Let $E/\mathbb {Q}(T)$ be a nonisotrivial elliptic curve of rank r. A theorem due to Silverman [‘Heights and the specialization map for families of abelian varieties’, J. reine angew. Math. 342 (1983), 197–211] implies that the rank $r_t$ of the specialisation $E_t/\mathbb {Q}$ is at least r for all but finitely many $t \in \mathbb {Q}$. Moreover, it is conjectured that $r_t \leq r+2$, except for a set of density $0$. When $E/\mathbb {Q}(T)$ has a torsion point of order $2$, under an assumption on the discriminant of a Weierstrass equation for $E/\mathbb {Q}(T)$, we produce an upper bound for $r_t$ that is valid for infinitely many t. We also present two examples of nonisotrivial elliptic curves $E/\mathbb {Q}(T)$ such that $r_t \leq r+1$ for infinitely many t.

Adam Smith saw the division of labour and specialisation as the driver of ‘universal opulence’, a process limited by the scope of the market. He also believed that competition was essential to ensure growth benefited the public. Yet eventually there could be a trade-off between these two mechanisms. In today’s era of global production networks, the markets at certain links in supply chains may support just one specialised supplier; and in winner-take-all digital markets there is a single supplier even at global scale. When the scope of the market is global, there may be a trade-off between specialisation and competition.

Assuming $\mathrm{PFA}$ , we shall use internally club $\omega _1$ -guessing models as side conditions to show that for every tree T of height $\omega _2$ without cofinal branches, there is a proper and $\aleph _2$ -preserving forcing notion with finite conditions which specialises T. Moreover, the forcing has the $\omega _1$ -approximation property.

A function $f:X\rightarrow X$ determines a topology $P(f)$ on $X$ by taking the closed sets to be those sets $A\subseteq X$ with $f(A)\subseteq A$. The topological space $(X,P(f))$ is called a functionally Alexandroff space. We completely characterise the homogeneous functionally Alexandroff spaces.

Historical contingency complicates a reading of skill as a self-explanatory and always positive attribute. By focusing on the attempts of the first generation of neurosurgeons to build a community and fashion a collective neurosurgical self, this article highlights the extent to which the relationship between surgical skill and professional judgement is reflected in broader concerns that shape the landscape of medicine at a given time. Some early twentieth-century surgeons expressed concern about the spectacularisation of surgery and the skilful but problematic work of ‘brilliant operators’. The neurosurgeons’ policies of inclusion and exclusion show that in the process of fashioning a neurosurgical persona, this first generation sanctioned specific norms of conduct underwritten by similar moral imperatives, such as self-control. These norms governed the doctors’ work both in the operating room and on the public stage (in their engagement with the press). The meetings of the first neurosurgical society staged a critical encounter between the host neurosurgeon and the members who watched him perform surgery. These technical performances in the operating theatre, followed by discussions, were designed to encourage particular norms, to negotiate surgical knowledge, and to demonstrate the skills and character of the neurosurgeon. The performances acted as a technology of the self that aligned the operator to a community and helped that community refine its norms of surgical conduct. The awkward surgeon with inferior technical ability was preferable to the brilliant but vain operator who lacked the capacity to judge when he should not deploy his spectacular skills.

Significant attention has been paid to the history of public health in England during the final part of the twentieth century. Within this, however, the field that came to be known as specialist health promotion (SHP) has been relatively neglected. Between 1980 and 2000 those working in this field, generally known as health promotion specialists (HPSs), enjoyed a relative rise in policy and practice prominence before SHP was effectively abandoned by government and others charged with developing and sustaining public-health structures. This paper seeks to explain why the fall of SHP is important; to move towards explaining its rise and decline; and to argue for greater historical attention to be paid to an important but neglected field within health and health care. Essentially, SHP emerged from a set of loose and contingent practices known as health education. A range of important social, economic, organisational and political influences contributed to the slow construction of a putative specialism in health promotion, accompanied by the desire on the part of some (but not all) HPSs to ‘professionalise’ their role. Finally the projects of both specialisation and professionalisation failed, again as a result of then prevailing organisational and political influences. The importance of such a failure in a so-called era of public health is discussed. In the light of this, the paper concludes by briefly setting out an agenda for further research related to the history of SHP.

This Presidential Address considers what needs to be done to enable the United Kingdom actuarial profession to flourish in a more competitive environment. It addresses the need for continued modernisation of the actuarial skill-set, and the need to pay greater attention to the way we communicate our findings. The Address briefly reviews some of the recent changes to the regulation of life assurance in the U.K. before considering the role and structure of the professional body in the post-Morris era. It ends with some thoughts on developments in education and CPD.

Financial support and practical help between older parents and their middle-aged children vary greatly among the regions of Europe. Northern and Western Europe is characterised by a high likelihood of practical help to and financial transfers from parents, while in Southern and Eastern Europe these kinds of support are much less likely. Financial transfers to parents show an almost opposite distribution, with more children supporting a parent in Southern and Eastern welfare regimes. Using the second wave of the Survey of Health, Ageing and Retirement in Europe encompassing 14 European countries conducted in 2006–07, these country differences can be linked to different social policies. Controlling for different aspects of country composition in terms of individual characteristics and family structures impacting on intergenerational support, it was found that the more services and transfers provided publicly, the more people aged 50 or more years helped their older parents sporadically, and the less monetary support they provided. On the other hand, generous public transfers enabled parents aged 64 or more years to support their offspring financially. Thus, neither ‘crowding in’ nor ‘crowding out’, but a modification of private transfers depending on public transfers and vice versa is found, suggesting a specialisation of private and public support.

Correlations between the amount of energy received by an assemblage and the number of species that it contains are very general, and at the macro-scale such species–energy relationships typically follow a monotonically increasing curve. Whilst the ecological literature contains frequent reports of such relationships, debate on their causal mechanisms is limited and typically focuses on the role of energy availability in controlling the number of individuals in an assemblage. Assemblages from high-energy areas may contain more individuals enabling species to maintain larger, more viable populations, whose lower extinction risk elevates species richness. Other mechanisms have, however, also been suggested. Here we identify and clarify nine principal mechanisms that may generate positive species–energy relationships at the macro-scale. We critically assess their assumptions and applicability over a range of spatial scales, derive predictions for each and assess the evidence that supports or refutes them. Our synthesis demonstrates that all mechanisms share at least one of their predictions with an alternative mechanism. Some previous studies of species–energy relationships appear not to have recognised the extent of shared predictions, and this may detract from their contribution to the debate on causal mechanisms. The combination of predictions and assumptions made by each mechanism is, however, unique, suggesting that, in principle, conclusive tests are possible. Sufficient testing of all mechanisms has yet to be conducted, and no single mechanism currently has unequivocal support. Each may contribute to species–energy relationships in some circumstances, but some mechanisms are unlikely to act simultaneously. Moreover, a limited number appear particularly likely to contribute frequently to species–energy relationships at the macro-scale. The increased population size, niche position and diversification rate mechanisms are particularly noteworthy in this context.

Max Weber's Protestant Ethic and the Spirit of Capitalism and Politics as a Vocation are interpreted in light of Johann Wolfgang von Goethe's Wilhelm Meister and Faust. The significance of Goethe's faith in human striving, the renunciation of wholly contemplative aspirations, and the subsequent undertaking of a specialised vocation are discussed. Following this, the way in which these themes influenced substantive dimensions of Weber's sociology is developed. This explication contends that Goethe's vision of active asceticism, the motivational power of conviction, and a transcendent deed which contributes to the vitality of future generations, influenced Weber's understanding of meaningful and responsible social and political action.