Stability and convergence of a new explicit finite-difference approximation for the variable-order nonlinear fractional diffusion equation

In this paper, we consider the variable-order nonlinear fractional diffusion equation View the MathML source where xRα(x,t) is a generalized Riesz fractional derivative of variable order View the MathML source and the nonlinear reaction term f(u,x,t) satisfies the Lipschitz condition |f(u1,x,t)-f(u2,x,t)|less-than-or-equals, slantL|u1-u2|. A new explicit finite-difference approximation is introduced. The convergence and stability of this approximation are proved. Finally, some numerical examples are provided to show that this method is computationally efficient. The proposed method and techniques are applicable to other variable-order nonlinear fractional differential equations.

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.

Dragline automation: experimental evaluation through productivity trial

Since 1993 we have been working on the automation of dragline excavators, the largest earthmoving machines that exist. Recently we completed a large-scale experimental program where the automation system was used for production purposes over a two week period and moved over 200,000 tonnes of overburden. This is a landmark achievement in the history of automated excavation. In this paper we briefly describe the robotic system and how it works cooperatively with the machine operator. We then describe our methodology for gauging machine performance, analyze results from the production trial and comment on the effectiveness of the system that we have created. © Springer-Verlag Berlin Heidelberg 2006.

An assessment of construction labour productivity in Malaysia

The construction industry is one of major strategic importance. Its level of productivity has a significant effect on national economic growth. The analysis of published census/biannual surveys of construction by the Department of Statistics of Malaysia shows that Malaysia managed to achieve construction labour productivity growth between 1996 and 2005 despite increases in cost per employee. The decrease in unit labour costs is attributed to the value added improvement per worker through the increase in capital intensity. The marginal decline in capital productivity is due to the gestation period and the overcapacity of the industry. The civil engineering sub-sector recorded the highest labour productivity and is the most labour competitive in terms of unit labour cost and added value per labour cost. The residential sub-sectors recorded greatest change in the productivity indicators between 1996 and 2005.

International comparisons of Malaysian construction labour productivity

Productivity is basic statistical information for many international comparisons and country performance assessments. This study estimates the construction labour productivity of 79 selected economies. The real (purchasing power parities converted) and nominal construction expenditure from the Report of 2005 International Comparison Programme published by the World Bank and construction employment from the database of labour statistics (LABORSTA) operated by the Bureau of Statistics of International Labour Organization were used in the estimation. The inference statistics indicate that the descending order of nominal construction labour productivity from high income economies to low income economies is not established. The average construction labour productivity of low income economies is higher than middle income economies when the productivity calculation uses purchasing power parities converted data. Malaysia ranked 50th and 63rd position among the 79 selected economies on real and nominal measurement respectively.

Dragline automation - a decade of development : shared autonomy for improving mining equipment productivity

Draglines are massive machines commonly used in surface mining to strip overburden, revealing the targeted minerals for extraction. Automating some or all of the phases of operation of these machines offers the potential for significant productivity and maintenance benefits. The mining industry has a history of slow uptake of automation systems due to the challenges contained in the harsh, complex, three-dimensional (3D), dynamically changing mine operating environment. Robotics as a discipline is finally starting to gain acceptance as a technology with the potential to assist mining operations. This article examines the evolution of robotic technologies applied to draglines in the form of machine embedded intelligent systems. Results from this work include a production trial in which 250,000 tons of material was moved autonomously, experiments demonstrating steps towards full autonomy, and teleexcavation experiments in which a dragline in Australia was tasked by an operator in the United States.

Economic growth, inequality and technology adoption in transitional economies

The stylized facts that motivate this thesis include the diversity in growth patterns that are observed across countries during the process of economic development, and the divergence over time in income distributions both within and across countries. This thesis constructs a dynamic general equilibrium model in which technology adoption is costly and agents are heterogeneous in their initial holdings of resources. Given the households‟ resource level, this study examines how adoption costs influence the evolution of household income over time and the timing of transition to more productive technologies. The analytical results of the model constructed here characterize three growth outcomes associated with the technology adoption process depending on productivity differences between the technologies. These are appropriately labeled as „poverty trap‟, „dual economy‟ and „balanced growth‟. The model is then capable of explaining the observed diversity in growth patterns across countries, as well as divergence of incomes over time. Numerical simulations of the model furthermore illustrate features of this transition. They suggest that that differences in adoption costs account for the timing of households‟ decision to switch technology which leads to a disparity in incomes across households in the technology adoption process. Since this determines the timing of complete adoption of the technology within a country, the implications for cross-country income differences are obvious. Moreover, the timing of technology adoption appears to be impacts on patterns of growth of households, which are different across various income groups. The findings also show that, in the presence of costs associated with the adoption of more productive technologies, inequalities of income and wealth may increase over time tending to delay the convergence in income levels. Initial levels of inequalities in the resources also have an impact on the date of complete adoption of more productive technologies. The issue of increasing income inequality in the process of technology adoption opens up another direction for research. Specifically increasing inequality implies that distributive conflicts may emerge during the transitional process with political- economy consequences. The model is therefore extended to include such issues. Without any political considerations, taxes would leads to a reduction in inequality and convergence of incomes across agents. However this process is delayed if politico-economic influences are taken into account. Moreover, the political outcome is sub optimal. This is essentially due to the fact that there is a resistance associated with the complete adoption of the advanced technology.

Stability and convergence of an effective numerical method for the time-space fractional Fokker-Planck equation with a nonlinear source term

Fractional Fokker-Planck equations (FFPEs) have gained much interest recently for describing transport dynamics in complex systems that are governed by anomalous diffusion and nonexponential relaxation patterns. However, effective numerical methods and analytic techniques for the FFPE are still in their embryonic state. In this paper, we consider a class of time-space fractional Fokker-Planck equations with a nonlinear source term (TSFFPE-NST), which involve the Caputo time fractional derivative (CTFD) of order α ∈ (0, 1) and the symmetric Riesz space fractional derivative (RSFD) of order μ ∈ (1, 2). Approximating the CTFD and RSFD using the L1-algorithm and shifted Grunwald method, respectively, a computationally effective numerical method is presented to solve the TSFFPE-NST. The stability and convergence of the proposed numerical method are investigated. Finally, numerical experiments are carried out to support the theoretical claims.

Sustained convergence, axial length, and corneal topography

Purpose: To investigate the influence of convergence on axial length and corneal topography in young adult subjects.---------- Methods: Fifteen emmetropic young adult subjects with normal binocular vision had axial length and corneal topography measured immediately before and after a 15-min period of base out (BO) prismatic spectacle lens wear. Two different magnitude prismatic spectacles were worn in turn (8 [DELTA] BO and 16 [DELTA] BO), and for both tasks, distance fixation was maintained for the duration of lens wear. Eight subjects returned on a separate day for further testing and had axial length measured before, during, and immediately after a 15-min convergence task.---------- Results: No significant change was found to occur in axial length either during or after the sustained convergence tasks (p > 0.6). Some small but significant changes in corneal topography were found to occur after sustained convergence. The most significant corneal change was observed after the 16 [DELTA] BO prism wear. The corneal refractive power spherocylinder power vector J0 was found to change by a small (mean change of 0.03 D after the 16 [DELTA] BO task) but statistically significant (p = 0.03) amount as a result of the convergence task (indicative of a reduction in with-the-rule corneal astigmatism after convergence). Corneal axial power was found to exhibit a significant flattening in superior regions. Conclusions: Axial length appears largely unchanged by a period of sustained convergence. However, small but significant changes occur in the topography of the cornea after convergence.

Urban telecommunications network : technology convergence and urban infrastructure

Rapidly developing information and telecommunication technologies and their platforms in the late 20th Century helped improve urban infrastructure management and influenced quality of life. Telecommunication technologies make it possible for people to deliver text, audio and video material using wired, wireless or fibre-optic networks. Technologies convergence amongst these digital devices continues to create new ways in which the information and telecommunication technologies are used. The 21st Century is an era where information has converged, in which people are able to access a variety of services, including internet and location based services, through multi-functional devices such as mobile phones. This chapter discusses the recent developments in telecommunication networks and trends in convergence technologies, their implications for urban infrastructure planning, and for the quality of life of urban residents.

Ubiquitous eco cities : telecommunication infrastructure, technology convergence and urban management

Efficient and effective urban management systems for Ubiquitous Eco Cities require having intelligent and integrated management mechanisms. This integration includes bringing together economic, socio-cultural and urban development with a well orchestrated, transparent and open decision-making system and necessary infrastructure and technologies. In Ubiquitous Eco Cities telecommunication technologies play an important role in monitoring and managing activities via wired and wireless networks. Particularly, technology convergence creates new ways in which information and telecommunication technologies are used and formed the backbone of urban management. The 21st Century is an era where information has converged, in which people are able to access a variety of services, including internet and location based services, through multi-functional devices and provides new opportunities in the management of Ubiquitous Eco Cities. This chapter discusses developments in telecommunication infrastructure and trends in convergence technologies and their implications on the management of Ubiquitous Eco Cities