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.

Characteristics of the Internet for Criminal Child Sexual Abuse by Online Groomers

This paper presents a number of characteristics of the Internet that makes it attractive to online groomers. Relevant Internet characteristics include disconnected personal communication, mediating technology, universality, network externalities, distribution channel, time moderator, low‐cost standard, electronic double, electronic double manipulation, information asymmetry, infinite virtual capacity, independence in time and space, cyberspace, and dynamic social network. Potential sex offenders join virtual communities, where they meet other persons who have the same interest. A virtual community provides an online meeting place where people with similar interests can communicate and find useful information. Communication between members may be via email, bulletin boards, online chat, web‐based conferencing or other computer‐based media.

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.

Food insecurity among Australian children : potential determinants, health and developmental consequences

Children in food-insecure households may be at risk of poor health, developmental or behavioural problems. This study investigated the associations between food insecurity, potential determinants and health and developmental outcomes among children. Data on household food security, socio-demographic characteristics and children’s weight, health and behaviour were collected from households with children aged 3–17 years in socioeconomically disadvantaged suburbs by mail survey using proxy-parental reports (185 households). Data were analysed using logistic regression. Approximately one-in-three households (34%) were food insecure. Low household income was associated with an increased risk of food insecurity [odds ratio (OR), 16.20; 95% confidence interval (CI), 3.52–74.47]. Children with a parent born outside of Australia were less likely to experience food insecurity (OR, 0.42; 95% CI, 0.19–0.93). Children in food-insecure households were more likely to miss days from school or activities (OR, 3.52; 95% CI, 1.46–8.54) and were more likely to have borderline or atypical emotional symptoms (OR, 2.44; 95% CI, 1.11–5.38) or behavioural difficulties (OR, 2.35; 95% CI, 1.04–5.33). Food insecurity may be prevalent among socioeconomically disadvantaged households with children. The potential developmental consequences of food insecurity during childhood may result in serious adverse health and social implications.