its shift to urbanisation and suburbanisation, is also being persuaded to adjust its planning schemes according to these aspirational representations of green spaces (Yu et al, 2006, p.237; Zhang and Wang, 2006, p.455). The failure of other countries to achieve regional goals of natural and cultural heritage protection on the ground in this way (Peterson et al, 2007; Ryan et al, 2006; von Haaren and Reich, 2006) suggests that there may be flaws in the underpinning concepts that are widely circulated in North American and Western European literature (Jongman et al, 2004; Walmsley, 2006). In China, regional open space networks, regional green infrastructure or regional ecological corridors as we know them in the West, are also likely to be problematic, at least in the foreseeable future. Reasons supporting this view can be drawn from lessons learned from project experience in landscape planning and related fields of study in China and overseas. Implementation of valuable regional green space networks is problematic because: • the concept of region as a spatial unit for planning green space networks is ambiguous and undefinable for practical purposes; • regional green space networks traditionally require top down inter-governmental cooperation and coordination which are generally hampered by inequalities of influence between and within government agencies; • no coordinating body with funding powers exists for regional green space development and infrastructure authorities are still in transition from engineering authorities; • like other infrastructure projects, green space is likely to become a competitive rather than a complementary resource for city governments; • stable long-term management, maintenance and uses of green space networks must fit into a ‘family’ social structure rather than a ‘public good’ social structure, particularly as rural and urban property rights are being re-negotiated with city governments; and • green space provision is a performance indicator of urban improvement in cities within the city hierarchy and remains quantitatively-based (land area, tree number and per capita share) rather than qualitatively-based with local people as the focus.
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This chapter is about the role of law in the creation and operation of Australian health systems. Accordingly, this chapter discusses how law regulates the way in which health services in Australia are funded, organised, regulated, managed, operated and governed. (The question of how health professionals are regulated is discussed in Chapter 15.) Although the focus of much of health law is on legal mechanisms for the resolution of disputes or disagreements between the state, health providers, professionals, patients and families and friends, and through dispute resolutions processes setting standards for practice, these are only some of the “jobs” that health law performs. In health systems where the state undertakes a significant role in regulating, funding, managing and providing health services, health law also performs an important constitutive function. Health law declares the values upon which the health system is based, shapes social processes to achieve public ends and provides a structure for the complex interactions that occur within a modern health system. Health law regulates decision-makers in health systems by establishing who has the power to participate in decisions and in what circumstances, establishing processes through which decisions are made and creating mechanisms for decision-makers to be held publicly accountable. It is this broader constitutive function of health law that is a primary focus of much of this chapter — how and why governments use their legislative powers to structure and shape the health system.
Resumo:
Recently, the numerical modelling and simulation for anomalous subdiffusion equation (ASDE), which is a type of fractional partial differential equation( FPDE) and has been found with widely applications in modern engineering and sciences, are attracting more and more attentions. The current dominant numerical method for modelling ASDE is Finite Difference Method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings. This paper aims to develop an implicit meshless approach based on the radial basis functions (RBF) for numerical simulation of the non-linear ASDE. The discrete system of equations is obtained by using the meshless shape functions and the strong-forms. The stability and convergence of this meshless approach are then discussed and theoretically proven. Several numerical examples with different problem domains are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. The results obtained by the meshless formulations are also compared with those obtained by FDM in terms of their accuracy and efficiency. It is concluded that the present meshless formulation is very effective for the modeling and simulation of the ASDE. Therefore, the meshless technique should have good potential in development of a robust simulation tool for problems in engineering and science which are governed by the various types of fractional differential equations.