Implicit stochastic Runge-Kutta methods for stochastic differential equations

In this paper we construct implicit stochastic Runge-Kutta (SRK) methods for solving stochastic differential equations of Stratonovich type. Instead of using the increment of a Wiener process, modified random variables are used. We give convergence conditions of the SRK methods with these modified random variables. In particular, the truncated random variable is used. We present a two-stage stiffly accurate diagonal implicit SRK (SADISRK2) method with strong order 1.0 which has better numerical behaviour than extant methods. We also construct a five-stage diagonal implicit SRK method and a six-stage stiffly accurate diagonal implicit SRK method with strong order 1.5. The mean-square and asymptotic stability properties of the trapezoidal method and the SADISRK2 method are analysed and compared with an explicit method and a semi-implicit method. Numerical results are reported for confirming convergence properties and for comparing the numerical behaviour of these methods.

Reappraising contemporary theories of subcortical participation in language: Proposing an interhemispheric regulatory function for the subthalamic nucleus (STN) in the mediation of high-level linguistic processes

Apropos the basal ganglia, the dominant striatum and globus pallidus internus (GPi) have been hypothesised to represent integral components of subcortical language circuitry. Working subcortical language theories, however, have failed thus far to consider a role for the STN in the mediation of linguistic processes, a structure recently defined as the driving force of basal ganglia output. The aim of this research was to investigate the impact of surgically induced functional inhibition of the STN upon linguistic abilities, within the context of established models of basal ganglia participation in language. Two males with surgically induced 'lesions' of the dominant and non-dominant dorsolateral STN, aimed at relieving Parkinsonian motor symptoms, served as experimental subjects. General and high-level language profiles were compiled for each subject up to 1 month prior to and 3 months following neurosurgery, within the drug-on state (i.e., when optimally medicated). Comparable post-operative alterations in linguistic performance were observed subsequent to surgically induced functional inhibition of the left and right STN. More specifically, higher proportions of reliable decline as opposed to improvement in post-operative performance were demonstrated by both subjects on complex language tasks, hypothesised to entail the interplay of cognitive-linguistic processes. The outcomes of the current research challenge unilateralised models of functional basal ganglia organisation with the proposal of a potential interhemispheric regulatory function for the STN in the mediation of high-level linguistic processes.

Stability for parametric implicit vector equilibrium problems

In this paper, we consider a class of parametric implicit vector equilibrium problems in Hausdorff topological vector spaces where a mapping f and a set K are perturbed by parameters is an element of and lambda respectively. We establish sufficient conditions for the upper semicontinuity and lower semicontinuity of the solution set mapping S : Lambda(1) x A(2) -> 2(X) for such parametric implicit vector equilibrium problems. (c) 2005 Elsevier Ltd. All rights reserved.

The communication rights in the information society (CRIS) campaign: Applying social movement theories to an analysis of global media reform

Social movement theories offer useful conceptual and analytical tools to the study and research of global media reform movements. This article is a critical analysis of the Communication Rights in the Information Society (CRIS) campaign. It explores its successes and blind-spots in the light of social movement theory, in particular resource mobilization theory (RMT), and offers practical directions for the movement to move on from where it is to where it ought to be.

Analysis of trigonometric implicit Runge-Kutta methods

Using generalized collocation techniques based on fitting functions that are trigonometric (rather than algebraic as in classical integrators), we develop a new class of multistage, one-step, variable stepsize, and variable coefficients implicit Runge-Kutta methods to solve oscillatory ODE problems. The coefficients of the methods are functions of the frequency and the stepsize. We refer to this class as trigonometric implicit Runge-Kutta (TIRK) methods. They integrate an equation exactly if its solution is a trigonometric polynomial with a known frequency. We characterize the order and A-stability of the methods and establish results similar to that of classical algebraic collocation RK methods. (c) 2006 Elsevier B.V. All rights reserved.

Exact eigenvalue correspondences between laminated plate theories via membrane vibration

Based on Reddy's third-order theory, the first-order theory and the classical theory, exact explicit eigenvalues are found for compression buckling, thermal buckling and vibration of laminated plates via analogy with membrane vibration, These results apply to symmetrically laminated composite plates with transversely isotropic laminae and simply supported polygonal edges, Comprehensive consideration of a Winkler-Pasternak elastic foundation, a hydrostatic inplane force, an initial temperature increment and rotary inertias is incorporated. Bridged by the vibrating membrane, exact correspondences are readily established between any pairs of buckling and vibration eigenvalues associated with different theories. Positive definiteness of the critical hydrostatic pressure at buckling, the thermobukling temperature increment and, in the range of either tension loading or compression loading prior to occurrence of buckling, the natural vibration frequency is proved. (C) 2000 Elsevier Science Ltd. All rights reserved.

Small firm internationalisation; understanding the practice through an interpretive approach

The unit of analysis in firm internationalisation studies is the firm but this overlooks the importance of the individual in the internationalisation process. An evaluation of the dominant theories of firm internationalisation highlights an implicit dualistic ontology, that is, where research subject and object are considered to be separate and independent. Implications of this assumption are discussed after reviewing the dominant literatures on firm internationalisation. An alternative approach is proposed that focuses on understanding internationalisation of the firm from an individual practitioner’s perspective. It is suggested that contemporary firm internationalisation research has been hindered by its basic assumptions and its inherent researcher orientation. An interpretive phenomenographic approach is proposed as a means of achieving a first-person, practitioner’s perspective of the process of firm internationalisation, specifically in the context of the small firm. Preliminary interpretations of interviews with owners/managers of small Australian wineries are presented.