A constructive approach to the soliton solutions of integrable quadrilateral lattice equations

Scalar multidimensionally consistent quadrilateral lattice equations are studied. We explore a confluence between the superposition principle for solutions related by the Backlund transformation, and the method of solving a Riccati map by exploiting two kn own particular solutions. This leads to an expression for the N-soliton-type solutions of a generic equation within this class. As a particular instance we give an explicit N-soliton solution for the primary model, which is Adler's lattice equation (or Q4).Comment: 22 page

Volume Comparison for Hypersurfaces in Lorentzian Manifolds and Singularity Theorems

We develop area and volume comparison theorems for the evolution of spacelike, acausal, causally complete hypersurfaces in Lorentzian manifolds, where one has a lower bound on the Ricci tensor along timelike curves, and an upper bound on the mean curvature of the hypersurface. Using these results, we give a new proof of Hawking's singularity theorem.Comment: 15 pages, LaTe

Law, politics and the governance of English and Scottish joint-stock companies 1600-1850

This article examines the impact of law on corporate governance by means of a case study of joint-stock enterprise in England and Scotland before 1850. Based on a dataset of over 450 company constitutions together with qualitative information on governance practice, it finds little evidence to support the hypothesis that common-law regimes such as England were more supportive of economic growth than civil-law jurisdictions such as Scotland: indeed, levels of shareholder protection were slightly stronger in the civil-law zone. Other factors, such as local political institutions, played a bigger role in shaping organisational forms and business practice

Placing Joseph Banks in the North Pacific

The South Pacific was a fulcrum of Joseph Banks's maritime world and global networks. The North Pacific was a distance and intangible fringe. This article is concerned with how Banks should be ‘placed’ in the North Pacific. It tracks how Banks's activities have been delineated in terms of languages and categories of global and local, and centre and margin, and then considers the historical and geographical specifics apposite to his connection to the North Pacific. In this setting, ideas of place (as location and assignment) and capital (as a circulatory and everyday practice of exchange and opportunism) come into view and question the distinction between science and commerce in Banks historiography. The article considers a diverse group of non-Indigenous figures – explorers, traders, cartographers, scientists, collectors – operating in the North Pacific in the 1780s and 1790s whose initiatives and missives passed across Banks's desk, and assesses their place in Banks's archive by drawing on Peter Sloterdijk's ideas about the interiorising and exteriorising logic of capital.PostprintPeer reviewe

Lorentz invariance violation in top-down scenarios of ultrahigh energy cosmic ray creation

The violation of Lorentz invariance (LI) has been invoked in a number of ways to explain issues dealing with ultrahigh energy cosmic ray (UHECR) production and propagation. These treatments, however, have mostly been limited to examples in the proton-neutron system and photon-electron system. In this paper we show how a broader violation of Lorentz invariance would allow for a series of previously forbidden decays to occur, and how that could lead to UHECR primaries being heavy baryonic states or Higgs bosons.Comment: Replaced with heavily revised (see new Abstract) version accepted by Phys. Rev. D. 6 page

Does Conservation Planning Matter in a Dynamic and Uncertain World?

We show that while comprehensive reserve network design is best when the entire network can be implemented immediately, when conservation investments must be staged over years, such solutions actually may be sub-optimal in the context of biodiversity loss and uncertainty

Structural and dielectric properties of Sr2_{2}TiO4_{4} from first principles

We have investigated the structural and dielectric properties of Sr$_{2}$TiO$_{4}$,the first member of the Sr$_{n+1}$Ti$_{n}$O$_{3n+1}$ Ruddlesden-Popper series, within density functional theory. Motivated by recent work in which thin films of Sr$_{2}$TiO$_{4}$ were grown by molecular beam epitaxy (MBE) on SrTiO$_{3}$ substrates, the in-plane lattice parameter was fixed to the theoretically optimized lattice constant of cubic SrTiO$_{3}$ (n=$\infty$), while the out-of-plane lattice parameter and the internal structural parameters were relaxed. The fully relaxed structure was also investigated. Density functional perturbation theory was used to calculate the zone-center phonon frequencies, Born effective charges, and the electronic dielectric permittivity tensor. A detailed study of the contribution of individual infrared-active modes to the static dielectric permittivity tensor was performed. The calculated Raman and infrared phonon frequencies were found to be in agreement with experiment where available. Comparisons of the calculated static dielectric permittivity with experiments on both ceramic powders and epitaxial thin films are discussed.Comment: 11 pages, 1 figure, 8 tables, submitted to Phys. Rev.

The complex relationship between asset wealth, adaptation, and diversification in tropical fisheries

Marine small-scale fisheries are complex social and ecological systems that are currently pressurised by climate change, increasing demand for food, and expectation to sustain livelihoods. Species diversification and occupational diversification are often offered as adaptation strategies to increase the resilience of these fisheries to natural and economic shocks. However, little is known about the nature of species diversification within marine tropical fisheries. Based on 293 interviews with artisanal fishers from six coastal communities located at the isles of Zanzibar, Pemba, Mafia, and Mainland Tanga in Tanzania - we assess if fishers with the highest level of species diversification are the most financially secure and able to adapt to changes in the fishing industry. By creating an Asset Wealth Index (AWI) based on a Multiple Correspondence Approach (MCA), we investigate the relative levels of adaptive capacity and fishery connectivity within the different regional wealth quartiles. We find that less wealthy fishers target fewer species, making them less able to absorb changes in management measures focused on species, area, and closures. Likewise, fishers with higher wealth scores and higher adaptive capacity are able to better absorb the short-term losses of fisheries closures when compared to those with lower wealth and adaptive scores reliant on higher levels of fishery connectivity

Black Holes from Cosmic Rays: Probes of Extra Dimensions and New Limits on TeV-Scale Gravity

If extra spacetime dimensions and low-scale gravity exist, black holes will be produced in observable collisions of elementary particles. For the next several years, ultra-high energy cosmic rays provide the most promising window on this phenomenon. In particular, cosmic neutrinos can produce black holes deep in the Earth's atmosphere, leading to quasi-horizontal giant air showers. We determine the sensitivity of cosmic ray detectors to black hole production and compare the results to other probes of extra dimensions. With n \ge 4 extra dimensions, current bounds on deeply penetrating showers from AGASA already provide the most stringent bound on low-scale gravity, requiring a fundamental Planck scale M_D > 1.3 - 1.8 TeV. The Auger Observatory will probe M_D as large as 4 TeV and may observe on the order of a hundred black holes in 5 years. We also consider the implications of angular momentum and possible exponentially suppressed parton cross sections; including these effects, large black hole rates are still possible. Finally, we demonstrate that even if only a few black hole events are observed, a standard model interpretation may be excluded by comparison with Earth-skimming neutrino rates.Comment: 30 pages, 18 figures; v2: discussion of gravitational infall, AGASA and Fly's Eye comparison added; v3: Earth-skimming results modified and strengthened, published versio