Lang's Conjecture and Sharp Height Estimates for the elliptic curves y2=x3+axy^{2}=x^{3}+ax

For elliptic curves given by the equation $E_{a}: y^{2}=x^{3}+ax$, we establish the best-possible version of Lang's conjecture on the lower bound of the canonical height of non-torsion points along with best-possible upper and lower bounds for the difference between the canonical and logarithmic height.Comment: published version. Lemmas 5.1 and 6.1 now precise (with resultant refinement to Theorem 1.2). Small corrections to

Challenging the Moral Status of Blood Donation

The World Health Organisation encourages that blood donation becomes voluntary and unremunerated, a system already operated in the UK. Drawing on public documents and videos, this paper argues that blood donation is regarded and presented as altruistic and supererogatory. In advertisements, donation is presented as something undertaken for the benefit of others, a matter attracting considerable gratitude from recipients and the collecting organisation. It is argued that regarding blood donation as an act of supererogation is wrongheaded, and an alternative account of blood donation as moral obligation is presented. Two arguments are offered in support of this position. First, the principle of beneficence, understood in a broad consequentialist framework obliges donation where the benefit to the recipient is large and the cost to the donor relatively small. This argument can be applied, with differing levels of normativity, to various acts of donation. Second, the wrongness of free riding requires individuals to contribute to collective systems from which they benefit. Alone and in combination these arguments present moral reasons for donation, recognised in communication strategies elsewhere. Research is required to evaluate the potential effects on donation of a campaign which presents blood donation as moral obligation, but of wider importance is the recognition that other-regarding considerations in relation to our own as well as others’ health result in a range not only of choices but also of obligations

Local diversity in settlement, demography and subsistence across the southern Indian Neolithic-Iron Age transition: site growth and abandonment at Sanganakallu-Kupgal

The Southern Indian Neolithic-Iron Age transition demonstrates considerable regional variability in settlement location, density, and size. While researchers have shown that the region around the Tungabhadra and Krishna River basins displays significant subsistence and demographic continuity, and intensification, from the Neolithic into the Iron Age ca. 1200 cal. BC, archaeological and chronometric records in the Sanganakallu region point to hilltop village expansion during the Late Neolithic and ‘Megalithic’ transition period (ca. 1400–1200 cal. BC) prior to apparent abandonment ca. 1200 cal. BC, with little evidence for the introduction of iron technology into the region. We suggest that the difference in these settlement histories is a result of differential access to stable water resources during a period of weakening and fluctuating monsoon across a generally arid landscape. Here, we describe well-dated, integrated chronological, archaeobotanical, archaeozoological and archaeological survey datasets from the Sanganakallu-Kupgal site complex that together demonstrate an intensification of settlement, subsistence and craft production on local hilltops prior to almost complete abandonment ca. 1200 cal. BC. Although the southern Deccan region as a whole may have witnessed demographic increase, as well as subsistence and cultural continuity, at this time, this broader pattern of continuity and resilience is punctuated by local examples of abandonment and mobility driven by an increasing practical and political concern with water

An Archaeological Watching Brief on Land behind 48 Church Street, Willingham

The machining of foundation trenches for a small housing development behind 48 Church Street, Willingham (TL406 705) was monitored, and a number of possible archaeological features recorded in the sections of the trenches. None of these produced any datable material. Two were large pits which may be associated with a medieval pit recorded in the previous evaluation of the site, but may also be modern

Archaeological Investogations at the Hoyle Building Site, Madingley Rise, Cambridge

Two evaluation trenches, each measuring 3m x 1.5m, were hand-excavated in advance of the proposed construction of an extension to the Hoyle Building (TL43155945) on the University of Cambridge Madingley Rise Site. In both, large backfilled pits were partially revealed, probably associated with the gravel quarrying known to have taken place in the locality from the medieval period, if not earlier. While the pitting in one trench was clearly 18th-19th century in date, the backfill in the other trench contained sherds of exclusively Iron Age pottery (both Late and Early). Although the excavated area was small and the features consequently difficult to interpret, and residuality cannot be ruled out, this material at least confirms the presence of later prehistoric occupation in a location that more circumstantial evidence has long suggested may have been an important focus of early settlement in the area

Archaeological Excavations at West Fen Road and St. John's Road, Ely, Cambridgeshire: The Trinity and Runciman Lands: Assessment Report

Excavations in advance of housing development on the western edge of the city of Ely revealed archaeological evidence from the Neolithic, Late Bronze Age, Middle to Late Iron Age and Early Roman periods. The Neolithic was represented only by a spread of burnt material associated with a tree throw. Sporadic activity in the Late Bronze Age was associated with a small pond which had subsequently silted up. Elements of ditched enclosures which may be of Middle Iron Age date were succeeded by a phase of Late Iron Age (1st century BC/AD) settlement characterized by ephemeral ring gullies, shallow pits and spreads of midden deposits. Subsequently, in the late 1st or early 2nd century AD, two rectilinear ditched enclosures were laid out to the south of the Late Iron Age settlement, further up the slope, probably for the control of livestock or to mark out cultivated fields. Later in the same period, the southern of the two enclosures went out of use and was replaced by systems of narrow linear gullies possibly associated with early Roman lazybed or strip field cultivation

The Cambridge Centre for Recycling, Ely Road, Waterbeach: Archaeological Evaluation of Graves' Field, Undertakers, Webster's Field and IWM Park

Trench-based evaluation was carried out on four areas in Cottenham and Landbeach parishes, known as Graves' Field, The Undertakers, Webster's Field and the IWM Park, covering a total area of 45 hectares, which would be affected by the proposed Cambridge Centre for Recycling. All the evaluation areas lie at or below 3 metres OD on the fen margin near the confluence of the Cam and the Old West River, an area known to have been densely settled in the Roman period. In The Undertakers, postholes and pits were identified, relating to a small Late Bronze Age settlement located on a slight rise that would have formed a peninsula of dry land extending into the fen. In Graves' Field, a Roman ditch was excavated, possibly the continuation of a droveway visible as a cropmark feature in the adjacent field, associated with two small gullies and re-cut by a modern field ditch. Webster's field, which is bounded on one side by the Car Dyke, contained a Roman double-ditched droveway, three other ditches which are probably also of Roman date, and several undated postholes. In the IWM Park, late 3rd-4th century occupation deposits including a midden and traces of structures were recorded in one corner, overlying earlier Roman ditches, some of which may be associated with a droveway which is visible as a cropmark in the adjacent field. Other ditches, mostly restricted to an area along one edge of the field, were also predominantly late Roman in date, and related to field systems associated with the settlement, with the exception of one ditch which was of Late Bronze Age or Early Iron Age date. A fourth century temple, now lost to quarrying, formerly stood just beyond the edge of the evaluation area: except for a single undated cremation, no associated features were identified within 120 metres of it, suggesting that the area surrounding the temple was deliberately avoided by Roman settlement and cultivation

Archaeological Evaluation at the Junction of Union Lane and High Street, Chesterton, Cambridge: The Phase II Site

A trench-based evaluation was carried out by the Cambridge Archaeological Unit on a plot of land at the junction of High Street and Union Lane, Chesterton. The area evaluated lies across the road from a recently-developed site (the Phase 1 site) on which previous excavations have revealed a sequence of settlement activity dating back to the 12th century. The evaluation revealed a number of ditches and quarry pits of medieval date, though the density of features does appear to be less than on the Phase 1 site. Although buildings (now demolished) were constructed on both the street frontages in the late 19th century, their foundations do not appear to have disturbed the archaeologically significant levels except on the High Street frontage, where a backfilled cellar was encountered