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.

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.

Malnutrition and pressure ulcer risk in adults in Australian health care facilities

Aims To determine the effect of nutritional status on the presence and severity of pressure ulcers in statewide? public healthcare facilities, in Queensland, Australia. Research Methods A multicentre, cross sectional audit of nutritional status of a convenience sample of subjects was carried out as part of a large audit of pressure ulcers in a sample of state based public healthcare facilities in 2002 and 2003. Dietitians in 20 hospitals and six residential aged care facilities conducted single day nutritional status audits of 2208 acute and 839 aged care subjects using the Subjective Global Assessment. The effect of nutritional status on the presence, highest stage and number of pressure ulcers was determined by logistic regression in a model controlling for age, gender, medical specialty and facility location. The potential clustering effect of facility was accounted for in the model using an analysis of correlated data approach. Results Subjects with malnutrition had an adjusted odds risk of 2.6 (95% CI 1.8-3.5, p<0.001) of having a pressure ulcer in acute facilities and 2.0 (95% CI 1.5-2.7, p<0.001) for residential aged care facilities. There was also increased odds risk of having a pressure ulcer, having a higher stage pressure ulcer and a higher number of pressure ulcers with increased severity of malnutrition. Conclusion Malnutrition was associated with at least twice the odds risk of having a pressure ulcer of in public healthcare facilities in Queensland. Action must be taken to identify, prevent and treat malnutrition, especially in patients at risk of pressure ulcer.

Intraocular pressure in keratoconus

Aims: To investigate IOP measurements with the dynamic contour tonometer (DCT) and non contact tonometer (NCT) in subjects with keratoconus. Methods: Twenty keratoconic subjects and 20 age-matched control subjects had IOP measurements taken using DCT and NCT instruments. Central and offcentre measures were taken with the DCT in order to highlight any systematic errors associated with corneal biomechanical factors. Measures of anterior and posterior corneal topography and thickness were also taken for each subject. Results: No significant difference was found between the central and off-centre DCT IOP readings for the keratoconics and age-matched controls (p>0.05). The average DCT IOP for the keratoconics was 14.2 ± 1.4 mmHg and for the agematched controls was 14.2 ± 1.6 mmHg. However, the average NCT readings differed significantly (p<0.001) between the keratoconics (9.2 ± 1.5 mmHg) and age-matched controls (12.9 ± 2.4 mmHg). DCT IOP showed no significant (p>0.05) correlation with the severity of keratoconus, as determined through measures of corneal topography and thickness. NCT IOP was correlated significantly with certain measures of corneal curvature and thickness in the keratoconic population. The difference between DCT and NCT IOP was strongly correlated with measures of corneal topography and thickness, with differences increasing for more advanced keratoconus. Conclusions: The measurements from the DCT do not appear to be dependent upon corneal factors, unlike the NCT. The presence or severity of keratoconus was not correlated with DCT IOP values.