Birth-death processes with mass annihilation and state-dependent immigration

A birth-death process is subject to mass annihilation at rate β with subsequent mass immigration occurring into state j at rateα j . This structure enables the process to jump from one sector of state space to another one (via state 0) with transition rate independent of population size. First, we highlight the difficulties encountered when using standard techniques to construct both time-dependent and equilibrium probabilities. Then we show how to overcome such analytic difficulties by means of a tool developed in Chen and Renshaw (1990, 1993b); this approach is applicable to many processes whose underlying generator on E\{0} has known probability structure. Here we demonstrate the technique through application to the linear birth-death generator on which is superimposed an annihilation/immigration process.

Birth-death processes with disaster and instantaneous resurrection

A new structure with the special property that instantaneous resurrection and mass disaster are imposed on an ordinary birth-death process is considered. Under the condition that the underlying birth-death process is exit or bilateral, we are able to give easily checked existence criteria for such Markov processes. A very simple uniqueness criterion is also established. All honest processes are explicitly constructed. Ergodicity properties for these processes are investigated. Surprisingly, it can be proved that all the honest processes are not only recurrent but also ergodic without imposing any extra conditions. Equilibrium distributions are then established. Symmetry and reversibility of such processes are also investigated. Several examples are provided to illustrate our results.

Urban labour, voice and legitimacy: economic development and the emergence of community unionism

Community unionism has emerged in the past decade as a growing strand of industrial relations research and is influencing trade union strategies for renewal. This article seeks to further develop the concept, while exploring the potential roles for unions in communities subject to projects of urban regeneration.

Debating the division of labour in healthcare in France and England

As Larson (1990) states, professions are historically specific and ‘there is no pattern of social closure around an occupation that is not inflected by the latter’s past, its specific activity and typical context of performance or…the political context in which closure is obtained.’ Larson’s work focuses particularly on the differences between the establishment of professions in France, where there was considerable state intervention, with that in the US and UK, both of which were more market-oriented. This paper is based on data from an evaluation of a large European exchange programme of staff between Kent and Lille, from 2005 to 2008 and discusses the division of labour in healthcare between two occupational groups, medicine and nursing, in England and in France. This division of labour has been extensively discussed in the UK, particularly since from the mid 1990s the nursing role has been extended and innovations such as nurse prescribing have been introduced, whereas such extended roles have not been introduced in France. The paper draws particularly on interview data from mental health practitioners, in which it is argued that whilst the English nurses may on the surface seem to have a wider range of competences and autonomy, in reality they are more constrained, as they operate under protocols and therefore do not exercise professional judgement. Not only do these data illustrate the centrality of professional judgement in discussions about practice, they also demonstrate the circularity of many debates on extended roles.

The emotional costs of caring incurred by men and women in the British labour market

This study investigates whether men and women in caring occupations experience more negative job-related feelings at the end of the day compared to the rest of the working population. The data are from Wave Nine of the British Household Panel Survey (1999) where respondents were asked whether, at the end of the working day, they tended to keep worrying or have trouble unwinding, and the extent to which work left them feeling exhausted or “used up.” Their responses to these questions were used to develop ordinal dependent variables. Control variables in the models include: number of children, age, hours worked per week, managerial responsibilities and job satisfaction, all of which have been shown in previous research to be significantly related to “job burnout.” The results are that those in caring occupations are more likely to feel worried, tense, drained and exhausted at the end of the working day. Women in particular appear to pay a high emotional cost for working in caring occupations. Men do not emerge unscathed, but report significantly lower levels of worry and exhaustion at the end of the day than do women.