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.

Educational markets in space : gamekeeping professionals across Australian communities

This paper argues that the logic of neoliberal choice policy is typically blind to considerations of space and place, but inevitably impacts on rural and remote locations in the way that middle class professionals view the opportunities available in their local educational markets. The paper considers the value of middle class professionals’ educational capitals in regional communities and their problematic distribution, given that class fraction’s particular investment in choice strategies to ensure their children’s future. It then profiles the educational market in six communities along a transect between a major regional centre and a remote ‘outback’ town, using publicly available data from the Australian government’s ‘My School’ website. Comparison of the local markets shows how educational outcomes are distributed across the local markets and how dimensions of ‘choice’ thin out over the transect. Interview data offers insights into how professional families in these localities engage selectively with these local educational markets, or plan to transcend them. The discussion reflects on the growing importance of educational choices as a marker of place in the competition between localities to attract and retain professionals to staff vital human services in their communities.

Green Exercise in the UK Countryside: Effects on Health and Psychological Well-being and Implications for Policy and Planning

There is evidence that contact with the natural environment and green space promotes good health. It is also well known that participation in regular physical activity generates physical and psychological health benefits. The authors have hypothesised that ‘green exercise’ will improve health and psychological well-being, yet few studies have quantified these effects. This study measured the effects of 10 green exercise case studies (including walking, cycling, horse-riding, fishing, canal-boating and conservation activities) in four regions of the UK on 263 participants. Even though these participants were generally an active and healthy group, it was found that green exercise led to a significant improvement in self-esteem and total mood disturbance (with anger-hostility, confusion-bewilderment, depression-dejection and tension-anxiety all improving post-activity). Self-esteem and mood were found not to be affected by the type, intensity or duration of the green exercise, as the results were similar for all 10 case studies. Thus all these activities generated mental health benefits, indicating the potential for a wider health and well-being dividend from green exercise. Green exercise thus has important implications for public and environmental health, and for a wide range of policy sectors.

Space, place and power : the spatial turn in literacy research

Place matters to literacy because the meanings of our language and actions are always materially and socially placed in the world (Scollon & Scollon, 2003). We cannot interpret signs, whether an icon, symbol, gesture, word, or action, without taking into account their associations with other meanings and objects in places. This chapter maps an emergent strand of literacy research that foregrounds place and space as constitutive, rather than a backdrop for the real action. Space and place are seen as relational and dynamic, not as fixed and unchanging. Space and place are socially produced, and hence, can be contested, re-imagined and re-made. In bringing space and place into the frame of literacy studies we see a subtle shift – a rebalancing of the semiotic with the materiality of lived, embodied, and situated experience. ...

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.

Their space, my space, our space? Report of the 2009 Redland City Council Youth and Public Space Survey

This report analyses data collected through the Redland City Council’s Young People and Public Space Survey of 2148 high school students aged 12-19. The survey conducted in 2009 explored their sense of safety and experiences in public spaces across the City, and views on what Council could do to improve these. It is apparent they base their assessment of a space as ‘public’ on their ‘use’ of a space alone or with friends, and where strangers may be present, rather than on a type of ownership of a space (public/ private). The findings of the survey are summarised according to the themes of safety, community attitudes towards young people being in public spaces, young people and authorities, young people’s views of what is needed, and understanding different young people’s experiences of public space.

Eliciting Expert Knowledge in Conservation Science

Expert knowledge is used widely in the science and practice of conservation because of the complexity of problems, relative lack of data, and the imminent nature of many conservation decisions. Expert knowledge is substantive information on a particular topic that is not widely known by others. An expert is someone who holds this knowledge and who is often deferred to in its interpretation. We refer to predictions by experts of what may happen in a particular context as expert judgments. In general, an expert-elicitation approach consists of five steps: deciding how information will be used, determining what to elicit, designing the elicitation process, performing the elicitation, and translating the elicited information into quantitative statements that can be used in a model or directly to make decisions. This last step is known as encoding. Some of the considerations in eliciting expert knowledge include determining how to work with multiple experts and how to combine multiple judgments, minimizing bias in the elicited information, and verifying the accuracy of expert information. We highlight structured elicitation techniques that, if adopted, will improve the accuracy and information content of expert judgment and ensure uncertainty is captured accurately. We suggest four aspects of an expert elicitation exercise be examined to determine its comprehensiveness and effectiveness: study design and context, elicitation design, elicitation method, and elicitation output. Just as the reliability of empirical data depends on the rigor with which it was acquired so too does that of expert knowledge.

Australian lungfish (Neoceratodus forsteri: Dipnoi) have low genetic variation at allozyme and mitochondrial DNA loci : a conservation alert?

Genetic variation at allozyme and mitochondrial DNA loci was investigated in the Australian lungfish, Neoceratodus forsteri Krefft 1870. Tissue samples for genetic analysis were taken non-lethally from 278 individuals representing two spatially distinct endemic populations (Mary and Burnett rivers), as well as one population thought to be derived from an anthropogenic translocation in the 1890's (Brisbane river). Two of 24 allozyme loci resolved from muscle tissue were polymorphic. Mitochondrial DNA nucleotide sequence diversity estimated across 2,235 base pairs in each of 40 individuals ranged between 0.000423 and 0.001470 per river. Low genetic variation at allozyme and mitochondrial loci could be attributed to population bottlenecks, possibly induced by Pleistocene aridity. Limited genetic differentiation was detected among rivers using nuclear and mitochondrial markers suggesting that admixture may have occurred between the endemic Mary and Burnett populations during periods of low sea level when the drainages may have converged before reaching the ocean. Genetic data was consistent with the explanation that lungfish were introduced to the Brisbane river from the Mary river. Further research using more variable genetic loci is needed before the conservation status of populations can be determined, particularly as anthropogenic demands on lungfish habitat are increasing. In the interim we recommend a management strategy aimed at conserving existing genetic variation within and between rivers.

Orthogonality defect and reduced search-space size for solving integer least-squares problems

In the context of ambiguity resolution (AR) of Global Navigation Satellite Systems (GNSS), decorrelation among entries of an ambiguity vector, integer ambiguity search and ambiguity validations are three standard procedures for solving integer least-squares problems. This paper contributes to AR issues from three aspects. Firstly, the orthogonality defect is introduced as a new measure of the performance of ambiguity decorrelation methods, and compared with the decorrelation number and with the condition number which are currently used as the judging criterion to measure the correlation of ambiguity variance-covariance matrix. Numerically, the orthogonality defect demonstrates slightly better performance as a measure of the correlation between decorrelation impact and computational efficiency than the condition number measure. Secondly, the paper examines the relationship of the decorrelation number, the condition number, the orthogonality defect and the size of the ambiguity search space with the ambiguity search candidates and search nodes. The size of the ambiguity search space can be properly estimated if the ambiguity matrix is decorrelated well, which is shown to be a significant parameter in the ambiguity search progress. Thirdly, a new ambiguity resolution scheme is proposed to improve ambiguity search efficiency through the control of the size of the ambiguity search space. The new AR scheme combines the LAMBDA search and validation procedures together, which results in a much smaller size of the search space and higher computational efficiency while retaining the same AR validation outcomes. In fact, the new scheme can deal with the case there are only one candidate, while the existing search methods require at least two candidates. If there are more than one candidate, the new scheme turns to the usual ratio-test procedure. Experimental results indicate that this combined method can indeed improve ambiguity search efficiency for both the single constellation and dual constellations respectively, showing the potential for processing high dimension integer parameters in multi-GNSS environment.

Hospital utilisation among people born in refugee-source countries : an analysis of hospital admissions, Victoria, 1998–2004

Objective: To investigate whether hospital utilisation and health outcomes in Victoria differ between people born in refugee-source countries and those born in Australia. Design and setting: Analysis of a statewide hospital discharge dataset for the 6 financial years from 1 July 1998 to 30 June 2004. Hospital admissions of people born in eight countries for which the majority of entrants to Australia arrived as refugees were included in the analysis. Main outcome measures: Age-standardised rates and rate ratios for: total hospital admissions; emergency admissions; surgical admissions; total days in hospital; discharge at own risk; hospital deaths; admissions due to infectious and parasitic diseases; and admissions due to mental and behavioural disorders. Results: In 2003–04, compared with the Australia-born Victorian population, people born in refugee-source countries had lower rates of surgical admission (rate ratio [RR], 0.85; 95% CI, 0.81–0.88), total days in hospital (RR, 0.74; 95% CI, 0.73–0.75), and admission due to mental and behavioural disorders (RR, 0.70; 95% CI, 0.65–0.76). Over the 6-year period, rates of total days in hospital and rates of admission due to mental and behavioural disorders for people born in refugee-source countries increased towards Australian-born averages, while rates of total admissions, emergency admissions, and admissions due to infectious and parasitic diseases increased above the Australian-born averages. Conclusions: Use of hospital services among people born in refugee-source countries is not higher than that of the Australian-born population and shows a trend towards Australian-born averages. Our findings indicate that the Refugee and Humanitarian Program does not currently place a burden on the Australian hospital system.