960 resultados para Riemann-Liouville Derivative


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This document is a collection of ‘cases’ adapted from interviews with supervisors of higher degree research students from the technology disciplines. The supervisors come from a wide range of sub disciplines and represent many levels of experience. We follow in this document Hammond and Ryland’s (2009)2 suggested ranking of supervision experience:  No completions – No experience or new supervisors, with no doctoral completions as principal supervisor  Experienced – 1 to 5 doctoral completions as principal supervisor  Very experienced – over 6 doctoral completions as principal supervisor The cases focus attention on thinking about supervision as a teaching and learning practice; a dimension of higher degree research supervision that is increasingly being recognized as important. They are offered as prompts for individuals and groups of supervisors in thinking about their supervision as a teaching and learning practice.

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The materials presented here are intended to: a) accompany the document Supervisor Resource and b) provide technology supervisors with materials that may be readily shared with students. These resources are not designed to be distributed to students without contextualization, they are intended for use in workshops or in discussions between supervisors and students. As authors, we anticipate that supervisors or workshop facilitators are most likely to extract individual resources of interest for particular occasions. The materials have been developed from conversations with supervisors from the technology disciplines.

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The framework presented in the resource is intended to provide technology supervisors with a range of options available to them with respect to supervisory pedagogy. It has been developed to highlight different aspects of thinking about supervision as a teaching and learning practice; as well as approaches, strategies and roles associated with supervision. It will enable technology supervisors to become aware of the diverse options available to them and provide systematic ways of thinking about supervisory practices. Use of this framework will encourage supervisors to make choices based on broader, rather than more limited, repertoires. It will also encourage thinking about supervision as a teaching and learning practice.

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Context The School of Information Technology at QUT has recently undertaken a major restructuring of their Bachelor of Information Technology (BIT) course. Some of the aims of this restructuring include a reduction in first year attrition and to provide an attractive degree course that meets both student and industry expectations. Emphasis has been placed on the first semester in the context of retaining students by introducing a set of four units that complement one another and provide introductory material on technology, programming and related skills, and generic skills that will aid the students throughout their undergraduate course and in their careers. This discussion relates to one of these four fist semester units, namely Building IT Systems. The aim of this unit is to create small Information Technology (IT) systems that use programming or scripting, databases as either standalone applications or web applications. In the prior history of teaching introductory computer programming at QUT, programming has been taught as a stand alone subject and integration of computer applications with other systems such as databases and networks was not undertaken until students had been given a thorough grounding in those topics as well. Feedback has indicated that students do not believe that working with a database requires programming skills. In fact, the teaching of the building blocks of computer applications have been compartmentalized and taught in isolation from each other. The teaching of introductory computer programming has been an industry requirement of IT degree courses as many jobs require at least some knowledge of the topic. Yet, computer programming is not a skill that all students have equal capabilities of learning (Bruce et al., 2004) and this is clearly shown by the volume of publications dedicated to this topic in the literature over a broad period of time (Eckerdal & Berglund, 2005; Mayer, 1981; Winslow, 1996). The teaching of this introductory material has been done pretty much the same way over the past thirty years. During this period of time that introductory computer programming courses have been taught at QUT, a number of different programming languages and programming paradigms have been used and different approaches to teaching and learning have been attempted in an effort to find the golden thread that would allow students to learn this complex topic. Unfortunately, computer programming is not a skill that can be learnt in one semester. Some basics can be learnt but it can take many years to master (Norvig, 2001). Faculty data typically has shown a bimodal distribution of results for students undertaking introductory programming courses with a high proportion of students receiving a high mark and a high proportion of students receiving a low or failing mark. This indicates that there are students who understand and excel with the introductory material while there is another group who struggle to understand the concepts and practices required to be able to translate a specification or problem statement into a computer program that achieves what is being requested. The consequence of a large group of students failing the introductory programming course has been a high level of attrition amongst first year students. This attrition level does not provide good continuity in student numbers in later years of the degree program and the current approach is not seen as sustainable.

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Event-specific scales commonly have greater power than generalized scales in prediction of specific disorders and in testing mediator models for predicting such disorders. Therefore, in a preliminary study, a 6-item Alcohol Helplessness Scale was constructed and found to be reliable for a sample of 98 problem drinkers. Hierarchical multiple regression and its derivative path analysis were used to test whether helplessness and self-efficacy moderate or mediate the link between alcohol dependence and depression, A test of a moderation model was not supported, whereas a test of a mediation model was supported. Helplessness and self-efficacy both significantly and independently mediated between alcohol dependence and depression. Nevertheless, a significant direct effect of alcohol dependence on depression also remained.

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A non-destructive, diffuse reflectance near infrared spectroscopy (DR-NIRS)approach is considered as a potential tool for determining the component-level structural properties of articular cartilage. To this end, DR-NIRS was applied in vitro to detect structural changes, using principal component analysis as the statistical basis for characterization. The results show that this technique, particularly with first-derivative pretreatment, can distinguish normal, intact cartilage from enzymatically digested cartilage. Further, this paper establishes that the use of DR-NIRS enables the probing of the full depth of the uncalcified cartilage matrix, potentially allowing the assessment of degenerative changes in joint tissue, independent of the site of initiation of the osteoarthritic process.

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Avatars perform a complex range of inter-related functions. They not only allow us to express a digital identity, they facilitate the expression of physical motility and, through non-verbal expression, help to mediate social interaction in networked environments. When well designed, they can contribute to a sense of “presence” (a sense of being there) and a sense of “co-presence” (a sense of being there with others) in digital space. Because of this complexity, the study of avatars can be enriched by theoretical insights from a range of disciplines. This paper considers avatars from the perspectives of critical theory, visual communication, and art theory (on portraiture) to help elucidate the role of avatars as an expression of identity. It goes on to argue that identification with an avatar is also produced through their expression of motility and discusses the benefits of film theory for explaining this process. Conceding the limits of this approach, the paper draws on philosophies of body image, Human Computer Interaction (HCI) theory on embodied interaction, and fields as diverse as dance to explain the sense of identification, immersion, presence and co-presence that avatars can produce.

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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

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In this paper, we consider a variable-order fractional advection-diffusion equation with a nonlinear source term on a finite domain. Explicit and implicit Euler approximations for the equation are proposed. Stability and convergence of the methods are discussed. Moreover, we also present a fractional method of lines, a matrix transfer technique, and an extrapolation method for the equation. Some numerical examples are given, and the results demonstrate the effectiveness of theoretical analysis.

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In this paper, the numerical simulation of the 3D seepage flow with fractional derivatives in porous media is considered under two special cases: non-continued seepage flow in uniform media (NCSFUM) and continued seepage flow in non-uniform media (CSF-NUM). A fractional alternating direction implicit scheme (FADIS) for the NCSF-UM and a modified Douglas scheme (MDS) for the CSF-NUM are proposed. The stability, consistency and convergence of both FADIS and MDS in a bounded domain are discussed. A method for improving the speed of convergence by Richardson extrapolation for the MDS is also presented. Finally, numerical results are presented to support our theoretical analysis.

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In this paper, we consider the variable-order nonlinear fractional diffusion equation View the MathML source where xRα(x,t) is a generalized Riesz fractional derivative of variable order View the MathML source and the nonlinear reaction term f(u,x,t) satisfies the Lipschitz condition |f(u1,x,t)-f(u2,x,t)|less-than-or-equals, slantL|u1-u2|. A new explicit finite-difference approximation is introduced. The convergence and stability of this approximation are proved. Finally, some numerical examples are provided to show that this method is computationally efficient. The proposed method and techniques are applicable to other variable-order nonlinear fractional differential equations.

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In this paper, we consider the following non-linear fractional reaction–subdiffusion process (NFR-SubDP): Formula where f(u, x, t) is a linear function of u, the function g(u, x, t) satisfies the Lipschitz condition and 0Dt1–{gamma} is the Riemann–Liouville time fractional partial derivative of order 1 – {gamma}. We propose a new computationally efficient numerical technique to simulate the process. Firstly, the NFR-SubDP is decoupled, which is equivalent to solving a non-linear fractional reaction–subdiffusion equation (NFR-SubDE). Secondly, we propose an implicit numerical method to approximate the NFR-SubDE. Thirdly, the stability and convergence of the method are discussed using a new energy method. Finally, some numerical examples are presented to show the application of the present technique. This method and supporting theoretical results can also be applied to fractional integrodifferential equations.

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In this paper, we consider the numerical solution of a fractional partial differential equation with Riesz space fractional derivatives (FPDE-RSFD) on a finite domain. Two types of FPDE-RSFD are considered: the Riesz fractional diffusion equation (RFDE) and the Riesz fractional advection–dispersion equation (RFADE). The RFDE is obtained from the standard diffusion equation by replacing the second-order space derivative with the Riesz fractional derivative of order αset membership, variant(1,2]. The RFADE is obtained from the standard advection–dispersion equation by replacing the first-order and second-order space derivatives with the Riesz fractional derivatives of order βset membership, variant(0,1) and of order αset membership, variant(1,2], respectively. Firstly, analytic solutions of both the RFDE and RFADE are derived. Secondly, three numerical methods are provided to deal with the Riesz space fractional derivatives, namely, the L1/L2-approximation method, the standard/shifted Grünwald method, and the matrix transform method (MTM). Thirdly, the RFDE and RFADE are transformed into a system of ordinary differential equations, which is then solved by the method of lines. Finally, numerical results are given, which demonstrate the effectiveness and convergence of the three numerical methods.