Analytical solutions for the two- and three-dimensional time-fractional telegraph equations by the method of separating variables

In this paper, a method of separating variables is effectively implemented for solving a time-fractional telegraph equation (TFTE) in two and three dimensions. We discuss and derive the analytical solution of the TFTE in two and three dimensions with nonhomogeneous Dirichlet boundary condition. This method can be extended to other kinds of the boundary conditions.

Analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations on a finite domain

Generalized fractional partial differential equations have now found wide application for describing important physical phenomena, such as subdiffusive and superdiffusive processes. However, studies of generalized multi-term time and space fractional partial differential equations are still under development. In this paper, the multi-term time-space Caputo-Riesz fractional advection diffusion equations (MT-TSCR-FADE) with Dirichlet nonhomogeneous boundary conditions are considered. The multi-term time-fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0, 1], [1, 2] and [0, 2], respectively. These are called respectively the multi-term time-fractional diffusion terms, the multi-term time-fractional wave terms and the multi-term time-fractional mixed diffusion-wave terms. The space fractional derivatives are defined as Riesz fractional derivatives. Analytical solutions of three types of the MT-TSCR-FADE are derived with Dirichlet boundary conditions. By using Luchko's Theorem (Acta Math. Vietnam., 1999), we proposed some new techniques, such as a spectral representation of the fractional Laplacian operator and the equivalent relationship between fractional Laplacian operator and Riesz fractional derivative, that enabled the derivation of the analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations. © 2012.

Numerical techniques for the variable order time fractional diffusion equation

In this paper we consider the variable order time fractional diffusion equation. We adopt the Coimbra variable order (VO) time fractional operator, which defines a consistent method for VO differentiation of physical variables. The Coimbra variable order fractional operator also can be viewed as a Caputo-type definition. Although this definition is the most appropriate definition having fundamental characteristics that are desirable for physical modeling, numerical methods for fractional partial differential equations using this definition have not yet appeared in the literature. Here an approximate scheme is first proposed. The stability, convergence and solvability of this numerical scheme are discussed via the technique of Fourier analysis. Numerical examples are provided to show that the numerical method is computationally efficient. Crown Copyright © 2012 Published by Elsevier Inc. All rights reserved.

Analytical solutions for the multi-term time-fractional diffusion-wave/diffusion equations in a finite domain

Multi-term time-fractional differential equations have been used for describing important physical phenomena. However, studies of the multi-term time-fractional partial differential equations with three kinds of nonhomogeneous boundary conditions are still limited. In this paper, a method of separating variables is used to solve the multi-term time-fractional diffusion-wave equation and the multi-term time-fractional diffusion equation in a finite domain. In the two equations, the time-fractional derivative is defined in the Caputo sense. We discuss and derive the analytical solutions of the two equations with three kinds of nonhomogeneous boundary conditions, namely, Dirichlet, Neumann and Robin conditions, respectively.

Capping computation time and storage requirements for appearance-based localization with CAT-SLAM

Appearance-based localization is increasingly used for loop closure detection in metric SLAM systems. Since it relies only upon the appearance-based similarity between images from two locations, it can perform loop closure regardless of accumulated metric error. However, the computation time and memory requirements of current appearance-based methods scale linearly not only with the size of the environment but also with the operation time of the platform. These properties impose severe restrictions on longterm autonomy for mobile robots, as loop closure performance will inevitably degrade with increased operation time. We present a set of improvements to the appearance-based SLAM algorithm CAT-SLAM to constrain computation scaling and memory usage with minimal degradation in performance over time. The appearance-based comparison stage is accelerated by exploiting properties of the particle observation update, and nodes in the continuous trajectory map are removed according to minimal information loss criteria. We demonstrate constant time and space loop closure detection in a large urban environment with recall performance exceeding FAB-MAP by a factor of 3 at 100% precision, and investigate the minimum computational and memory requirements for maintaining mapping performance.

Disobedient Citizens : Press Depictions of Striking School Teachers in NSW and Anti-Vietnam War Demonstrators in NSW and Victoria in 1968

Across Australia in 1968, students demonstrating against the Vietnam War engaged in confrontational behaviour. The metropolitan daily newspapers,the most important source of news for most people, enthusiastically reported the scenes. The demonstrations were exciting. Sensational headlines and photographs captured the interest of readers and influenced their opinions. But radical opposition to government policies at the time was not limited to university students opposing the Vietnam War. Teachers had become increasingly critical of conditions in schools, with Victorian secondary school teachers having stopped work on a number of occasions since 1965. In October 1968, both primary and secondary school teachers in New South Wales participated in eastern Australia’s first state-wide teachers’ strike. As Sydney’s Sun commented on 1 October 1968, “The teachers’ strike threw the ... education system into chaos ... A huge proportion of the State’s 2764 schools were silent and empty.” Similarities with the anti-war demonstrations were obvious. Although not as confrontational, the New South Wales teachers’ strike was a publicity-seeking action. This examination of the teachers’ more restrained, but more effective, approach to challenging government policies provides a new voice and vision to our understandings of the diverse nature of radicalism in Australia in the 1960s.

Fully private revocable predicate encryption

We introduce the concept of Revocable Predicate Encryption (RPE), which extends current predicate encryption setting with revocation support: private keys can be used to decrypt an RPE ciphertext only if they match the decryption policy (defined via attributes encoded into the ciphertext and predicates associated with private keys) and were not revoked by the time the ciphertext was created. We formalize the notion of attribute hiding in the presence of revocation and propose an RPE scheme, called AH-RPE, which achieves attribute-hiding under the Decision Linear assumption in the standard model. We then present a stronger privacy notion, termed full hiding, which further cares about privacy of revoked users. We propose another RPE scheme, called FH-RPE, that adopts the Subset Cover Framework and offers full hiding under the Decision Linear assumption in the standard model. The scheme offers very flexible privacy-preserving access control to encrypted data and can be used in sender-local revocation scenarios.

School Leadership, Literacy and Social Justice : The Place of Local School Curriculum Planning and Reform

School reform is a matter of both redistributive social justice and recognitive social justice. Following Fraser (Justice interruptus: critical reflections on the “postsocialist” condition. Routledge, New York, 1997), we begin from a philosophical and political commitment to the more equitable redistribution of knowledge, credentials, competence, and capacity to children of low socioeconomic, cultural, and linguistic minority and Indigenous communities whose access, achievement, and participation historically have “lagged” behind system norms and benchmarks set by middle class and dominant culture communities. At the same time, we argue that the recognition of these students and their communities’ lifeworlds, knowledges, and experiences in the curriculum, in classroom teaching, and learning is both a means and an end: a means toward improved achievement measured conventionally and a goal for reform and alteration of mainstream curriculum knowledge and what is made to count in the school as valued cultural knowledge and practice. The work that we report here was based on an ongoing 4-year project where a team of university teacher educators/researchers have partnered with school leadership and staff to build relationships within community. The purpose has been to study whether and how engagement with new digital arts and multimodal literacies could have effects on students “conventional” print literacy achievement and, secondly, to study whether and how the overall performance of a school could be generated through a focus on professional conversations and partnerships in curriculum and instruction – rather than the top-down implementation of a predetermined pedagogical scheme, package, or approach.

School-community engagement : a critical approach to involving young people in an urban planning project

This study examines the participation of a group of high school students in designing a Heritage Journey as part of an urban redevelopment project in their community. School-community engagement offers young people an opportunity to engage in community life and influence decisions that affect them. Forging links between community and school is becoming more important for teachers as they attempt to create new authentic learning opportunities for young people within a changing world. Increasingly, researchers and urban planners are including children and young people as active decision makers and participants in community engagement projects. However, models of participation tend to be adult-focussed, conceive participation in terms of low to high graduated levels and lack a clearly articulated theoretical basis. The research problem in this study focuses on investigating whether the inclusion of young people in school-community engagement results in value adding to urban planning and is an example of genuine participation. The aim of the study is to provide a theoretically informed, empirically rich understanding of the inclusion of young people in a community engagement strategy for an urban planning project. Theories of space developed by Henri Lefebvre and Edward Soja are drawn upon for understanding how space is understood, used, and redeveloped by the students and other stakeholders. The study also draws on David Harvey’s notion of utopia and space to consider the imaginative possibilities of the students’ designs and ideas. The study uses a participatory research approach and documents the opportunities and challenges of this methodology. The thesis argues that school-community engagement within a "Thirdspace" offers many new opportunities for the emergence of authentic learning situations. Key findings from the study show young people’s participation in an urban planning project can achieve successful results when young people are given opportunities for full participation in decision-making processes; multiple pathways for active engagement are incorporated into the research design; opportunities for mentoring are provided; realistic timelines are communicated to all stakeholders and the needs and social practices of the local community are acknowledged. A new spatial model of community engagement is proposed as an outcome of the study. Unlike previous models of participation, this model demonstrates how exclusion and inclusion can be conceived visually, and may prove effective for conceptualising future community engagement projects that involve young people.

ACE research vignette 018 : experiments in the MBA classroom : the case of time frames in project teams

This series of research vignettes is aimed at sharing current and interesting research findings from our team of international Entrepeneurship researchers. In this vignette, Dr Rene Bakker considers project team dynamics and how executive education can be enriched by studying them in the classroom.

Multimodal and monomodal discourses of marketization in higher education : power, ideology, and the absence of the image

The ubiquity of multimodality in hypermedia environments is undeniable. Bezemer and Kress (2008) have argued that writing has been displaced by image as the central mode for representation. Given the current technical affordances of digital technology and user-friendly interfaces that enable the ease of multimodal design, the conspicuous absence of images in certain domains of cyberspace is deserving of critical analysis. In this presentation, I examine the politics of discourses implicit within hypertextual spaces, drawing textual examples from a higher education website. I critically examine the role of writing and other modes of production used in what Fairclough (1993) refers to as discourses of marketisation in higher education, tracing four pervasive discourses of teaching and learning in the current economy: i) materialization, ii) personalization, iii) technologisation, and iv) commodification (Fairclough, 1999). Each of these arguments is supported by the critical analysis of multimodal texts. The first is a podcast highlighting the new architectonic features of a university learning space. The second is a podcast and transcript of a university Open Day interview with prospective students. The third is a time-lapse video showing the construction of a new science and engineering precinct. These three multimodal texts contrast a final web-based text that exhibits a predominance of writing and the powerful absence or silencing of the image. I connect the weightiness of words and the function of monomodality in the commodification of discourses, and its resistance to the multimodal affordances of web-based technologies, and how this is used to establish particular sets of subject positions and ideologies through which readers are constrained to occupy. Applying principles of critical language study by theorists that include Fairclough, Kress, Lemke, and others whose semiotic analysis of texts focuses on the connections between language, power, and ideology, I demonstrate how the denial of image and the privileging of written words in the multimodality of cyberspace is an ideological effect to accentuate the dominance of the institution.

Strategy use of children with Down syndrome in a delay of gratification situation

Background: The capacity to delay gratification has been shown to be a very important developmental task for children who are developing typically. There is evidence that children with Down syndrome have more difficulty with a delay of gratification task than typically developing children of the same mental age. This study focused on the strategies children with Down syndrome use while in a delay of gratification situation to ascertain if these contribute to the differences in delay times from those of typically developing children. Method: Thirty-two children with Down syndrome (15 females) and 50 typically developing children participated in the study. Children with Down syndrome had a mental age, as measured by the Stanford-Binet IV, between 36 and 66 months (M = 45.66). The typically developing children had a mean chronological age of 45.76 months. Children participated in a delay of gratification task where they were offered two or one small treats and asked which they preferred. They were then told that they could have the two treats if they waited for the researcher to return (an undisclosed time of 15 min). If they did not want to wait any longer they could call the researcher back but then they could have only one treat. Twenty-two of the children with Down syndrome and 43 of the typically developing children demonstrated understanding of the task and their data are included here. Sessions were videotaped for later analysis. Results: There were significant differences in the mean waiting times of the two groups. The mean of the waiting times for children with Down syndrome was 181.32 s (SD = 347.62) and was 440.21 s (SD = 377.59) for the typically developing children. Eighteen percent of the group with Down syndrome waited for the researcher to return in comparison to 35% of the typically developing group. Sixty-four percent of children with Down syndrome called the researcher back and the remainder (18%) violated. In the typically developing group 37% called the researcher back and 28% violated. The mean waiting time for the group of children with Down syndrome who called the researcher back was 24 s. Examination of strategy use in this group was therefore very limited. There appeared to be quite similar strategy use across the groups who waited the full 15 min. Conclusions: These results confirm the difficulty children with Down syndrome have in delaying gratification. Teaching strategies for waiting, using information drawn from the behaviours of children who are developing typically may be a useful undertaking. Examination of other contributors to delay ability (e.g., language skills) is also likely to be helpful in understanding the difficulties demonstrated in delaying gratification.

Analytical and numerical solutions of the space and time fractional bloch-torrey equation

Fractional order dynamics in physics, particularly when applied to diffusion, leads to an extension of the concept of Brown-ian motion through a generalization of the Gaussian probability function to what is termed anomalous diffusion. As MRI is applied with increasing temporal and spatial resolution, the spin dynamics are being examined more closely; such examinations extend our knowledge of biological materials through a detailed analysis of relaxation time distribution and water diffusion heterogeneity. Here the dynamic models become more complex as they attempt to correlate new data with a multiplicity of tissue compartments where processes are often anisotropic. Anomalous diffusion in the human brain using fractional order calculus has been investigated. Recently, a new diffusion model was proposed by solving the Bloch-Torrey equation using fractional order calculus with respect to time and space (see R.L. Magin et al., J. Magnetic Resonance, 190 (2008) 255-270). However effective numerical methods and supporting error analyses for the fractional Bloch-Torrey equation are still limited. In this paper, the space and time fractional Bloch-Torrey equation (ST-FBTE) is considered. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. Firstly, we derive an analytical solution for the ST-FBTE with initial and boundary conditions on a finite domain. Secondly, we propose an implicit numerical method (INM) for the ST-FBTE, and the stability and convergence of the INM are investigated. We prove that the implicit numerical method for the ST-FBTE is unconditionally stable and convergent. Finally, we present some numerical results that support our theoretical analysis.