Problem solving for the 21st century

Mathematical problem solving has been the subject of substantial and often controversial research for several decades. We use the term, problem solving, here in a broad sense to cover a range of activities that challenge and extend one’s thinking. In this chapter, we initially present a sketch of past decades of research on mathematical problem solving and its impact on the mathematics curriculum. We then consider some of the factors that have limited previous research on problem solving. In the remainder of the chapter we address some ways in which we might advance the fields of problem-solving research and curriculum development.

Three Carrier Ambiguity Resolutions : Generalised problems, models and solutions

In this paper, the problems of three carrier phase ambiguity resolution (TCAR) and position estimation (PE) are generalized as real time GNSS data processing problems for a continuously observing network on large scale. In order to describe these problems, a general linear equation system is presented to uniform various geometry-free, geometry-based and geometry-constrained TCAR models, along with state transition questions between observation times. With this general formulation, generalized TCAR solutions are given to cover different real time GNSS data processing scenarios, and various simplified integer solutions, such as geometry-free rounding and geometry-based LAMBDA solutions with single and multiple-epoch measurements. In fact, various ambiguity resolution (AR) solutions differ in the floating ambiguity estimation and integer ambiguity search processes, but their theoretical equivalence remains under the same observational systems models and statistical assumptions. TCAR performance benefits as outlined from the data analyses in some recent literatures are reviewed, showing profound implications for the future GNSS development from both technology and application perspectives.

Some critical legal issues affecting insurance transaction globally

Increasingly, major insurers and reinsurers are operating on a global basis. For example, General Re Corporation and Cologne Re operate in almost 150 countries : see "General Re Corporation 1999 Annual Report". This is also true for the world's major brokers, and the emergence of large broking conglomerates such as Aon and Marsh are good examples of global service providers. Against the background of this increasingly global insurance market with global participants, there are a range of common legal issues in this article but a selection of certain critical matters are canvassed in the secitons below. First there are a range of regulatory issues that must be addressed. Secondly globalisation of the industry does create added incentive for a common legal regime to cover the formation of insurance transactions and the resolution of disputes about claims, coverage and termination. In this contect codifcation of insurance laws is a critical issue. Thirdly, major advances in genetic research and biotechnology over recent years have resulted in a dramatic increase in the availability of genetic testing. These developments have given rise to concerns worldwide about the potential for misuse of genetic information by third parties such as insurers and employers. Fourthly, the essence of an insurance transaction is the transference of risk from one person to anther. It is generally accepted that this transference should occur in informed circumstances and without undue advantage being bestowed upon either party. Finally this article will consider some legal matter in relation to transacting insurance on the internet

Beyond charity : outlines of a jurisprudence for civil society

There is not a single, coherent, jurisprudence for civil society organisations. Pressure for a clearly enuciated body of law applying to the whole of this sector of society continues to increase. The rise of third sector scholarship, the retreat of the welfare state, the rediscovery of the concept of civil society and pressures to strengthen social capital have all contributed to an ongoing stream of inquiry into the laws that regulate and favour civil society organisations. There have been almost thirty inquiries over the last sixty years into the doctrine of charitable purpose in common law countries. Those inquiries have established that problems with the law applying to civil society organisations are rooted in the common law adopting a ‘technical’ definition of charitable purpose and the failure of this body of law to develop in response to societal changes. Even though it is now well recognised that problems with law reform stem from problems inherent in the doctrine of charitable purpose, statutory reforms have merely ‘bolted on’ additions to the flawed ‘technical’ definition. In this way the scope of operation of the law has been incrementally expanded to include a larger number of civil society organisations. This piecemeal approach continues the exclusion of most civil society organisations from the law of charities discourse, and fails to address the underlying jurisprudential problems. Comprehensive reform requires revisiting the foundational problems embedded in the doctrine of charitable purpose, being informed by recent scholarship, and a paradigm shift that extends the doctrine to include all civil society organisations. Scholarly inquiry into civil society organisations, particularly from within the discipline of neoclassical economics, has elucidated insights that can inform legal theory development. This theory development requires decoupling the two distinct functions performed by the doctrine of charitable purpose which are: setting the scope of regulation, and determining entitlement to favours, such as tax exemption. If the two different functions of the doctrine are considered separately in the light of theoretical insights from other disciplines, the architecture for a jurisprudence emerges that facilitates regulation, but does not necessarily favour all civil society organisations. Informed by that broader discourse it is argued that when determining the scope of regulation, civil society organisations are identified by reference to charitable purposes that are not technically defined. These charitable purposes are in essence purposes which are: Altruistic, for public Benefit, pursued without Coercion. These charitable puposes differentiate civil society organisations from organisations in the three other sectors namely; Business, which is manifest in lack of altruism; Government, which is characterised by coercion; and Family, which is characterised by benefits being private not public. When determining entitlement to favour, it is theorised that it is the extent or nature of the public benefit evident in the pursuit of a charitable purpose that justifies entitlement to favour. Entitlement to favour based on the extent of public benefit is the theoretically simpler – the greater the public benefit the greater the justification for favour. To be entitled to favour based on the nature of a purpose being charitable the purpose must fall within one of three categories developed from the first three heads of Pemsel’s case (the landmark categorisation case on taxation favour). The three categories proposed are: Dealing with Disadvantage, Encouraging Edification; and Facilitating Freedom. In this alternative paradigm a recast doctrine of charitable purpose underpins a jurisprudence for civil society in a way similar to the way contract underpins the jurisprudence for the business sector, the way that freedom from arbitrary coercion underpins the jurisprudence of the government sector and the way that equity within families underpins succession and family law jurisprudence for the family sector. This alternative architecture for the common law, developed from the doctrine of charitable purpose but inclusive of all civil society purposes, is argued to cover the field of the law applying to civil society organisations and warrants its own third space as a body of law between public law and private law in jurisprudence.

Disclosure under the prescribed insurance contracts regime : Section 35 of the Insurance Contracts Act 1984 and consumer protection revisited

Section 35 of the Insurance Contracts Act 1984 requires insurers offering insurance policies in six prescribed areas "to clearly inform" prospective insureds of any departure their policies may constitute from the standard covers established by the Act and its accompanying Regulations. This prescribed insurance contracts regime was designed to remedy comprehension problems generated by the length and complexity of insurance documents and to alleviate misunderstanding over the terms and conditions of individual policies. This article examines the rationale underpinning s 35 and the prescribed insurance contracts regime and looks at the operation of the legislation with particular reference to home contents insurance in Australia. It is argued that the means whereby disclosure of derogation from standard cover may be effected largely negates the thrust of the prescribed insurance contract reform. Recommendations to address these operational deficiencies are made.

COLLABORATORY : characteristics of collaborative creativity

Teaching and learning in working groups is a challenge to both teacher and student. Collaboration is an elusive concept, difficult to teach, impossible to enforce, yet the ability to work in this way is an essential characteristic of any Creative Industries professional. In 2006, a group of creative industries students were charged with the task of collaboratively creating a performance as part of their coursework. This research project closely followed their development as agents of collaborative creativity using an innovative methodology which combined performance and documentary making. The result is COLLABORATORY - a DVD documentary isolating key behaviours and features of collaborative learning: Convergence and divergence of ideas, Characters and behaviours in collaboration, Leadership and facilitation, Motivation and Intersubjectivity. An engaging presentation of theory and practice capturing what Meill and Littleton (2004) call “the emotional dance of collaboration”.

Improved image contrast of the bone-muscle interface with 3T MRI compared to 1.5T MRI [Abstract]

Virtual 3D models of long bones are increasingly being used for implant design and research applications. The current gold standard for the acquisition of such data is Computed Tomography (CT) scanning. Due to radiation exposure, CT is generally limited to the imaging of clinical cases and cadaver specimens. Magnetic Resonance Imaging (MRI) does not involve ionising radiation and therefore can be used to image selected healthy human volunteers for research purposes. The feasibility of MRI as alternative to CT for the acquisition of morphological bone data of the lower extremity has been demonstrated in recent studies [1, 2]. Some of the current limitations of MRI are long scanning times and difficulties with image segmentation in certain anatomical regions due to poor contrast between bone and surrounding muscle tissues. Higher field strength scanners promise to offer faster imaging times or better image quality. In this study image quality at 1.5T is quantitatively compared to images acquired at 3T. --------- The femora of five human volunteers were scanned using 1.5T and 3T MRI scanners from the same manufacturer (Siemens) with similar imaging protocols. A 3D flash sequence was used with TE = 4.66 ms, flip angle = 15° and voxel size = 0.5 × 0.5 × 1 mm. PA-Matrix and body matrix coils were used to cover the lower limb and pelvis respectively. Signal to noise ratio (SNR) [3] and contrast to noise ratio (CNR) [3] of the axial images from the proximal, shaft and distal regions were used to assess the quality of images from the 1.5T and 3T scanners. The SNR was calculated for the muscle and bone-marrow in the axial images. The CNR was calculated for the muscle to cortex and cortex to bone marrow interfaces, respectively. --------- Preliminary results (one volunteer) show that the SNR of muscle for the shaft and distal regions was higher in 3T images (11.65 and 17.60) than 1.5T images (8.12 and 8.11). For the proximal region the SNR of muscles was higher in 1.5T images (7.52) than 3T images (6.78). The SNR of bone marrow was slightly higher in 1.5T images for both proximal and shaft regions, while it was lower in the distal region compared to 3T images. The CNR between muscle and bone of all three regions was higher in 3T images (4.14, 6.55 and 12.99) than in 1.5T images (2.49, 3.25 and 9.89). The CNR between bone-marrow and bone was slightly higher in 1.5T images (4.87, 12.89 and 10.07) compared to 3T images (3.74, 10.83 and 10.15). These results show that the 3T images generated higher contrast between bone and the muscle tissue than the 1.5T images. It is expected that this improvement of image contrast will significantly reduce the time required for the mainly manual segmentation of the MR images. Future work will focus on optimizing the 3T imaging protocol for reducing chemical shift and susceptibility artifacts.

The Federal circuit in Bilski : the machine-or-transformation test

In a much anticipated judgment, the Federal Circuit has sought to clarify the standards applicable in determining whether a claimed method constitutes patent-eligible subject matter. In Bilski, the Federal Circuit identified a test to determine whether a patentee has made claims that pre-empt the use of a fundamental principle or an abstract idea or whether those claims cover only a particular application of a fundamental principle or abstract idea. It held that the sole test for determining subject matter eligibility for a claimed process under § 101 is that: (1) it is tied to a particular machine or apparatus, or (2) it transforms a particular article into a different state or thing. The court termed this the “machine-or-transformation test.” In so doing it overruled its earlier State Street decision to the extent that it deemed its “useful, tangible and concrete result” test as inadequate to determine whether an alleged invention recites patent-eligible subject matter.

Extending the dynamic range of robotic vision

Conventional cameras have limited dynamic range, and as a result vision-based robots cannot effectively view an environment made up of both sunny outdoor areas and darker indoor areas. This paper presents an approach to extend the effective dynamic range of a camera, achieved by changing the exposure level of the camera in real-time to form a sequence of images which collectively cover a wide range of radiance. Individual control algorithms for each image have been developed to maximize the viewable area across the sequence. Spatial discrepancies between images, caused by the moving robot, are improved by a real-time image registration process. The sequence is then combined by merging color and contour information. By integrating these techniques it becomes possible to operate a vision-based robot in wide radiance range scenes.

The researcher’s perspective on procuring public works projects

Purpose: As part of a comprehensive research study looking at implementing PPPs, interviews with experienced researchers were conducted to realize their views on private sector involvement in public works projects. Design / methodology / approach: Amongst these interviews, five were launched with academics from Hong Kong and Australia, and two were conducted with Legislative Councillors of the Hong Kong Special Administration Region (HKSAR) government. Findings: The interview findings show that both Hong Kong and Australian interviewees had previously conducted some kind of research in the field of PPP. The interviewees highlighted that “Different risk profiles” and “Private sector more innovative / efficient” were the main differences between projects that were procured by PPP and traditionally. Other differences include risk transfer. In a PPP arrangement the public sector passes on a substantial amount of the project risks to the private sector, whereas in a traditional case the public sector would take the largest responsibility in bearing these risks. Another common feature of the private sector is that they tend to be more efficient and innovative when compared to the public sector hence their expertise is often reflected in PPP projects. The interviewees agreed that the key performance indicators for PPP projects were unique depending on the individual project. The critical success factors mentioned by both groups of interviewees included “Transparent process”, “Project dependent” and “Market need”. Due to the fact that PPP projects tend to be large scaled costly projects, adequate transparency in the process is necessary in order to demonstrate that a fair selection and tendering process is conducted. A market need for the project is also important to ensure that the project will be financially secure and that the private sector can make a reasonable profit to cover their project expenditure. Originality / value: The findings from this study have enabled a comparative analysis between the views of researchers in two completely different jurisdictions. With the growing popularity to implement PPP projects, it is believed that the results presented in this paper would be of interest to the industry at large.

Flexible high-power multi DC-DC converters for train systems

This thesis reports on the investigations, simulations and analyses of novel power electronics topologies and control strategies. The research is financed by an Australian Research Council (ARC) Linkage (07-09) grant. Therefore, in addition to developing original research and contributing to the available knowledge of power electronics, it also contributes to the design of a DC-DC converter for specific application to the auxiliary power supply in electric trains. Specifically, in this regard, it contributes to the design of a 7.5 kW DC-DC converter for the industrial partner (Schaffler and Associates Ltd) who supported this project. As the thesis is formatted as a ‘thesis by publication’, the contents are organized around published papers. The research has resulted in eleven papers, including seven peer reviewed and published conference papers, one published journal paper, two journal papers accepted for publication and one submitted journal paper (provisionally accepted subject to few changes). In this research, several novel DC-DC converter topologies are introduced, analysed, and tested. The similarity of all of the topologies devised lies in their ‘current circulating’ switching state, which allows them to store some energy in the inductor, as extra inductor current. The stored energy may be applied to enhance the performance of the converter in the occurrence of load current or input voltage disturbances. In addition, when there is an alternating load current, the ability to store energy allows the converter to perform satisfactorily despite frequently and highly varying load current. In this research, the capability of current storage has been utilised to design topologies for specific applications, and the enhancement of the performance of the considered applications has been illustrated. The simplest DC-DC converter topology, which has a ‘current circulating’ switching state, is the Positive Buck-Boost (PBB) converter (also known as the non-inverting Buck-Boost converter). Usually, the topology of the PBB converter is operating as a Buck or a Boost converter in applications with widely varying input voltage or output reference voltage. For example, in electric railways (the application of our industrial partner), the overhead line voltage alternates from 1000VDC to 500VDC and the required regulated voltage is 600VDC. In the course of this research, our industrial partner (Schaffler and Associates Ltd) industrialized a PBB converter–the ‘Mudo converter’–operating at 7.5 kW. Programming the onboard DSP and testing the PBB converter in experimental and nominal power and voltage was part of this research program. In the earlier stages of this research, the advantages and drawbacks of utilization of the ‘current circulating’ switching state in the positive Buck-Boost converter were investigated. In brief, the advantages were found to be robustness against input voltage and current load disturbances, and the drawback was extra conduction and switching loss. Although the robustness against disturbances is desirable for many applications, the price of energy loss must be minimized to attract attention to the utilization of the PBB converter. In further stages of this research, two novel control strategies for different applications were devised to minimise the extra energy loss while the advantages of the positive Buck-Boost converter were fully utilized. The first strategy is Smart Load Controller (SLC) for applications with pre-knowledge or predictability of input voltage and/or load current disturbances. A convenient example of these applications is electric/hybrid cars where a master controller commands all changes in loads and voltage sources. Therefore, the master controller has a pre-knowledge of the load and input voltage disturbances so it can apply the SLC strategy to utilize robustness of the PBB converter. Another strategy aiming to minimise energy loss and maximise the robustness in the face of disturbance is developed to cover applications with unexpected disturbances. This strategy is named Dynamic Hysteresis Band (DHB), and is used to manipulate the hysteresis band height after occurrence of disturbance to reduce dynamics of the output voltage. When no disturbance has occurred, the PBB converter works with minimum inductor current and minimum energy loss. New topologies based on the PBB converter have been introduced to address input voltage disturbances for different onboard applications. The research shows that the performance of applications of symmetrical/asymmetrical multi-level diode-clamped inverters, DC-networks, and linear-assisted RF amplifiers may be enhanced by the utilization of topologies based on the PBB converter. Multi-level diode-clamped inverters have the problem of DC-link voltage balancing when the power factor of their load closes to unity. This research has shown that this problem may be solved with a suitable multi-output DC-DC converter supplying DClink capacitors. Furthermore, the multi-level diode-clamped inverters supplied with asymmetrical DC-link voltages may improve the quality of load voltage and reduce the level of Electromagnetic Interference (EMI). Mathematical analyses and experiments on supplying symmetrical and asymmetrical multi-level inverters by specifically designed multi-output DC-DC converters have been reported in two journal papers. Another application in which the system performance can be improved by utilization of the ‘current circulating’ switching state is linear-assisted RF amplifiers in communicational receivers. The concept of ‘linear-assisted’ is to divide the signal into two frequency domains: low frequency, which should be amplified by a switching circuit; and the high frequency domain, which should be amplified by a linear amplifier. The objective is to minimize the overall power loss. This research suggests using the current storage capacity of a PBB based converter to increase its bandwidth, and to increase the domain of the switching converter. The PBB converter addresses the industrial demand for a DC-DC converter for the application of auxiliary power supply of a typical electric train. However, after testing the industrial prototype of the PBB converter, there were some voltage and current spikes because of switching. To attenuate this problem without significantly increasing the switching loss, the idea of Active Gate Signalling (AGS) is presented. AGS suggests a smart gate driver that selectively controls the switching process to reduce voltage/current spikes, without unacceptable reduction in the efficiency of switching.

Elliptic curves, group law, and efficient computation

This thesis is about the derivation of the addition law on an arbitrary elliptic curve and efficiently adding points on this elliptic curve using the derived addition law. The outcomes of this research guarantee practical speedups in higher level operations which depend on point additions. In particular, the contributions immediately find applications in cryptology. Mastered by the 19th century mathematicians, the study of the theory of elliptic curves has been active for decades. Elliptic curves over finite fields made their way into public key cryptography in late 1980’s with independent proposals by Miller [Mil86] and Koblitz [Kob87]. Elliptic Curve Cryptography (ECC), following Miller’s and Koblitz’s proposals, employs the group of rational points on an elliptic curve in building discrete logarithm based public key cryptosystems. Starting from late 1990’s, the emergence of the ECC market has boosted the research in computational aspects of elliptic curves. This thesis falls into this same area of research where the main aim is to speed up the additions of rational points on an arbitrary elliptic curve (over a field of large characteristic). The outcomes of this work can be used to speed up applications which are based on elliptic curves, including cryptographic applications in ECC. The aforementioned goals of this thesis are achieved in five main steps. As the first step, this thesis brings together several algebraic tools in order to derive the unique group law of an elliptic curve. This step also includes an investigation of recent computer algebra packages relating to their capabilities. Although the group law is unique, its evaluation can be performed using abundant (in fact infinitely many) formulae. As the second step, this thesis progresses the finding of the best formulae for efficient addition of points. In the third step, the group law is stated explicitly by handling all possible summands. The fourth step presents the algorithms to be used for efficient point additions. In the fifth and final step, optimized software implementations of the proposed algorithms are presented in order to show that theoretical speedups of step four can be practically obtained. In each of the five steps, this thesis focuses on five forms of elliptic curves over finite fields of large characteristic. A list of these forms and their defining equations are given as follows: (a) Short Weierstrass form, y2 = x3 + ax + b, (b) Extended Jacobi quartic form, y2 = dx4 + 2ax2 + 1, (c) Twisted Hessian form, ax3 + y3 + 1 = dxy, (d) Twisted Edwards form, ax2 + y2 = 1 + dx2y2, (e) Twisted Jacobi intersection form, bs2 + c2 = 1, as2 + d2 = 1, These forms are the most promising candidates for efficient computations and thus considered in this work. Nevertheless, the methods employed in this thesis are capable of handling arbitrary elliptic curves. From a high level point of view, the following outcomes are achieved in this thesis. - Related literature results are brought together and further revisited. For most of the cases several missed formulae, algorithms, and efficient point representations are discovered. - Analogies are made among all studied forms. For instance, it is shown that two sets of affine addition formulae are sufficient to cover all possible affine inputs as long as the output is also an affine point in any of these forms. In the literature, many special cases, especially interactions with points at infinity were omitted from discussion. This thesis handles all of the possibilities. - Several new point doubling/addition formulae and algorithms are introduced, which are more efficient than the existing alternatives in the literature. Most notably, the speed of extended Jacobi quartic, twisted Edwards, and Jacobi intersection forms are improved. New unified addition formulae are proposed for short Weierstrass form. New coordinate systems are studied for the first time. - An optimized implementation is developed using a combination of generic x86-64 assembly instructions and the plain C language. The practical advantages of the proposed algorithms are supported by computer experiments. - All formulae, presented in the body of this thesis, are checked for correctness using computer algebra scripts together with details on register allocations.

NSW rural land performance : 1990-2008

The annual income return for rural property is based on two major factors being commodity prices and production yields. Commodity prices paid to rural producers can vary depending on the agricultural policies of their respective countries. Free trade countries, such as Australia and New Zealand are subject to the volatility of the world commodity markets to a greater extent than those farmers in protected or subsidised markets. In countries where rural production is protected or subsidised the annual income received by rural producers has been relatively stable. However, the high cost of agricultural protection is now being questioned, particularly in relation to the increasing economic costs of government services such as health, education and housing. When combined with the agricultural production limitations of climate, topography, chemical residues and disease issues, the impact of commodity prices on rural property income is crucial in the ability of rural producers to enter into or expand their holdings in agricultural land. These problems are then reflected in the volatility of the rural land capital returns and the investment performance of this property class. This paper will address the total and capital return performance of a major agricultural area and compare these returns on the basis of both location of land and land use. The comparison will be used to determine if location or actual land use has a greater influence on rural property capital returns. This performance analysis is based on over 35,000 rural sales transactions. These transactions cover all market based rural property transactions in New South Wales, Australia for the period January 1990 to December 2008. Correlation analysis and investment performance analysis has also been carried out to determine the possible relationships between location and land use and subsequent changes in rural land capital values.

An examination of communication across cultures in news media and at informal/personal levels : with concentration on relations among two South East Asian countries and Australia and those two countries and Germany

In the age of globalisation dominated by mass communication, the flow of information contributes to a big extent to the worldviews of its "global citizens". From this point of view the mass media can be seen as one of the most salient sources of cross-cultural communication. This study investigates mass communication across cultures, focusing on South East Asia (Malaysia and Singapore), Australia and Germany. The centre of attention is the Western media coverage of South East Asia and vice versa. In this context a content analysis of newspapers of the three regions has been conducted. In addition, working practices and conditions of Western foreign correspondents in South East Asia have been examined. Apart from the investigation of inter-cultural media coverage, another focus of attention will be the examination of two levels of communication: The business level, concentrating on issues like e.g. the Asian business etiquette; and the private level, looking into the transition to a different culture from the perspective of Australian and German expatriates. Apart from investigating mass communication across cultures and to provide a written analysis of the findings, a series of radio documentaries in English and in German has been produced. They cover the following issues: Foreign correspondents in South East Asia, the expatriate-lifestyle of Australians and Germans in South East Asia, business etiquette in Asia, student exchange Germany-Asia, image and prejudices East-West and Tourism.