Ω-results for Beurling's zeta function and lower bounds for the generalised Dirichlet divisor problem

In this paper we study generalised prime systems for which the integer counting function NP(x) is asymptotically well behaved, in the sense that NP(x)=ρx+O(xβ), where ρ is a positive constant and . For such systems, the associated zeta function ζP(s) is holomorphic for . We prove that for , for any ε>0, and also for ε=0 for all such σ except possibly one value. The Dirichlet divisor problem for generalised integers concerns the size of the error term in NkP(x)−Ress=1(ζPk(s)xs/s), which is O(xθ) for some θ<1. Letting αk denote the infimum of such θ, we show that .

Bad reduction of genus three curves with complex multiplication

Let C be a smooth, absolutely irreducible genus 3 curve over a number field M. Suppose that the Jacobian of C has complex multiplication by a sextic CM-field K. Suppose further that K contains no imaginary quadratic subfield. We give a bound on the primes p of M such that the stable reduction of C at p contains three irreducible components of genus 1.

Computing the Cassels–Tate pairing on the 3-Selmer group of an elliptic curve

We extend the method of Cassels for computing the Cassels-Tate pairing on the 2-Selmer group of an elliptic curve, to the case of 3-Selmer groups. This requires significant modifications to both the local and global parts of the calculation. Our method is practical in sufficiently small examples, and can be used to improve the upper bound for the rank of an elliptic curve obtained by 3-descent.

Shadow lines in the arithmetic of elliptic curves

Let E/Q be an elliptic curve and p a rational prime of good ordinary reduction. For every imaginary quadratic field K/Q satisfying the Heegner hypothesis for E we have a corresponding line in E(K)\otimes Q_p, known as a shadow line. When E/Q has analytic rank 2 and E/K has analytic rank 3, shadow lines are expected to lie in E(Q)\otimes Qp. If, in addition, p splits in K/Q, then shadow lines can be determined using the anticyclotomic p-adic height pairing. We develop an algorithm to compute anticyclotomic p-adic heights which we then use to provide an algorithm to compute shadow lines. We conclude by illustrating these algorithms in a collection of examples.

Gál-type GCD sums beyond the critical line

We prove that ∑k,ℓ=1N(nk,nℓ)2α(nknℓ)α≪N2−2α(logN)b(α) holds for arbitrary integers 1≤n1<⋯

Equatorial Kelvin waves as revealed by EOS Microwave Limb Sounder observations and European Centre for Medium-Range Weather Forecasts analyses: Evidence for slow Kelvin waves of zonal wave number 3

[1] Temperature and ozone observations from the Microwave Limb Sounder (MLS) on the EOS Aura satellite are used to study equatorial wave activity in the autumn of 2005. In contrast to previous observations for the same season in other years, the temperature anomalies in the middle and lower tropical stratosphere are found to be characterized by a strong wave-like eastward progression with zonal wave number equal to 3. Extended empirical orthogonal function (EOF) analysis reveals that the wave 3 components detected in the temperature anomalies correspond to a slow Kelvin wave with a period of 8 days and a phase speed of 19 m/s. Fluctuations associated with this Kelvin wave mode are also apparent in ozone profiles. Moreover, as expected by linear theory, the ozone fluctuations observed in the lower stratosphere are in phase with the temperature perturbations, and peak around 20–30 hPa where the mean ozone mixing ratios have the steepest vertical gradient. A search for other Kelvin wave modes has also been made using both the MLS observations and the analyses from one experiment where MLS ozone profiles are assimilated into the European Centre for Medium-Range Weather Forecasts (ECMWF) data assimilation system via a 6-hourly 3D var scheme. Our results show that the characteristics of the wave activity detected in the ECMWF temperature and ozone analyses are in good agreement with MLS data.

Testing the limits of quasi-geostrophic theory: application to observed laboratory flows outside the quasi-geostrophic regime

We compare laboratory observations of equilibrated baroclinic waves in the rotating two-layer annulus, with numerical simulations from a quasi-geostrophic model. The laboratory experiments lie well outside the quasi-geostrophic regime: the Rossby number reaches unity; the depth-to-width aspect ratio is large; and the fluid contains ageostrophic inertia–gravity waves. Despite being formally inapplicable, the quasi-geostrophic model captures the laboratory flows reasonably well. The model displays several systematic biases, which are consequences of its treatment of boundary layers and neglect of interfacial surface tension and which may be explained without invoking the dynamical effects of the moderate Rossby number, large aspect ratio or inertia–gravity waves. We conclude that quasi-geostrophic theory appears to continue to apply well outside its formal bounds.

The impact of harvesting on a formerly endangered tropical bird: insights from life-history theory

1. Life-history theory assumes that trade-offs exist between an individual's life-history components, such that an increased allocation of a resource to one fitness trait might be expected to result in a cost for a conflicting fitness trait. Recent evidence from experimental manipulations of wild individuals supports this assumption. 2. The management of many bird populations involves harvesting for both commercial and conservation purposes. One frequently harvested life-history stage is the egg, but the consequences of repeated egg harvesting for the individual and the long-term dynamics of the population remain poorly understood. 3. We used a well-documented restored population of the Mauritius kestrel Falco punctatus as a model system to explore the consequences of egg harvesting (and associated management practices) for an individual within the context of life-history theory. 4. Our analysis indicated that management practices enhanced both the size and number of clutches laid by managed females, and improved mid-life male and female adult survival relative to unmanaged adult kestrels. 5. Although management resulted in an increased effort in egg production, it reduced parental effort during incubation and the rearing of offspring, which could account for these observed changes. 6. Synthesis and applications. This study demonstrates how a commonly applied harvesting strategy, when examined within the context of life-history theory, can identify improvements in particular fitness traits that might alleviate some of the perceived negative impact of harvesting on the long-term dynamics of a managed population.

Rate-limiting steps in the development of atherosclerosis: the response-to-influx theory

A large number of processes are involved in the pathogenesis of atherosclerosis but it is unclear which of them play a rate-limiting role. One way of resolving this problem is to investigate the highly non-uniform distribution of disease within the arterial system; critical steps in lesion development should be revealed by identifying arterial properties that differ between susceptible and protected sites. Although the localisation of atherosclerotic lesions has been investigated intensively over much of the 20th century, this review argues that the factor determining the distribution of human disease has only recently been identified. Recognition that the distribution changes with age has, for the first time, allowed it to be explained by variation in transport properties of the arterial wall; hitherto, this view could only be applied to experimental atherosclerosis in animals. The newly discovered transport variations which appear to play a critical role in the development of adult disease have underlying mechanisms that differ from those elucidated for the transport variations relevant to experimental atherosclerosis: they depend on endogenous NO synthesis and on blood flow. Manipulation of transport properties might have therapeutic potential. Copyright (C) 2004 S. Karger AG, Basel.

Understanding construction consortia: Theory, practice and opinions

Firms form consortia in order to win contracts. Once a project has been awarded to a consortium each member then concentrates on his or her own contract with the client. Therefore, consortia are marketing devices, which present the impression of teamworking, but the production process is just as fragmented as under conventional procurement methods. In this way, the consortium forms a barrier between the client and the actual construction production process. Firms form consortia, not as a simple development of normal ways of working, but because the circumstances for specific projects make it a necessary vehicle. These circumstances include projects that are too large or too complex to undertake alone or projects that require on-going services which cannot be provided by the individual firms inhouse. It is not a preferred way of working, because participants carry extra risk in the form of liability for the actions of their partners in the consortium. The behaviour of members of consortia is determined by their relative power, based on several factors, including financial commitment and ease of replacement. The level of supply chain visibility to the public sector client and to the industry is reduced by the existence of a consortium because the consortium forms an additional obstacle between the client and the firms undertaking the actual construction work. Supply chain visibility matters to the client who otherwise loses control over the process of construction or service provision, while remaining accountable for cost overruns. To overcome this separation there is a convincing argument in favour of adopting the approach put forward in the Project Partnering Contract 2000 (PPC2000) Agreement. Members of consortia do not necessarily go on to work in the same consortia again because members need to respond flexibly to opportunities as and when they arise. Decision-making processes within consortia tend to be on an ad hoc basis. Construction risk is taken by the contractor and the construction supply chain but the reputational risk is carried by all the firms associated with a consortium. There is a wide variation in the manner that consortia are formed, determined by the individual circumstances of each project; its requirements, size and complexity, and the attitude of individual project leaders. However, there are a number of close working relationships based on generic models of consortia-like arrangements for the purpose of building production, such as the Housing Corporation Guidance Notes and the PPC2000.