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.

Analysis of phasor measurement method in tracking the power frequency of distorted signals

This paper presents an analysis of phasor measurement method for tracking the fundamental power frequency to show if it has the performance necessary to cope with the requirements of power system protection and control. In this regard, several computer simulations presenting the conditions of a typical power system signal especially those highly distorted by harmonics, noise and offset, are provided to evaluate the response of the Phasor Measurement (PM) technique. A new method, which can shorten the delay of estimation, has also been proposed for the PM method to work for signals free of even-order harmonics.

Development of a method to measure upper eyelid pressure on the cornea

Purpose: The cornea is known to be susceptible to forces exerted by eyelids. There have been previous attempts to quantify eyelid pressure but the reliability of the results is unclear. The purpose of this study was to develop a technique using piezoresistive pressure sensors to measure upper eyelid pressure on the cornea. Methods: The technique was based on the use of thin (0.18 mm) tactile piezoresistive pressure sensors, which generate a signal related to the applied pressure. A range of factors that influence the response of this pressure sensor were investigated along with the optimal method of placing the sensor in the eye. Results: Curvature of the pressure sensor was found to impart force, so the sensor needed to remain flat during measurements. A large rigid contact lens was designed to have a flat region to which the sensor was attached. To stabilise the contact lens during measurement, an apparatus was designed to hold and position the sensor and contact lens combination on the eye. A calibration system was designed to apply even pressure to the sensor when attached to the contact lens, so the raw digital output could be converted to actual pressure units. Conclusions: Several novel procedures were developed to use tactile sensors to measure eyelid pressure. The quantification of eyelid pressure has a number of applications including eyelid reconstructive surgery and the design of soft and rigid contact lenses.