Detailed analysis of a conservative difference approximation for the time fractional diffusion equation

Diffusion equations that use time fractional derivatives are attractive because they describe a wealth of problems involving non-Markovian Random walks. The time fractional diffusion equation (TFDE) is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order α ∈ (0, 1). Developing numerical methods for solving fractional partial differential equations is a new research field and the theoretical analysis of the numerical methods associated with them is not fully developed. In this paper an explicit conservative difference approximation (ECDA) for TFDE is proposed. We give a detailed analysis for this ECDA and generate discrete models of random walk suitable for simulating random variables whose spatial probability density evolves in time according to this fractional diffusion equation. The stability and convergence of the ECDA for TFDE in a bounded domain are discussed. Finally, some numerical examples are presented to show the application of the present technique.

Numerical approximation of a fractional-in-space diffusion equation (II) - with nonhomogeneous boundary conditions

In this paper, a space fractional di®usion equation (SFDE) with non- homogeneous boundary conditions on a bounded domain is considered. A new matrix transfer technique (MTT) for solving the SFDE is proposed. The method is based on a matrix representation of the fractional-in-space operator and the novelty of this approach is that a standard discretisation of the operator leads to a system of linear ODEs with the matrix raised to the same fractional power. Analytic solutions of the SFDE are derived. Finally, some numerical results are given to demonstrate that the MTT is a computationally e±cient and accurate method for solving SFDE.

M-technology, Consumption and Gambling: A Conceptualisation of Consumer Vulnerability in an M-gambling Marketplace

Technology imbued m-marketing systems influence the consumptive lives of citizens, by facilitating anytime, anywhere business-to-consumer interactions. Business pundits’ enthusiasm towards mobile services (m-services) has been driven by the promise of a marketspace context involving seamless, business-to-consumer interactions that can be simultaneously impulse-driven, highly entertaining and omnipresent. Arguably, gambling too is impulse-driven, exciting and easily accessible. An important question that needs to be addressed is: how the convergence of mobile technology and gambling will impact the millennial consumer. The authors address this question by examining the contextually bounded interactions between internal and external factors that make mobile phone users potentially vulnerable during m-gambling interactions. By examining key themes that describe the convergence of m-technology and gambling, we clarify the experiential nature of m-gambling and its relationship to consumer vulnerability.

Towards a literacy of attention

In 1997, business trend analyst Linda Stone proposed the term "continuous partial attention" to characterise the contemporary experience of wanting to be ‘a live node on the network’. She argued that while it can be a positive and functional behaviour, it also has the potential to be disabling, compromising reflective and creative thought. Subsequent studies have explored the ways in which technology has slowly disrupted the idea and experience of a "centred" and "bounded" self. Studies of ‘Gen Y’ show the ease with which young people accommodate this multiplying of the self as they negotiate their partial friendships and networks of interest with family and work. In teaching and learning circles in tertiary education we talk a lot about problems of student ‘disengagement’. In characterising our challenge this way, are we undermining our potential to understand the tendencies of contemporary learners? This paper begins a consideration of how traditional models, frameworks and practices might oppose these partially engaged but continuously connected and interpersonal "dividuals". What questions does this provoke for learning environments towards harnessing yet counterpointing the crisis students might experience; to recognise but also integrate their multiple selves towards what they aim to become through the process of learning?

Delay-dependent robust H-infinity control for uncertain systems with time-varying delay

This paper proposes a new approach for delay-dependent robust H-infinity stability analysis and control synthesis of uncertain systems with time-varying delay. The key features of the approach include the introduction of a new Lyapunov–Krasovskii functional, the construction of an augmented matrix with uncorrelated terms, and the employment of a tighter bounding technique. As a result, significant performance improvement is achieved in system analysis and synthesis without using either free weighting matrices or model transformation. Examples are given to demonstrate the effectiveness of the proposed approach.

The role of decision-maker preferences in tenancy selection of CBD office accommodation – preliminary literature review

The literature and anecdotal evidence suggests that that there is more to tenancy selection (firm location) than the profit maximisation drive that traditional neo-classical economic location theory suggests. In the first instance these models assume property markets are rational and perfectly competitive; the CBD office market is clearly neither rational nor perfectly competitive. This fact alone relegates such models to the margins of usefulness for an industry that seeks to satisfy tenant demand in order to optimise returns on capital invested. Acknowledgment of property market imperfections are universally accepted to the extent that all contemporary texts discuss the lack of a coherent centralised market place and incomplete and poorly disseminated information processes as fundamental inadequacies which characterise the property market inefficiencies. Less well researched are the facets of the market which allow the observer to determine market activity to be significantly irrational. One such facet is that of ‘decision maker preferences’. The decision to locate a business operation at one location as opposed to another seems ostensibly a routine choice based on short, medium and long term business objectives. These objectives are derived from a process of strategic planning by one or more individuals whose goal is held to be to optimise outcomes which benefit the business (and presumably those employed within it). However the decision making processes appear bounded by how firms function, the institutional context in which they operate, as well as by opportunistic behaviour by individual decision makers who allow personal preferences to infiltrate and ‘corrupt’ the process. In this way, history, culture, geography, as well as institutions all become significant to the extent that these influence and shape individual behaviour which in turn determine the morphology of individual preferences, as well as providing a conduit for them to take effect. This paper exams historical and current literature on the impact of individual behaviour in the decision making process within organisations as a precursor to an investigation of the tenancy decision making process within the CBD office market. Literature on the topic falls within a number of research disciplines, philosophy, psychology and economics to name a few.

Cognitive behaviour therapy vs rational-emotive education : impact on children's self-talk, self-esteem and irrational beliefs

This study investigated the impact of Cognitive-Behavioural Therapy (CBT) and Rational~Emotive Education (REE) self-enhancement programs on children's self-talk, self-esteem and irrational beliefs. A total of 116 children (50.9% girls) with a mean age of 9.8 years attending Years 4 and 6 at two primary schools participated in the study. eBT resulted in a reduction in negative self-talk while REE seemed to enhance independence beliefs. Both programs were associated with increased positive self-talk and with having increased rationality in Conformity and Discomfort Intolerance beliefs.

A study of entrepreneurship : Taiwanese digital content companies in China

China’s accession to the World Trade Organisation (WTO) has greatly enhanced global interest in investment in the Chinese media market, where demand for digital content is growing rapidly. The East Asian region is positioned as a growth area in many forms of digital content and digital service industries. China is attempting to catch up and take its place as a production centre to offset challenges from neighbouring countries. Meanwhile, Taiwan is seeking to use China both as an export market and as a production site for its digital content. This research investigates entry strategies of Taiwanese digital content firms into the Chinese market. By examining the strategies of a sample of Taiwan-based companies, this study also explores the evolution of their market strategies. However, the focus is on how distinctive business practices such as guanxi are important to Taiwanese business and to relations with Mainland China. This research examines how entrepreneurs manage the characteristics of digital content products and in turn how digital content entrepreneurs adapt to changing market circumstances. This project selected five Taiwan-based digital content companies that have business operations in China: Wang Film, Artkey, CnYES, Somode and iPartment. The study involved a field trip, undertaken between November 2006 and March 2007 to Shanghai and Taiwan to conduct interviews and to gather documentation and archival reports. Six senior managers and nine experts were interviewed. Data were analysed according to Miller’s firm-level entrepreneurship theory, foreign direct investment theory, Life Cycle Model and guanxi philosophy. Most studies of SMEs have focused on free market (capitalist) environments. In contrast, this thesis examines how Taiwanese digital content firms’ strategies apply in the Chinese market. I identified three main types of business strategy: cost-reduction, innovation and quality-enhancement; and four categories of functional strategies: product, marketing, resource acquisition and organizational restructuring. In this study, I introduce the concept of ‘entrepreneurial guanxi’, special relationships that imply mutual obligation, assurance and understanding to secure and exchange favors in entrepreneurial activities. While guanxi is a feature of many studies of business in Pan-Chinese society, it plays an important mediating role in digital content industries. In this thesis, I integrate the ‘Life Cycle Model’ with the dynamic concept of strategy. I outline the significant differences in the evolution of strategy between two types of digital content companies: off-line firms (Wang Film and Artkey) and web-based firms (CnYES, Somode and iPartment). Off-line digital content firms tended to adopt ‘resource acquisition strategies’ in their initial stages and ‘marketing strategies’ in second and subsequent stages. In contrast, web-based digital content companies mainly adopted product and marketing strategies in the early stages, and would adopt innovative approaches towards product and marketing strategies in the whole process of their business development. Some web-based digital content companies also adopted organizational restructuring strategies in the final stage. Finally, I propose the ‘Taxonomy Matrix of Entrepreneurial Strategies’ to emphasise the two dimensions of this matrix: innovation, and the firm’s resource acquisition for entrepreneurial strategy. This matrix is divided into four cells: Effective, Bounded, Conservative, and Impoverished.

Interpersonal coordination tendencies, decision-making and information governing dynamics in rugby union

In this chapter, ideas from ecological psychology and nonlinear dynamics are integrated to characterise decision-making as an emergent property of self-organisation processes in the interpersonal interactions that occur in sports teams. A conceptual model is proposed to capture constraints on dynamics of decisions and actions in dyadic systems, which has been empirically evaluated in simulations of interpersonal interactions in team sports. For this purpose, co-adaptive interpersonal dynamics in team sports such as rubgy union have been studied to reveal control parameter and collective variable relations in attacker-defender dyads. Although interpersonal dynamics of attackers and defenders in 1 vs 1 situations showed characteristics of chaotic attractors, the informational constraints of rugby union typically bounded dyadic systems into low dimensional attractors. Our work suggests that the dynamics of attacker-defender dyads can be characterised as an evolving sequence since players' positioning and movements are connected in diverse ways over time.

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.

Asynchronicity and the ‘time envelope’ of online annotation : the case of the photosharing website, Flickr

This paper examines a sequence of asynchronous interaction on the photosharing website, Flickr. In responding to a call for a focus on the performative aspects of online annotation (Wolff & Neuwirth, 2001), we outline and apply an interaction order approach to identify temporal and cultural aspects of the setting that provide for commonality and sharing. In particular, we study the interaction as a feature of a synthetic situation (Knorr Cetina, 2009) focusing on the requirements of maintaining a sense of an ongoing discussion online. Our analysis suggests that the rhetorical system of the Flickr environment, its appropriation by participants as a context for bounded activities, and displays of commonality, affiliation, and shared access provide for a common sense of participation in a time envelope. This, in turn, is argued to be central to new processes of consociation (Schutz, 1967; Zhao, 2004) occurring in the life world of Web 2.0 environments.

Numerical simulation for the 3D seepage flow with fractional derivatives in porous media

In this paper, the numerical simulation of the 3D seepage flow with fractional derivatives in porous media is considered under two special cases: non-continued seepage flow in uniform media (NCSFUM) and continued seepage flow in non-uniform media (CSF-NUM). A fractional alternating direction implicit scheme (FADIS) for the NCSF-UM and a modified Douglas scheme (MDS) for the CSF-NUM are proposed. The stability, consistency and convergence of both FADIS and MDS in a bounded domain are discussed. A method for improving the speed of convergence by Richardson extrapolation for the MDS is also presented. Finally, numerical results are presented to support our theoretical analysis.

Modified alternating direction methods for solving a two-dimensional non-continuous seepage flow with fractional derivatives

In this paper, a two-dimensional non-continuous seepage flow with fractional derivatives (2D-NCSF-FD) in uniform media is considered, which has modified the well known Darcy law. Using the relationship between Riemann-Liouville and Grunwald-Letnikov fractional derivatives, two modified alternating direction methods: a modified alternating direction implicit Euler method and a modified Peaceman-Rachford method, are proposed for solving the 2D-NCSF-FD in uniform media. The stability and consistency, thus convergence of the two methods in a bounded domain are discussed. Finally, numerical results are given.

Motivation, development and validation of a new spectral greenness index : a spectral dimension related to foliage projective cover

A method is presented for the development of a regional Landsat-5 Thematic Mapper (TM) and Landsat-7 Enhanced Thematic Mapper plus (ETM+) spectral greenness index, coherent with a six-dimensional index set, based on a single ETM+ spectral image of a reference landscape. The first three indices of the set are determined by a polar transformation of the first three principal components of the reference image and relate to scene brightness, percent foliage projective cover (FPC) and water related features. The remaining three principal components, of diminishing significance with respect to the reference image, complete the set. The reference landscape, a 2200 km2 area containing a mix of cattle pasture, native woodland and forest, is located near Injune in South East Queensland, Australia. The indices developed from the reference image were tested using TM spectral images from 19 regionally dispersed areas in Queensland, representative of dissimilar landscapes containing woody vegetation ranging from tall closed forest to low open woodland. Examples of image transformations and two-dimensional feature space plots are used to demonstrate image interpretations related to the first three indices. Coherent, sensible, interpretations of landscape features in images composed of the first three indices can be made in terms of brightness (red), foliage cover (green) and water (blue). A limited comparison is made with similar existing indices. The proposed greenness index was found to be very strongly related to FPC and insensitive to smoke. A novel Bayesian, bounded space, modelling method, was used to validate the greenness index as a good predictor of FPC. Airborne LiDAR (Light Detection and Ranging) estimates of FPC along transects of the 19 sites provided the training and validation data. Other spectral indices from the set were found to be useful as model covariates that could improve FPC predictions. They act to adjust the greenness/FPC relationship to suit different spectral backgrounds. The inclusion of an external meteorological covariate showed that further improvements to regional-scale predictions of FPC could be gained over those based on spectral indices alone.