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This paper is part of a general program in complex dynamics to understand parameter spaces of transcendental maps with finitely many singular values. The simplest families of such functions have two asymptotic values and no critical values. These families, up to affine conjugation, depend on two complex parameters. Understanding their parameter spaces is key to understanding families with more asymptotic values, just as understanding quadratic polynomials was for rational maps more generally. The first such families studied were the one-dimensional slices of the exponential family, \exp (z) + a, and the tangent family \lambda \tan z. The exponential case exhibited phenomena not seen for rational maps: Cantor bouquets in both the dynamic and parameter spaces, and no bounded hyperbolic components. The tangent case, with its two finite asymptotic values \pm \lambda i, is closer to the rational case, a kind of infinite degree version of the latter. In this paper, we consider a general family that interpolates between \exp (z) + a and \lambda \tan z. Our new family has two asymptotic values and a one-dimensional slice for which one of the asymptotic values is constrained to be a pole, the "polar asymptotic value" of the title. We show how the dynamic and parameter planes for this slice exhibit behavior that is a surprisingly delicate interplay between that of the \exp (z) + a and \lambda \tan z families. [ABSTRACT FROM AUTHOR]

This paper continues our investigation of the dynamics of families of transcendental meromorphic functions with finitely many singular values all of which are finite. Here we look at a generalization of the family of polynomials Pa(z) = zd-1(z - da/(d-1)), the family fλ = λtanpzq. These functions have a super-attractive fixed point, and, depending on p, one or two asymptotic values. Although many of the dynamical properties generalize, the existence of an essential singularity and of poles of multiplicity greater than one implies that significantly different techniques are required here. Adding transcendental methods to standard ones, we give a description of the dynamical properties; in particular we prove the Julia set of a hyperbolic map is either connected and locally connected or a Cantor set. We also give a description of the parameter plane of the family fλ. Again there are similarities to and differences from the parameter plane of the family Pa and again there are new techniques. In particular, we prove there is dense set of points on the boundaries of the hyperbolic components that are accessible along curves and we characterize these points. [ABSTRACT FROM AUTHOR]

This paper continues our investigation of the dynamics of families of transcendental meromorphic functions with finitely many singular values all of which are finite. Here we look at a generalization of the family of polynomials Pa(z) = zd-1(z - da/(d-1)), the family fλ = λtanpzq. These functions have a super-attractive fixed point, and, depending on p, one or two asymptotic values. Although many of the dynamical properties generalize, the existence of an essential singularity and of poles of multiplicity greater than one implies that significantly different techniques are required here. Adding transcendental methods to standard ones, we give a description of the dynamical properties; in particular we prove the Julia set of a hyperbolic map is either connected and locally connected or a Cantor set. We also give a description of the parameter plane of the family fλ. Again there are similarities to and differences from the parameter plane of the family Pa and again there are new techniques. In particular, we prove there is dense set of points on the boundaries of the hyperbolic components that are accessible along curves and we characterize these points. [ABSTRACT FROM AUTHOR]

In the early 1980's, computers made it possible to observe that in complex dynamics, one often sees dynamical behavior reflected in parameter space and vice versa. This duality was first exploited by Douady, Hubbard and their students in early work on rational maps. Here, we extend these ideas to transcendental functions. In [16], it was shown that for the tangent family, {λ tan z}, the hyperbolic components meet at a parameter λ* such that ƒλn(λ*i) = ∞ for some n. The behavior there reflects the dynamic behavior of λ* tan z at infinity. In Part 1. we show that this duality extends to a more general class of transcendental meromorphic functions {ƒλ} for which infinity is not an asymptotic value. In particular, we show that in "dynamically natural" one-dimensional slices of parameter space, there are "hyperbolic-like" components Ω with a unique distinguished boundary point such that for λ ∈ Ω, the dynamics of ƒλ reflect the behavior of ƒλ at infinity. Our main result is that every parameter point λ in such a slice for which the iterate of the asymptotic value of ƒλ is a pole is such a distinguished boundary point.In the second part of the paper, we apply this result to the families λ tanp zq, p, q ∈ Z+, to prove that all hyperbolic components of period greater than 1 are bounded. [ABSTRACT FROM AUTHOR]

In this paper, we characterize those external rays that land on the bounded Fatou components of hyperbolic and parabolic quadratic maps. For those maps not in the main cardioid of the Mandelbrot set, we prove that the arguments of these rays form a Cantor subset of the circle at infinity. Our techniques involve both the orbit portraits of Goldberg and Milnor that relate the dynamic and parameter planes and the Thurston theory of laminations for quadratic maps. [ABSTRACT FROM AUTHOR]

Abstract In the UK early withdrawal from the labour market is seen as a risk and a cost, worsening the dependency ratio, raising public and private pension costs and threatening additional welfare expenditure over the longer term. Explanations of the retirement process have focused on the welfare state and the impact of pensions and other social security policies. This paper argues that a missing actor in these accounts is the employing organization. Early retirement in the UK has been predominantly driven by the labour requirements of employers rather than state policies to encourage older workers to take early retirement. There is a case for arguing that significant change in retirement behaviour in the UK will come primarily from the modification of employers’ policies. This research is a case study of three employers: one public-sector and two commercial. It examines the dynamics of the retirement decision. This paper reports the public-sector case. The findings indicate that employers, in order to reduce their pensions liabilities and stem the cost of early retirement, are trying to regain control of the retirement process. The employees interviewed felt they experienced little choice concerning their retirement, had limited knowledge of the options open to them and found pensions complicated and confusing. [ABSTRACT FROM AUTHOR]

Operating as purchasers or providers, middle managers play a key role in the implementation of the new market systems recently introduced within local authorities. However, relatively little empirical investigation has been undertaken into the first-hand experiences of the middle managers who are on the ‘receiving end’ of these market systems. After a brief review of the literature, this paper uses Williamson's (1975; 1985) model of behavioural attributes as an analytical framework for analysing the impact of the new Purchaser and Provider model on the performance of middle line managers working within a local authority well-known for its commitment to market service delivery systems.These managers' responses about the positive and negative aspects of their experiences of market systems varied significantly according to their roles as either Purchaser or Provider managers, and to their location within particular service departments. The paper draws attention to the important differences in the nature of the transactions within each of these departments which appeared to account, at least in part, for the managers' different responses, and argues against the wholesale application of market forms of service delivery across highly differentiated organisations such as local authorities. [ABSTRACT FROM PUBLISHER]

Linda Keen, who is Lecturer in Human Resource Management at the Canterbury Business School, uses a case study investigation of a local authority well advanced in its adoption of the 'new' devolved management systems, to identify the views of middle managers themselves about the extent to which devolved budgeting had brought about a real increase in their managerial autonomy, focusing on key elements of budgetary devolution identified in the literature, including the roles of devolved finance staff. She concludes that increases in these managers' budgetary responsibilities were generally not accompanied by corresponding increases in their autonomy over budgetary management decisions, and identifies a number of human resource management issues, arising from this non-alignment, in relation to management control systems, and training, motivation and reward management strategies. [ABSTRACT FROM AUTHOR]

In the context of the much-publicised moves within local government from traditional Personnel Management to new Human Resource Management (HRM) systems, this article explores the extent to which line managers' day-to-day people management practices had changed as a consequence of their local authority's formal adoption of HRM policies. While many of these managers had made real and substantial changes in their people management activities, it was nevertheless clear that barriers remained to the full realization of the HRM ideal, with potentially adverse consequences for the managers' motivation and performance levels and for overall organizational effectiveness. [ABSTRACT FROM AUTHOR]

Consider the two-parameter family of real analytic maps $$F_{a,b} :x \mapsto x + a + \tfrac{b}{{2\pi }}$$ sin(2π x) which are lifts of degree one endomorphisms of the circle. The purpose of this paper is to provide a proof that for any closed interval I, the set of maps F whose rotation interval is I, form a contractible set. [ABSTRACT FROM AUTHOR]

The article explores the impact of adopting new management systems on the work satisfaction levels experienced by middle managers, focusing on a case-study analysis of an English shire county council. Researchers found evidence to suggest a less positive attitude to organisational and management changes among the public sector managers. Evidence of increased work pressures also emerges from most of these studies of middle managers. Results of the case study research indicate that the most significant sources of job dissatisfaction for managers were the lack of job security and restricted opportunities for promotion.

A biography of mathematician Robert L. Devaney is presented, to whom this special issue of "Journal of Difference Equations and Applications" is dedicated. Devaney was born on April 9, 1948, and was brought up in Methuen, Massachusetts. He he did his graduation at the University of California at Berkeley during 1969-1973, and received his Ph.D. in 1973. Devaney chaired the Department of Mathematics at Boston University during 1983-1986, and was promoted to Professor of Mathematics in 1986.

The article announces that Nigel Hopes and Patrick Wiltshire reached the National Finals of the 2007 Young Horticulturist of the Year held in Ireland.