669 resultados para Mathematical-theory


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This project develops and evaluates a model of curriculum design that aims to assist student learning of foundational disciplinary ‘Threshold Concepts’. The project uses phenomenographic action research, cross-institutional peer collaboration and the Variation Theory of Learning to develop and trial the model. Two contrasting disciplines (Physics and Law) and four institutions (two research-intensive and two universities of technology) were involved in the project, to ensure broad applicability of the model across different disciplines and contexts. The Threshold Concepts that were selected for curriculum design attention were measurement uncertainty in Physics and legal reasoning in Law. Threshold Concepts are key disciplinary concepts that are inherently troublesome, transformative and integrative in nature. Once understood, such concepts transform students’ views of the discipline because they enable students to coherently integrate what were previously seen as unrelated aspects of the subject, providing new ways of thinking about it (Meyer & Land 2003, 2005, 2006; Land et al. 2008). However, the integrative and transformative nature of such threshold concepts make them inherently difficult for students to learn, with resulting misunderstandings of concepts being prevalent...

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"The focus of this chapter is on context-resonant systems perspectives in career theory and their implications for practice in diverse cultural and contextual settings. For over two decades, the potential of systems theory to offer a context-resonant approach to career development has been acknowledged. Career development theory and practice, however, have been dominated for most of their history by more narrowly defined theories informed by a trait-and-factor tradition of matching the characteristics of individuals to occupations. In contrast, systems theory challenges this parts-in-isolation approach and offers a response that can accommodate the complexity of both the lives of individuals and the world of the 21st century by taking a more holistic approach that considers individuals in context. These differences in theory and practice may be attributed to the underlying philosophies that inform them. For example, the philosophy informing the trait-and-factor theoretical position, logical positivism, places value on: studying individuals in isolation from their environments; content over process; facts over feelings; objectivity over subjectivity; and views individual behavior as observable, measurable, and linear. In practice, this theory base manifests in expert-driven practices founded on the assessment of personal traits such as interests, personality, values, or beliefs which may be matched to particular occupations. The philosophy informing more recent theoretical positions, constructivism, places value on: studying individuals in their contexts; making meaning of experience through the use of subjective narrative accounts; and a belief in the capacity of individuals known as agency. In practice, this theory base manifests in practices founded on collaborative relationships with clients, narrative approaches, and a reduced emphasis on expert-driven linear processes. Thus, the tenets of constructivism which inform the systems perspectives in career theory are context-resonant. Systems theory stresses holism where the interconnectedness of all elements of a system is considered. Systems may be open or closed. Closed systems have no relationship with their external environment whereas open systems interact with their external environment and are open to external influence which is necessary for regeneration. Congruent with general systems theory, the systems perspectives emerging within career theory are based on open systems. Such systems are complex and dynamic and comprise many elements and subsystems which recursively interact with each other as well as with influences from the surrounding environment. As elements of a system should not be considered in isolation, a systems approach is holistic. Patterns of behavior are found in the relationships between the elements of dynamic systems. Because of the multiplicity of relationships within and between elements of subsystems, the possibility of linear causal explanations is reduced. Story is the mechanism through which the relationships and patterns within systems are recounted by individuals. Thus the career guidance practices emanating from theories informed by systems perspectives are inherently narrative in orientation. Narrative career counseling encourages career development to be understood from the subjective perspective of clients. The application of systemic thinking in practice takes greater account of context. In so doing, practices informed by systems theory may facilitate relevance to a diverse client group in diverse settings. In a world that has become increasingly global and diverse it seems that context-resonant systems perspectives in career theory are essential to ensure the future of career development. Translating context-resonant systems perspectives into practice offers important possibilities for methods and approaches that are respectful of diversity."--publisher website

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Measuring Earth material behaviour on time scales of millions of years transcends our current capability in the laboratory. We review an alternative path considering multiscale and multiphysics approaches with quantitative structure-property relationships. This approach allows a sound basis to incorporate physical principles such as chemistry, thermodynamics, diffusion and geometry-energy relations into simulations and data assimilation on the vast range of length and time scales encountered in the Earth. We identify key length scales for Earth systems processes and find a substantial scale separation between chemical, hydrous and thermal diffusion. We propose that this allows a simplified two-scale analysis where the outputs from the micro-scale model can be used as inputs for meso-scale simulations, which then in turn becomes the micro-model for the next scale up. We present two fundamental theoretical approaches to link the scales through asymptotic homogenisation from a macroscopic thermodynamic view and percolation renormalisation from a microscopic, statistical mechanics view.

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Over the past decade, various paradigm shifts and challenges have rapidly changed learning and teaching in higher education including meeting student expectation for more engaging, more interactive learning experiences, the increased focus in the tertiary sector to deliver content online, and dealing with the complexities of fast-changing technologies. Rising to these challenges and responding to them is a complex and multi-faceted task. This paper discusses a case study undertaken applying a framework drawn from engineering education teaching and learning methods using the concept of academagogy, which is learner-centric, actively empowering students in building effective learning and engages facilitators in meaningful teaching and delivery methods.

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In this chapter we continue the exposition of crypto topics that was begun in the previous chapter. This chapter covers secret sharing, threshold cryptography, signature schemes, and finally quantum key distribution and quantum cryptography. As in the previous chapter, we have focused only on the essentials of each topic. We have selected in the bibliography a list of representative items, which can be consulted for further details. First we give a synopsis of the topics that are discussed in this chapter. Secret sharing is concerned with the problem of how to distribute a secret among a group of participating individuals, or entities, so that only predesignated collections of individuals are able to recreate the secret by collectively combining the parts of the secret that were allocated to them. There are numerous applications of secret-sharing schemes in practice. One example of secret sharing occurs in banking. For instance, the combination to a vault may be distributed in such a way that only specified collections of employees can open the vault by pooling their portions of the combination. In this way the authority to initiate an action, e.g., the opening of a bank vault, is divided for the purposes of providing security and for added functionality, such as auditing, if required. Threshold cryptography is a relatively recently studied area of cryptography. It deals with situations where the authority to initiate or perform cryptographic operations is distributed among a group of individuals. Many of the standard operations of single-user cryptography have counterparts in threshold cryptography. Signature schemes deal with the problem of generating and verifying electronic) signatures for documents.Asubclass of signature schemes is concerned with the shared-generation and the sharedverification of signatures, where a collaborating group of individuals are required to perform these actions. A new paradigm of security has recently been introduced into cryptography with the emergence of the ideas of quantum key distribution and quantum cryptography. While classical cryptography employs various mathematical techniques to restrict eavesdroppers from learning the contents of encrypted messages, in quantum cryptography the information is protected by the laws of physics.

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This special issue of Networking Science focuses on Next Generation Network (NGN) that enables the deployment of access independent services over converged fixed and mobile networks. NGN is a packet-based network and uses the Internet protocol (IP) to transport the various types of traffic (voice, video, data and signalling). NGN facilitates easy adoption of distributed computing applications by providing high speed connectivity in a converged networked environment. It also makes end user devices and applications highly intelligent and efficient by empowering them with programmability and remote configuration options. However, there are a number of important challenges in provisioning next generation network technologies in a converged communication environment. Some preliminary challenges include those that relate to QoS, switching and routing, management and control, and security which must be addressed on an urgent or emergency basis. The consideration of architectural issues in the design and pro- vision of secure services for NGN deserves special attention and hence is the main theme of this special issue.

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Unsaturated water flow in soil is commonly modelled using Richards’ equation, which requires the hydraulic properties of the soil (e.g., porosity, hydraulic conductivity, etc.) to be characterised. Naturally occurring soils, however, are heterogeneous in nature, that is, they are composed of a number of interwoven homogeneous soils each with their own set of hydraulic properties. When the length scale of these soil heterogeneities is small, numerical solution of Richards’ equation is computationally impractical due to the immense effort and refinement required to mesh the actual heterogeneous geometry. A classic way forward is to use a macroscopic model, where the heterogeneous medium is replaced with a fictitious homogeneous medium, which attempts to give the average flow behaviour at the macroscopic scale (i.e., at a scale much larger than the scale of the heterogeneities). Using the homogenisation theory, a macroscopic equation can be derived that takes the form of Richards’ equation with effective parameters. A disadvantage of the macroscopic approach, however, is that it fails in cases when the assumption of local equilibrium does not hold. This limitation has seen the introduction of two-scale models that include at each point in the macroscopic domain an additional flow equation at the scale of the heterogeneities (microscopic scale). This report outlines a well-known two-scale model and contributes to the literature a number of important advances in its numerical implementation. These include the use of an unstructured control volume finite element method and image-based meshing techniques, that allow for irregular micro-scale geometries to be treated, and the use of an exponential time integration scheme that permits both scales to be resolved simultaneously in a completely coupled manner. Numerical comparisons against a classical macroscopic model confirm that only the two-scale model correctly captures the important features of the flow for a range of parameter values.

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This paper presents the results of a qualitative action-research inquiry into how a highly diverse cohort of post-graduate students could develop significant capacity in sustainable development within a single unit (course), in this case a compulsory component of four built environment masters programs. The method comprised applying threshold learning theory within the technical discipline of sustainable development, to transform student understanding of sustainable business practice in the built environment. This involved identifying a number of key threshold concepts, which once learned would provide a pathway to having a transformational learning experience. Curriculum was then revised, to focus on stepping through these targeted concepts using a scaffolded, problem-based-learning approach. Challenges included a large class size of 120 students, a majority of international students, and a wide span of disciplinary backgrounds across the spectrum of built environment professionals. Five ‘key’ threshold learning concepts were identified and the renewed curriculum was piloted in Semester 2 of 2011. The paper presents details of the study and findings from a mixed-method evaluation approach through the semester. The outcomes of this study will be used to inform further review of the course in 2012, including further consideration of the threshold concepts. In future, it is anticipated that this case study will inform a framework for rapidly embedding sustainability within curriculum.

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Safety has long been a problem in the construction industry. Repair, maintenance, alteration and addition (RMAA) sector has emerged to play an important role in the construction industry. It accounted for 53% of the total construction market in Hong Kong in 2007. Safety performance of the RMAA words has been alarming. Statistics indicate that the percentage of fatal industrial accidents arising from RMAA work in Hong Kong was over 56% in 2006 while the remaining 44% was from new works. Effective safety measures to address the safety problems and improve safety performance of the RMAA sector are urgently needed. Unsafe behaviour has been attributed to one of the major causes of accidents. Traditional cost-benefit analysis of workers' safety behaviour seems to be inadequate. This paper proposes to adopt a game theoretical approach to analyse safety behaviour of RMAA workers. Game theory is concerned with the decision-making process in situations where outcomes depend upon choices made by one or more players. A game theoretical model between contractor and worker has been proffered. Mathematical analysis of this game model has been done and implications of the analysis have been discussed.

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Although there was substantial research into the occupational health and safety sector over the past forty years, this generally focused on statistical analyses of data related to costs and/or fatalities and injuries. There is a lack of mathematical modelling of the interactions between workers and the resulting safety dynamics of the workplace. There is also little work investigating the potential impact of different safety intervention programs prior to their implementation. In this article, we present a fundamental, differential equation-based model of workplace safety that treats worker safety habits similarly to an infectious disease in an epidemic model. Analytical results for the model, derived via phase plane and stability analysis, are discussed. The model is coupled with a model of a generic safety strategy aimed at minimising unsafe work habits, to produce an optimal control problem. The optimal control model is solved using the forward-backward sweep numerical scheme implemented in Matlab.

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This article deals with time-domain hydroelastic analysis of a marine structure. The convolution terms associated with fluid memory effects are replaced by an alternative state-space representation, the parameters of which are obtained by using realization theory. The mathematical model established is validated by comparison to experimental results of a very flexible barge. Two types of time-domain simulations are performed: dynamic response of the initially inert structure to incident regular waves and transient response of the structure after it is released from a displaced condition in still water. The accuracy and the efficiency of the simulations based on the state-space model representations are compared to those that integrate the convolutions.

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This paper presents a control design for tracking of attitude and speed of an underactuated slender-hull unmanned underwater vehicle (UUV). The control design is based on Port-Hamiltonian theory. The target dynamics (desired dynamic response) is shaped with particular attention to the target mass matrix so that the influence of the unactuated dynamics on the controlled system is suppressed. This results in achievable dynamics independent of uncontrolled states. Throughout the design, insight of the physical phenomena involved is used to propose the desired target dynamics. The performance of the design is demonstrated through simulation with a high-fidelity model.

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The interest in utilising multiple heterogeneous Unmanned Aerial Vehicles (UAVs) in close proximity is growing rapidly. As such, many challenges are presented in the effective coordination and management of these UAVs; converting the current n-to-1 paradigm (n operators operating a single UAV) to the 1-to-n paradigm (one operator managing n UAVs). This paper introduces an Information Abstraction methodology used to produce the functional capability framework initially proposed by Chen et al. and its Level Of Detail (LOD) indexing scale. This framework was validated through comparing the operator workload and Situation Awareness (SA) of three experiment scenarios involving multiple autonomously heterogeneous UAVs. The first scenario was set in a high LOD configuration with highly abstracted UAV functional information; the second scenario was set in a mixed LOD configuration; and the final scenario was set in a low LOD configuration with maximal UAV functional information. Results show that there is a significant statistical decrease in operator workload when a UAV’s functional information is displayed at its physical form (low LOD - maximal information) when comparing to the mixed LOD configuration.