A Numerical Solution Using an Adaptively Preconditioned Lanczos Method for a Class of Linear Systems Related with the Fractional Poisson Equation

This study considers the solution of a class of linear systems related with the fractional Poisson equation (FPE) (−∇2)α/2φ=g(x,y) with nonhomogeneous boundary conditions on a bounded domain. A numerical approximation to FPE is derived using a matrix representation of the Laplacian to generate a linear system of equations with its matrix A raised to the fractional power α/2. The solution of the linear system then requires the action of the matrix function f(A)=A−α/2 on a vector b. For large, sparse, and symmetric positive definite matrices, the Lanczos approximation generates f(A)b≈β0Vmf(Tm)e1. This method works well when both the analytic grade of A with respect to b and the residual for the linear system are sufficiently small. Memory constraints often require restarting the Lanczos decomposition; however this is not straightforward in the context of matrix function approximation. In this paper, we use the idea of thick-restart and adaptive preconditioning for solving linear systems to improve convergence of the Lanczos approximation. We give an error bound for the new method and illustrate its role in solving FPE. Numerical results are provided to gauge the performance of the proposed method relative to exact analytic solutions.

Practice as method : the ex/centric fixations project

In the past decade, scholars have proposed a range of terms to describe the relationship between practice and research in the creative arts, including increasingly nuanced definitions of practice-based research, practice-led research and practice-as-research. In this paper, I consider the efficacy of creative practice as method. I use the example of The Ex/Centric Fixations Project – a project in which I have embedded creative practice in a research project, rather than embedding research in a creative project. The Ex/Centric Fixations project investigates the way spectators interpret human experiences – especially human experiences of difference, marginalisation or discrimination – depicted onstage. In particular, it investigates the way postmodern performance writing strategies, and the presence of performing bodied to which the experience depicted can be attached, impacts on interpretations. It is part of a broader research project which examines the performativity of spectatorship, and intervenes in emergent debates about performance, ethics and spectatorship in the context of debate about whether live performance is a privileged site for the emergence of an ethical face-to-face encounter with the Other. Using the metaphor of the Mobius strip, I examines the way practice – as a method, rather than an output – has informed, influenced and problematised the broader research project.

Metal oxide nanofibres membranes assembled by spin-coating method

Ceramic membranes are of particular interest in many industrial processes due to their ability to function under extreme conditions while maintaining their chemical and thermal stability. Major structural deficiencies under conventional fabrication approach are pin-holes and cracks, and the dramatic losses of flux when pore sizes are reduced to enhance selectivity. We overcome these structural deficiencies by constructing hierarchically structured separation layer on a porous substrate using larger titanate nanofibres and smaller boehmite nanofibres. This yields a radical change in membrane texture. The differences in the porous supports have no substantial influences on the texture of resulting membranes. The membranes with top layer of nanofibres coated on different porous supports by spin-coating method have similar size of the filtration pores, which is in a range of 10–100 nm. These membranes are able to effectively filter out species larger than 60 nm at flow rates orders of magnitude greater than conventional membranes. The retention can attain more than 95%, while maintaining a high flux rate about 900 L m-2 h. The calcination after spin-coating creates solid linkages between the fibres and between fibres and substrate, in addition to convert boehmite into -alumina nanofibres. This reveals a new direction in membrane fabrication.

Within- and between-day repeatability and variability in children's physiological responses during submaximal treadmill exercise

The purpose of this study was to verify within- and between-day repeatability and variability in children's oxygen uptake (VO^sub 2^), gross economy (GE; VO^sub 2^ divided by speed) and heart rate (HR) during treadmill walking based on self-selected speed (SS). Fourteen children (10.1 ± 1.4 years) undertook three testing sessions over 2 days in which four walking speeds, including SS were tested. Within- and between-day repeatability were assessed using the Bland and Altman method, and coefficients of variability (CV) were determined for each child across exercise bouts and averaged to obtain a mean group CV value for VO^sub 2^, GE, and HR per speed. Repeated measures analysis of variance showed no statistically significant differences in within- or between-day CV for VO^sub 2^, GE, or HR at any speed. Repeatability within- and between-day for VO^sub 2^, GE, and HR for all speeds was verified. These results suggest that submaximal VO^sub 2^ during treadmill walking is stable and reproducible at a range of speeds based on children's SS.

Numerical method and analytical technique of the modified anomalous subdiffusion equation with a nonlinear source term

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

Stability and convergence of an implicit numerical method for the non-linear fractional reaction-subdiffusion process

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.

Marx as critical discourse analyst : the genesis of a critical method and its relevance to the critique of global capital.

In this paper we identify elements in Marx´s economic and political writings that are relevant to contemporary critical discourse analysis (CDA). We argue that Marx can be seen to be engaging in a form of discourse analysis. We identify the elements in Marx´s historical materialist method that support such a perspective, and exemplify these in a longitudinal comparison of Marx´s texts.

Health-related quality of life in obese children and adolescents

Objective: This review addresses the effect of overweight and obese weight status on pediatric health-related quality of life (HRQOL). Method: Web of Science, Medline, CINAHL, Cochrane Library, EMBASE, AMED and PubMed were searched for peer-reviewed studies in English reporting HRQOL and weight status in youth (<21 years), published before March 2008. Results: Twenty-eight articles were identified. Regression of HRQOL against body mass index (BMI) using pooled data from 13 studies utilizing the Pediatric Quality of Life Inventory identified an inverse relationship between BMI and pediatric HRQOL (r=−0.7, P=0.008), with impairments in physical and social functioning consistently reported. HRQOL seemed to improve with weight loss, but randomized controlled trials were few and lacked long-term follow-up. Conclusions: Little is known about the factors associated with reduced HRQOL among overweight or obese youth, although gender, age and obesity-related co-morbidities may play a role. Few studies have examined the differences in HRQOL between community and treatment-seeking samples. Pooled regressions suggest pediatric self-reported HRQOL can be predicted from parent proxy reports, although parents of obese youths tend to perceive worse HRQOL than children do about themselves. Thus, future research should include both pediatric and parent proxy perspectives.

Searching the self in Seoul : trans-youth and urban social networking in Korea

This paper presents a brief analysis of Seoul trans-youth’s search for identity through urban social networking, arguing that technological, socio-cultural and environmental (urban) contexts frame how mobility and ubiquity are (re)created in Seoul. The paper is empirically based on fieldwork conducted in Seoul, South Korea, from 2007 to 2008 as part of a research project on the mobile play culture of Seoul trans-youth(a term that will be explained in detail in the following section). Shared Visual Ethnography (SVE) was used as the research method which involved sharing of visual ethnographic data that were created by the participants. More specifically, the participants were asked to take photos, which were then shared and discussed with other participants and the researcher on the photo-sharing service Flickr. The research also involved a questionnaire and daily activity diaries, as well as interviews. A total of 44 Korean transyouths – including 23 females and 21 males – participated in interviews and photo-sharing. The paper draws specifically on the qualitative data from individual and/or group interviews, the total duration of which was 2–2.5 hours for each participant.

Generation in context : an exploratory method for musical enquiry

This paper discusses a method, Generation in Context, for interrogating theories of music analysis and music perception. Given an analytic theory, the method consists of creating a generative process that implements the theory in reverse. Instead of using the theory to create analyses from scores, the theory is used to generate scores from analyses. Subjective evaluation of the quality of the musical output provides a mechanism for testing the theory in a contextually robust fashion. The method is exploratory, meaning that in addition to testing extant theories it provides a general mechanism for generating new theoretical insights. We outline our initial explorations in the use of generative processes for music research, and we discuss how generative processes provide evidence as to the veracity of theories about how music is experienced, with insights into how these theories may be improved and, concurrently, provide new techniques for music creation. We conclude that Generation in Context will help reveal new perspectives on our understanding of music.

Numerical investigations of linear least squares methods for derivative estimation

The results of a numerical investigation into the errors for least squares estimates of function gradients are presented. The underlying algorithm is obtained by constructing a least squares problem using a truncated Taylor expansion. An error bound associated with this method contains in its numerator terms related to the Taylor series remainder, while its denominator contains the smallest singular value of the least squares matrix. Perhaps for this reason the error bounds are often found to be pessimistic by several orders of magnitude. The circumstance under which these poor estimates arise is elucidated and an empirical correction of the theoretical error bounds is conjectured and investigated numerically. This is followed by an indication of how the conjecture is supported by a rigorous argument.

Glycaemic index and glycaemic load intake patterns in older Australian women

Aims: Dietary glycemic index (GI) and glycemic load (GL) have been associated with risk of chronic diseases, yet limited research exists on patterns of consumption in Australia. Our aims were to investigate glycemic carbohydrate in a population of older women, identify major contributing food sources, and determine low, moderate and high ranges. Methods: Subjects were 459 Brisbane women aged 42-81 years participating in the Longitudinal Assessment of Ageing in Women. Diet history interviews were used to assess usual diet and results were analysed into energy and macronutrients using the FoodWorks dietary analysis program combined with a customised GI database. Results: Mean±SD dietary GI was 55.6±4.4% and mean dietary GL was 115±25. A low GI in this population was ≤52.0, corresponding to the lowest quintile of dietary GI, and a low GL was ≤95. GI showed a quadratic relationship with age (P=0.01), with a slight decrease observed in women aged in their 60’s relative to younger or older women. GL decreased linearly with age (P<0.001). Bread was the main contributor to carbohydrate and dietary GL (17.1% and 20.8%, respectively), followed by fruit (15.5% and 14.2%), and dairy for carbohydrate (9.0%) or breakfast cereals for GL (8.9%). Conclusions: In this population, dietary GL decreased with increasing age, however this was likely to be a result of higher energy intakes in younger women. Focus on careful selection of lower GI items within bread and breakfast cereal food groups would be an effective strategy for decreasing dietary GL in this population of older women.