Analytical solutions for the multi-term time-fractional diffusion-wave/diffusion equations in a finite domain

Multi-term time-fractional differential equations have been used for describing important physical phenomena. However, studies of the multi-term time-fractional partial differential equations with three kinds of nonhomogeneous boundary conditions are still limited. In this paper, a method of separating variables is used to solve the multi-term time-fractional diffusion-wave equation and the multi-term time-fractional diffusion equation in a finite domain. In the two equations, the time-fractional derivative is defined in the Caputo sense. We discuss and derive the analytical solutions of the two equations with three kinds of nonhomogeneous boundary conditions, namely, Dirichlet, Neumann and Robin conditions, respectively.

Regulating Prostitution: Different Problems, Different Solutions, Same Old Story

This article looks at three main models of intervention that have informed recent policy and practice with people involved in the sex trade. It reveals the inherent contradictions within attempts to both help and punish workers in the existing prostitution strategy.

Unexpected issues and solutions: Emerge from environmental manipulation strategy

Environmental manipulation removes students from their everyday worlds to unfamiliar worlds, to facil- itate learning. This article reports that this strategy was effective when applied in a university design unit, using the tactic of immersion in the Second Life online virtual environment. The objective was for teams of stu- dents each to design a series of modules for an orbiting space station using supplied data. The changed and futuristic environment led the students to an important but previously unconsidered design decision which they were able to address in novel ways because of, rather than in spite of, the Second Life immersion.

Analytical and numerical solutions of the space and time fractional bloch-torrey equation

Fractional order dynamics in physics, particularly when applied to diffusion, leads to an extension of the concept of Brown-ian motion through a generalization of the Gaussian probability function to what is termed anomalous diffusion. As MRI is applied with increasing temporal and spatial resolution, the spin dynamics are being examined more closely; such examinations extend our knowledge of biological materials through a detailed analysis of relaxation time distribution and water diffusion heterogeneity. Here the dynamic models become more complex as they attempt to correlate new data with a multiplicity of tissue compartments where processes are often anisotropic. Anomalous diffusion in the human brain using fractional order calculus has been investigated. Recently, a new diffusion model was proposed by solving the Bloch-Torrey equation using fractional order calculus with respect to time and space (see R.L. Magin et al., J. Magnetic Resonance, 190 (2008) 255-270). However effective numerical methods and supporting error analyses for the fractional Bloch-Torrey equation are still limited. In this paper, the space and time fractional Bloch-Torrey equation (ST-FBTE) is considered. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. Firstly, we derive an analytical solution for the ST-FBTE with initial and boundary conditions on a finite domain. Secondly, we propose an implicit numerical method (INM) for the ST-FBTE, and the stability and convergence of the INM are investigated. We prove that the implicit numerical method for the ST-FBTE is unconditionally stable and convergent. Finally, we present some numerical results that support our theoretical analysis.

Pretreatment of sugarcane bagasse by acid-catalysed process in aqueous ionic liquid solutions

A biomass pretreatment process was developed using acidified ionic liquid (IL) solutions containing 10-30% water. Pretreatment of sugarcane bagasse at 130°C for 30min by aqueous 1-butyl-3-methylimidazolium chloride (BMIMCl) solution containing 1.2% HCl resulted in a glucan digestibility of 94-100% after 72h of enzymatic hydrolysis. HCl was found to be a more effective catalyst than H(2)SO(4) or FeCl(3). Increasing acid concentration (from 0.4% to 1.2%) and reaction temperature (from 90 to 130°C) increased glucan digestibility. The glucan digestibility of solid residue obtained with the acidified BMIMCl solution that was re-used for three times was >97%. The addition of water to ILs for pretreatment could significantly reduce IL solvent costs and allow for increased biomass loadings, making the pretreatment by ILs a more economic proposition.

Document clustering evaluation : Divergence from a random baseline

Divergence from a random baseline is a technique for the evaluation of document clustering. It ensures cluster quality measures are performing work that prevents ineffective clusterings from giving high scores to clusterings that provide no useful result. These concepts are defined and analysed using intrinsic and extrinsic approaches to the evaluation of document cluster quality. This includes the classical clusters to categories approach and a novel approach that uses ad hoc information retrieval. The divergence from a random baseline approach is able to differentiate ineffective clusterings encountered in the INEX XML Mining track. It also appears to perform a normalisation similar to the Normalised Mutual Information (NMI) measure but it can be applied to any measure of cluster quality. When it is applied to the intrinsic measure of distortion as measured by RMSE, subtraction from a random baseline provides a clear optimum that is not apparent otherwise. This approach can be applied to any clustering evaluation. This paper describes its use in the context of document clustering evaluation.

Literacy in Early Childhood and Primary Education : Issues, Challenges and Solutions

Literacy in Early Childhood and Primary Education provides a comprehensive introduction to literacy teaching and learning. The book explores the continuum of literacy learning and children’s transitions from early childhood settings to junior primary classrooms, and then to senior primary and beyond. Reader-friendly and accessible, this book equips pre-service teachers with the theoretical underpinnings and practical strategies and skills needed to teach literacy. It places the ‘reading wars’ firmly in the past as it examines contemporary research and practices. The book covers important topics such as literacy acquisition, family literacies and multiliteracies, foundation skills for literacy learning, reading difficulties, assessment, and supporting diverse literacy learners in early childhood and primary classrooms. It also addresses some of the challenges that teachers may face in the classroom and provides solutions to these. Each chapter includes learning objectives, reflective questions and definitions to key terms to engage and assist readers. Further resources are also available at www.cambridge.edu.au/academic/literacy. Written by an expert author team and featuring real-world examples from literacy teachers and learners. Literacy in Early Childhood and Primary Education will help pre-service teachers feel confident teaching literacy to diverse age groups and abilities.

An assessment tool for selection of appropriate daylighting solutions for buildings in tropical and subtropical regions : Validation using radiance simulation

A new decision-making tool that will assist designers in the selection of appropriate daylighting solutions for buildings in tropical locations has been previously proposed by the authors. Through an evaluation matrix that prioritizes the parameters that best respond to the needs of tropical climates (e.g. reducing solar gain and protection from glare) the tool determines the most appropriate devices for specific climate and building inputs. The tool is effective in demonstrating the broad benefits and limitations of the different daylight strategies for buildings in the tropics. However for thorough analysis and calibration of the tool, validation is necessary. This paper presents a first step in the validation process. RADIANCE simulations were conducted to compare simulation performance with the performance predicted by the tool. To this end, an office building case study in subtropical Brisbane, Australia, and five different daylighting devices including openings, light guiding systems and light transport systems were simulated. Illuminance, light uniformity, daylight penetration and glare analysis were assessed for each device. The results indicate the tool can appropriately rank and recommend daylighting strategies based on specific building inputs for tropical and subtropical regions, making it a useful resource for designers.

Velocity jump processes with proliferation

Cell invasion involves a population of cells that migrate along a substrate and proliferate to a carrying capacity density. These two processes, combined, lead to invasion fronts that move into unoccupied tissues. Traditional modelling approaches based on reaction–diffusion equations cannot incorporate individual–level observations of cell velocity, as information propagates with infinite velocity according to these parabolic models. In contrast, velocity jump processes allow us to explicitly incorporate individual–level observations of cell velocity, thus providing an alternative framework for modelling cell invasion. Here, we introduce proliferation into a standard velocity–jump process and show that the standard model does not support invasion fronts. Instead, we find that crowding effects must be explicitly incorporated into a proliferative velocity–jump process before invasion fronts can be observed. Our observations are supported by numerical and analytical solutions of a novel coupled system of partial differential equations, including travelling wave solutions, and associated random walk simulations.

Comparison of PCR, nested PCR, and random amplified polymorphic DNA PCR for detection and typing of Ureaplasma urealyticum in specimens from pregnant women

A PCR assay, using three primer pairs, was developed for the detection of Ureaplasma urealyticum, parvo biovar, mba types 1, 3, and 6, in cultured clinical specimens. The primer pairs were designed by using the polymorphic base positions within a 310- to 311-bp fragment of the 5* end and upstream control region of the mba gene. The specificity of the assay was confirmed with reference serovars 1, 3, 6, and 14 and by the amplified-fragment sizes (81 bp for mba 1, 262 bp for mba 3, and 193 bp for mba 6). A more sensitive nested PCR was also developed. This involved a first-step PCR, using the primers UMS-125 and UMA226, followed by the nested mba-type PCR described above. This nested PCR enabled the detection and typing of small numbers of U. urealyticum cells, including mixtures, directly in original clinical specimens. By using random amplified polymorphic DNA (RAPD) PCR with seven arbitrary primers, we were also able to differentiate the two biovars of U. urealyticum and to identify 13 RAPD-PCR subtypes. By applying these subtyping techniques to clinical samples collected from pregnant women, we established that (i) U. urealyticum is often a persistent colonizer of the lower genital tract from early midtrimester until the third trimester of pregnancy, (ii) mba type 6 was isolated significantly more often (P 5 0.048) from women who delivered preterm than from women who delivered at term, (iii) no particular ureaplasma subtype(s) was associated with placental infections and/or adverse pregnancy outcomes, and (iv) the ureaplasma subtypes most frequently isolated from women were the same subtypes most often isolated from infected placentas.

On the probability density function of the product of Rayleigh distributed random variables

In this paper we investigate the distribution of the product of Rayleigh distributed random variables. Considering the Mellin-Barnes inversion formula and using the saddle point approach we obtain an upper bound for the product distribution. The accuracy of this tail-approximation increases as the number of random variables in the product increase.

Numerical methods for strong solutions of stochastic differential equations : an overview

This paper gives a review of recent progress in the design of numerical methods for computing the trajectories (sample paths) of solutions to stochastic differential equations. We give a brief survey of the area focusing on a number of application areas where approximations to strong solutions are important, with a particular focus on computational biology applications, and give the necessary analytical tools for understanding some of the important concepts associated with stochastic processes. We present the stochastic Taylor series expansion as the fundamental mechanism for constructing effective numerical methods, give general results that relate local and global order of convergence and mention the Magnus expansion as a mechanism for designing methods that preserve the underlying structure of the problem. We also present various classes of explicit and implicit methods for strong solutions, based on the underlying structure of the problem. Finally, we discuss implementation issues relating to maintaining the Brownian path, efficient simulation of stochastic integrals and variable-step-size implementations based on various types of control.