Integrability and explicit solutions in some Bianchi cosmological dynamical systems

The Einstein field equations for several cosmological models reduce to polynomial systems of ordinary differential equations. In this paper we shall concentrate our attention to the spatially homogeneous diagonal G_2 cosmologies. By using Darboux's theory in order to study ordinary differential equations in the complex projective plane CP^2 we solve the Bianchi V models totally. Moreover, we carry out a study of Bianchi VI models and first integrals are given in particular cases

What e-patients want from the doctor-patient relationship: content analysis of posts on discussion boards.

People with long-term conditions are encouraged to take control and ownership of managing their condition. Interactions between health care staff and patients become partnerships with sharing of expertise. This has changed the doctor-patient relationship and the division of roles and responsibilities that traditionally existed, but what each party expects from the other may not always be clear. Information that people with long-term conditions share on Internet discussion boards can provide useful insights into their expectations of health care staff. This paper reports on a small study about the expectations that people with a long-term condition (diabetes) have of their doctors using information gleaned from Internet discussion boards

How reversible is sea ice loss?

It is well accepted that increasing atmospheric CO<sub>2</sub> results in global warming, leading to a decline in polar sea ice area. Here, the specific question of whether there is a tipping point in the sea ice cover is investigated. The global climate model HadCM3 is used to map the trajectory of sea ice area under idealised scenarios. The atmospheric CO<sub>2</sub> is first ramped up to four times pre-industrial levels (4 × CO<sub>2</sub>), then ramped down to pre-industrial levels. We also examine the impact of stabilising climate at 4 × CO<sub>2</sub> prior to ramping CO<sub>2</sub> down to pre-industrial levels. Against global mean temperature, Arctic sea ice area is reversible, while the Antarctic sea ice shows some asymmetric behaviour – its rate of change slower, with falling temperatures, than its rate of change with rising temperatures. However, we show that the asymmetric behaviour is driven by hemispherical differences in temperature change between transient and stabilisation periods. We find no irreversible behaviour in the sea ice cover

Ames collaborative study of cosmic-ray neutrons. 2: Low- and mid-latitude flights

Progress of the study of cosmic ray neutrons is described. Data obtained aboard flights from Hawaii at altitudes of 41,000 and 45,000 feet, and in the range of geomagnetic latitude 17 N less than or equal to lambda less than or equal to 21 N are reported. Preliminary estimates of neutron spectra are made

Dynamical systems approach to G2 cosmology

In this paper we present a new approach for studying the dynamics of spatially inhomogeneous cosmological models with one spatial degree of freedom. By introducing suitable scale-invariant dependent variables we write the evolution equations of the Einstein field equations as a system of autonomous partial differential equations in first-order symmetric hyperbolic format, whose explicit form depends on the choice of gauge. As a first application, we show that the asymptotic behaviour near the cosmological initial singularity can be given a simple geometrical description in terms of the local past attractor on the boundary of the scale-invariant dynamical state space. The analysis suggests the name ``asymptotic silence'' to describe the evolution of the gravitational field near the cosmological initial singularity.Comment: 28 pages, 3 tables, 1 *.eps figure, LaTeX2e (10pt), matches version accepted for publication by Classical and Quantum Gravit

The Asymptotic Behaviour of Tilted Bianchi type VI0_0 Universes

We study the asymptotic behaviour of the Bianchi type VI$_0$ universes with a tilted $\gamma$-law perfect fluid. The late-time attractors are found for the full 7-dimensional state space and for several interesting invariant subspaces. In particular, it is found that for the particular value of the equation of state parameter, $\gamma=6/5$, there exists a bifurcation line which signals a transition of stability between a non-tilted equilibrium point to an extremely tilted equilibrium point. The initial singular regime is also discussed and we argue that the initial behaviour is chaotic for $\gamma<2$.Comment: 22 pages, 4 figures, to appear in CQ

Information Costs and Reverse Payment Settlements: Bridging the Gap Between the Courts and the Antitrust Agencies

Reverse payment settlements have attracted increased scrutiny due to the controversial presence of a payment from a brand-name drug company to a generic company that is ostensibly preparing to infringe on the branded company’s patent. The antitrust agencies and the courts settled into an intergovernmental stalemate regarding the appropriate framework of analysis to apply when reviewing antitrust challenges to these settlements. The FTC and DOJ have viewed the deals skeptically as a vehicle for competitors to split monopoly profits, but the lower courts have generally been deferential to what they identified as an exercise of a patent holder’s lawful right to exclude. Much has been written about which side is correct, yet there has been relatively little exploration of the source of the persistent disagreement. Building off of Henry Smith’s property rights theory and the cognitive miser literature from Peter Lee, this Article explains that the long-standing disagreement stems from the judiciary’s application of information-cost-saving rules. Courts adopted a formalistic approach that would almost invariably uphold a reverse payment settlement because they tend to apply bright-line rules when dealing with property rights, and they are prone to adjudicate complex patent and patent-related cases in ways that economize on the costs of information processing. Although the Supreme Court resolved the disagreement by adopting a more information-demanding rule of reason approach in FTC v. Actavis, the cognitive miser phenomenon will continue to affect how courts adjudicate antitrust challenges to reverse-payment settlements

FOULING DURING THE USE OF ‘FRESH’ WATER AS COOLANT- THE DEVELOPMENT OF A ‘USER GUIDE’

IHS ESDU recently published its latest ‘User Guide’ to fouling in heat exchange systems, for systems with fresh water as the coolant. ESDU 07006 [1] is the third in a group, following the development of the Crude Oil Fouling User Guide [2] issued in 2000 and the Seawater Fouling User Guide [3] issued in 2004. ESDU 07006 was developed by IHS ESDU over a period of five years under the guidance of the Oil Industry Fouling Working Party, a collaborative team of oil refiners, heat transfer equipment and services suppliers and Universities. It provides designers and operators of cooling water facilities with a practical source of guidance on the occurrence, the mechanisms and the mitigation of fresh water fouling in these systems. IHS ESDU’s Oil Industry Fouling Working Party was formed in recognition of the huge economic and environmental importance of heat exchanger fouling and the potential benefits that can accrue from better understanding of mitigation strategies. Work is now underway on reboiler and FCCU fouling. The development of the User Guide ESDU 07006 is discussed in this paper and its technical content is summarized