On Necessary and Sufficient Conditions for Preserving Convergence Rates to Equilibrium in Deterministically and Stochastically Perturbed Differential Equations with Regularly Varying Nonlinearity

This paper develops necessary and sufficient conditions for the preservation of asymptotic convergence rates of deterministically and stochastically perturbed ordinary differential equations with regularly varying nonlinearity close to their equilibrium. Sharp conditions are also established which preserve the asymptotic behaviour of the derivative of the underlying unperturbed equation. Finally, necessary and sufficient conditions are established which enable finite difference approximations to the derivative in the stochastic equation to preserve the asymptotic behaviour of the derivative of the unperturbed equation, even though the solution of the stochastic equation is nowhere differentiable, almost surely

The nature of practitioner research: critical distance, power and ethics

Researching within one’s place of practice allows the researcher to have the unique position of knowing the participants and the research context. The relationship the participants have with the researcher will impact upon the disclosure of information differently than research conducted by someone outside the area of practice. This can be a benefit and a drawback for the participants, the area of practice and the researcher. However, as is demonstrated within this paper, the role the researcher adopts throughout the process of gathering information is not always clear. As a student on the Doctorate of Education programme myself, the nature of practitioner research and the complexities of this type of research is of great interest to me. Beginning to develop my own research project through this taught programme has allowed an opportunity to think through these challenges and wrestle with the complexity and contradiction, dilemma and incongruity which emerges from being a researching practitioner. Within this piece it is suggested that these quandaries can be considered from the perspective of critical distance, relationships and power and ethical considerations. The idea of considering these conflicts reflexively will be explored here. Although this discussion was not based on empirical research findings as such, it is anticipated that this piece will further the understanding of practitioner research in higher education from the position of being a student and through scholastic analysis of the Ed D programme providing a particular perspective on the nature of research

Using change management theory to implement the international classification of functioning, disability and health (ICF) in clinical practice

Practice Evaluation The success of the International Classification of Functioning, Disability and Health (ICF) depends on its implementation in practice. This article describes an evaluation of the introduction of the ICF framework into an occupational therapy service. Reflections from the working party responsible for its introduction were related to change management theory. The experiences throughout the implementation project could be mapped to an eight-stage process of creating major change (Kotter 1996). The working party concluded that the explicit use of and closer adherence to change management theory could enhance the uptake of the ICF in clinical practice. Further exploratory research is required to support these reflections

Quantum Errors and Disturbances: Response to Busch, Lahti and Werner

Busch, Lahti and Werner (BLW) have recently criticized the operator approach to the description of quantum errors and disturbances. Their criticisms are justified to the extent that the physical meaning of the operator definitions has not hitherto been adequately explained. We rectify that omission. We then examine BLW's criticisms in the light of our analysis. We argue that, although the approach BLW favour (based on the Wasserstein 2-deviation) has its uses, there are important physical situations where an operator approach is preferable. We also discuss the reason why the error-disturbance relation is still giving rise to controversies almost a century after Heisenberg first stated his microscope argument. We argue that the source of the difficulties is the problem of interpretation, which is not so wholly disconnected from experimental practicalities as is sometimes supposed.Comment: AMS latex, 29 page

Almost sure subexponential decay rates of scalar Ito-Volterra equations.

The paper studies the subexponential convergence of solutions of scalar Itˆo-Volterra equations. First, we consider linear equations with an instantaneous multiplicative noise term with intensity . If the kernel obeys lim t!1 k0(t)/k(t) = 0, and another nonexponential decay criterion, and the solution X tends to zero as t ! 1, then limsup t!1 log |X(t)| log(tk(t)) = 1 − (||), a.s. where the random variable (||) ! 0 as ! 1 a.s. We also prove a decay result for equations with a superlinear diffusion coefficient at zero. If the deterministic equation has solution which is uniformly asymptotically stable, and the kernel is subexponential, the decay rate of the stochastic problem is exactly the same as that of the underlying deterministic problem