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.

A pilot study utilising cross-age peer tutoring as a method of intervention for anxious adolescents

Anxiety disorders are the most common psychopathology experienced by young people, with up to 18% of adolescents developing an anxiety disorder. The consequences of these disorders, if left untreated, include impaired peer relationships, school absenteeism and self-concept problems. In addition, anxiety disorders may play a causal role in the development of depression in young people, precede eating disorders and predispose adolescents to substance abuse disorders. While the school is often chosen as a place to provide early intervention for this debilitating disorder, the fact that excessive anxiety is often not recognised in school and that young people are reluctant to seek help, makes identifying these adolescents difficult. Even when these young people are identified, there are problems in providing sensitive programs which are not stigmatising to them within a school setting. One method which may engage this adolescent population could be cross-age peer tutoring. This paper reports on a small pilot study using the “Worrybusters” program and a cross-age peer tutoring method to engage the anxious adolescents. These anxious secondary school students planned activities for teacher-referred anxious primary school students for a term in the high school setting and then delivered those activities to the younger students weekly in the next term in the primary school. Although the secondary school students decreased their scores on anxiety self-report measures there were no significant differences for primary school students’ self-reports. However, the primary school parent reports indicated a significant decrease in their child’s anxiety.

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.

Decision support system for contractor pre-qualification : artificial neural network model

The selection criteria for contractor pre-qualification are characterized by the co-existence of both quantitative and qualitative data. The qualitative data is non-linear, uncertain and imprecise. An ideal decision support system for contractor pre-qualification should have the ability of handling both quantitative and qualitative data, and of mapping the complicated nonlinear relationship of the selection criteria, such that rational and consistent decisions can be made. In this research paper, an artificial neural network model was developed to assist public clients identifying suitable contractors for tendering. The pre-qualification criteria (variables) were identified for the model. One hundred and twelve real pre-qualification cases were collected from civil engineering projects in Hong Kong, and eighty-eight hypothetical pre-qualification cases were also generated according to the “If-then” rules used by professionals in the pre-qualification process. The results of the analysis totally comply with current practice (public developers in Hong Kong). Each pre-qualification case consisted of input ratings for candidate contractors’ attributes and their corresponding pre-qualification decisions. The training of the neural network model was accomplished by using the developed program, in which a conjugate gradient descent algorithm was incorporated for improving the learning performance of the network. Cross-validation was applied to estimate the generalization errors based on the “re-sampling” of training pairs. The case studies show that the artificial neural network model is suitable for mapping the complicated nonlinear relationship between contractors’ attributes and their corresponding pre-qualification (disqualification) decisions. The artificial neural network model can be concluded as an ideal alternative for performing the contractor pre-qualification task.

Limits of spherical blur determined with an adaptive optics mirror

We extended an earlier study (Vision Research, 45, 1967–1974, 2005) in which we investigated limits at which induced blur of letter targets becomes noticeable, troublesome and objectionable. Here we used a deformable adaptive optics mirror to vary spherical defocus for conditions of a white background with correction of astigmatism; a white background with reduction of all aberrations other than defocus; and a monochromatic background with reduction of all aberrations other than defocus. We used seven cyclopleged subjects, lines of three high-contrast letters as targets, 3–6 mm artificial pupils, and 0.1–0.6 logMAR letter sizes. Subjects used a method of adjustment to control the defocus component of the mirror to set the 'just noticeable', 'just troublesome' and 'just objectionable' defocus levels. For the white-no adaptive optics condition combined with 0.1 logMAR letter size, mean 'noticeable' blur limits were ±0.30, ±0.24 and ±0.23 D at 3, 4 and 6 mm pupils, respectively. White-adaptive optics and monochromatic-adaptive optics conditions reduced blur limits by 8% and 20%, respectively. Increasing pupil size from 3–6 mm decreased blur limits by 29%, and increasing letter size increased blur limits by 79%. Ratios of troublesome to noticeable, and of objectionable to noticeable, blur limits were 1.9 and 2.7 times, respectively. The study shows that the deformable mirror can be used to vary defocus in vision experiments. Overall, the results of noticeable, troublesome and objectionable blur agreed well with those of the previous study. Attempting to reduce higher-order aberrations or chromatic aberrations, reduced blur limits to only a small extent.

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.

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.

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.