The role of Mittag-Leffler functions in anomalous relaxation

The inertia-corrected Debye model of rotational Brownian motion of polar molecules was generalized by Coffey et al. [Phys. Rev. E, 65, 32 102 (2002)] to describe fractional dynamics and anomalous rotational diffusion. The linear- response theory of the normalized complex susceptibility was given in terms of a Laplace transform and as a function of frequency. The angular-velocity correlation function was parametrized via fractal Mittag-Leffler functions. Here we apply the latter method and complex-contour integral- representation methods to determine the original time-dependent amplitude as an inverse Laplace transform using both analytical and numerical approaches, as appropriate. (C) 2004 Elsevier B.V. All rights reserved.

Anomalous helicon wave absorption and parametric excitation of electrostatic fluctuations in a helicon-produced plasma

The nonlinear nature of the rf absorption in a helicon-produced plasma was recently evidenced by the observation that the helicon wave damping as well as the level of short-scale electrostatic fluctuations excited in the helicon plasma increases with rf power. Correlation methods using electrostatic probes as well as microwave back-scattering at the upper-hybrid resonance allow identifying the fluctuations as ion-sound and Trivelpiece– Gould waves satisfying the frequency and wavenumber matching conditions for the parametric decay instability of the helicon pump wave. Furthermore, the growth rates and thresholds deduced from their temporal growth are in good agreement with theoretical predictions for the parametric decay instability that takes into account realistic damping rates for the decay waves as well as a non-vanishing parallel wavenumber of the helicon pump. The close relationship between the rf absorption and the excitation of the fluctuations was investigated in more detail by performing time- and space-resolved measurements of the helicon wave field and the electrostatic fluctuations.

A Simultaneous Equation Approach to Estimating HIV Prevalence with Non-Ignorable Missing Responses

Estimates of HIV prevalence are important for policy in order to establish the health status of a country's population and to evaluate the effectiveness of population-based interventions and campaigns. However, participation rates in testing for surveillance conducted as part of household surveys, on which many of these estimates are based, can be low. HIV positive individuals may be less likely to participate because they fear disclosure, in which case estimates obtained using conventional approaches to deal with missing data, such as imputation-based methods, will be biased. We develop a Heckman-type simultaneous equation approach which accounts for non-ignorable selection, but unlike previous implementations, allows for spatial dependence and does not impose a homogeneous selection process on all respondents. In addition, our framework addresses the issue of separation, where for instance some factors are severely unbalanced and highly predictive of the response, which would ordinarily prevent model convergence. Estimation is carried out within a penalized likelihood framework where smoothing is achieved using a parametrization of the smoothing criterion which makes estimation more stable and efficient. We provide the software for straightforward implementation of the proposed approach, and apply our methodology to estimating national and sub-national HIV prevalence in Swaziland, Zimbabwe and Zambia.

What price harmony? Teachers' methods of delivering an ethos of tolerance and respect for diversity in an integrated school in Northern Ireland

The aim of the paper is to explore teachers’ methods of delivering an ethos of tolerance, respect
and mutual understanding in one integrated secondary school in Northern Ireland. Drawing on
interviews with teachers in the school, it is argued that most teachers make ‘critical choices’
which both reflect and reinforce a ‘culture of avoidance’, whereby politically or religiously contentious
issues are avoided rather than explored. Although teachers are well-intentioned in making
these choices, it is shown that they have the potential to create the conditions that maintain or even
harden psychological boundaries between Catholics and Protestants rather than dilute them.

A comparison of three standard methods of identifying mast cells in endobronchial biopsies in normal and asthmatic subjects

Reported mast-cell counts in endobronchial biopsies from asthmatic subjects are conflicting, with different methodologies often being used. This study compared three standard methods of counting mast cells in endobronchial biopsies from asthmatic and normal subjects. Endobronchial biopsies were obtained from atopic asthmatic subjects (n=17), atopic nonasthmatic subjects (n=6), and nonatopic nonasthmatic control subjects (n=5). After overnight fixation in Carnoy's fixative, mast cells were stained by the short and long toluidine blue methods and antitryptase immunohistochemistry and were counted by light microscopy. Method comparison was made according to Bland & Altman. The limits of agreement were unacceptable for each of the comparisons, suggesting that the methods are not interchangeable. Coefficients of repeatability were excellent, and not different for the individual techniques. These results suggest that some of the reported differences in mast-cell numbers in endobronchial biopsies in asthma may be due to the staining method used, making direct comparisons between studies invalid. Agreement on a standard method is required for counting mast cells in bronchial biopsies, and we recommend the immunohistochemical method, since fixation is less critical and the resultant tissue sections facilitate clear, accurate, and rapid counts.

A Van der Pol-Mathieu equation for the dynamics of dust grain charge in dusty plasmas

The chaotic profile of dust grain dynamics associated with dust-acoustic oscillations in a dusty plasma is considered. The collective behaviour of the dust plasma component is described via a multi-fluid model, comprising Boltzmann distributed electrons and ions, as well as an equation of continuity possessing a source term for the dust grains, the dust momentum and Poisson's equations. A Van der Pol–Mathieu-type nonlinear ordinary differential equation for the dust grain density dynamics is derived. The dynamical system is cast into an autonomous form by employing an averaging method. Critical stability boundaries for a particular trivial solution of the governing equation with varying parameters are specified. The equation is analysed to determine the resonance region, and finally numerically solved by using a fourth-order Runge–Kutta method. The presence of chaotic limit cycles is pointed out.