Numerical techniques for the variable order time fractional diffusion equation

In this paper we consider the variable order time fractional diffusion equation. We adopt the Coimbra variable order (VO) time fractional operator, which defines a consistent method for VO differentiation of physical variables. The Coimbra variable order fractional operator also can be viewed as a Caputo-type definition. Although this definition is the most appropriate definition having fundamental characteristics that are desirable for physical modeling, numerical methods for fractional partial differential equations using this definition have not yet appeared in the literature. Here an approximate scheme is first proposed. The stability, convergence and solvability of this numerical scheme are discussed via the technique of Fourier analysis. Numerical examples are provided to show that the numerical method is computationally efficient. Crown Copyright © 2012 Published by Elsevier Inc. All rights reserved.

Numerical methods for solving a two-dimensional variable-order anomalous subdiffusion equation

Anomalous subdiffusion equations have in recent years received much attention. In this paper, we consider a two-dimensional variable-order anomalous subdiffusion equation. Two numerical methods (the implicit and explicit methods) are developed to solve the equation. Their stability, convergence and solvability are investigated by the Fourier method. Moreover, the effectiveness of our theoretical analysis is demonstrated by some numerical examples. © 2011 American Mathematical Society.

Monocular amblyopia and higher order aberrations

This study compared the corneal and total higher order aberrations between the fellow eyes in monocular amblyopia. Nineteen amblyopic subjects (8 refractive and 11 strabismic) (mean age 30 ± 11 years) were recruited. A range of biometric and optical measurements were collected from the amblyopic and non-amblyopic eye including; axial length, corneal topography and total higher order aberrations. For a sub-group of eleven non-presbyopic subjects (6 refractive and 5 strabismic amblyopes, mean age 29 ± 10 years) total higher order aberrations were also measured during accommodation (2.5 D stimuli). Amblyopic eyes were significantly shorter and more hyperopic compared to non-amblyopic eyes and the interocular difference in axial length correlated with both the magnitude of anisometropia and amblyopia (both p < 0.01). Significant differences in higher order aberrations were observed between fellow eyes, which varied with the type of amblyopia. Refractive amblyopes displayed higher levels of 4th order corneal aberrations C(4, 0)(spherical aberration), C(4, 2)(secondary astigmatism 90°) and C(4, −2)(secondary astigmatism along 45°) in the amblyopic eye compared to the non-amblyopic eye. Strabismic amblyopes exhibited significantly higher levels of C(3, 3)(trefoil) in the amblyopic eye for both corneal and total higher order aberrations. During accommodation, the amblyopic eye displayed a significantly greater lag of accommodation compared to the non-amblyopic eye, while the changes in higher order aberrations were similar in magnitude between fellow eyes. Asymmetric visual experience during development appears to be associated with asymmetries in higher order aberrations, in some cases proportional to the magnitude of anisometropia and dependent upon the amblyogenic factor.

Stable strong order 1.0 schemes for solving stochastic ordinary differential equations

The Balanced method was introduced as a class of quasi-implicit methods, based upon the Euler-Maruyama scheme, for solving stiff stochastic differential equations. We extend the Balanced method to introduce a class of stable strong order 1. 0 numerical schemes for solving stochastic ordinary differential equations. We derive convergence results for this class of numerical schemes. We illustrate the asymptotic stability of this class of schemes is illustrated and is compared with contemporary schemes of strong order 1. 0. We present some evidence on parametric selection with respect to minimising the error convergence terms. Furthermore we provide a convergence result for general Balanced style schemes of higher orders.

Practice and Procedure: UCPR r 708 - costs order against several defendants and third party

Glenwood Homes Pty Ltd v Everhard [2008] QSC 192 involved the not uncommon situation where one costs order is made against several parties represented by a single firm of solicitors. Dutney J considered the implications when only some of the parties liable for the payment of the costs file a notice of objection to the costs statement served in respect of those costs.

Chinese fashion designers in Shanghai : identifying a fresh perspective about their role in the world order of fashion

Shanghai possesses an apt legacy, once referred to as “Paris of the East”. Municipal aspirations for Shanghai to assume a position among the great fashion cities of the world have been integrated in the recent re-shaping of this modern city into a role model for Chinese creative enterprise yet China is still known primarily as centre of clothing production. Increasingly however, “Made in China” is being replaced by “Created in China” drawing attention to two distinct consumer markets for Chinese designers. Fashion designers who have entered the global fashion system for education or by showing their collections have generally adopted a design aesthetic that aligns with Western markets, allowing little competitive advantage. In contrast, Chinese designers who rest their attention on the domestic Chinese market find a disparate, highly competitive marketplace. The pillars of authenticity that for foreign fashion brands extend far into their cultural and creative histories, often for many decades in the case of Louis Vuitton, Hermes and Christian Dior do not yet exist in China in this era of rapid globalisation. Here, the cultural bedrock allows these same pillars to extend only thirty years or so into the past reaching the moments when Deng Xiaoping granted China’s creative entrepreneurs passage. To this end, interviews with fashion designers in Shanghai have been undertaken during the last twelve months for a PhD dissertation. Production of culture theory has been used to identify working methods, practices of production and the social and cultural milieu necessary for designers to achieve viability. Preliminary findings indicate that some fashion designers have adopted an as-yet unexplored strategy of business and brand development with a distinct Chinese aesthetic at its core, in contrast to the clichéd cultural iconography often viewed by Western viewers as representative of Chinese creativity.