Three constructive examples of separable pre-Hilbert spaces nonisomorphic to their closed hyperplanes

An example of a sigma -compact infinite-dimensional pre-Hilbert space H is constructed such that any continuous linear operator T: H --> H is of the form T = lambdaI + F for some lambda is an element of R and for a finite-dimensional continuous linear operator F. A class of simple examples of pre-Hilbert spaces nonisomorphic to their closed hyperplanes is given. A sigma -compact pre-Hilbert space H isomorphic to H x R x R and nonisomorphic to H x R is also constructed.

An infinite-dimensional separable pre-Hilbert space non-homeomorphic to any of its closed hyperplanes

An example is constructed of an infinite-dimensional separable pre-Hilbert space non-homeomorphic to any of its closed hyperplanes.

Fighting for shells: how private information about resource value changes hermit crab pre-fight displays and escalated fight behaviour

Pre-fight displays typically provide honest, but sometimes dishonest, information about resource holding potential and may be influenced by assessment of resource value and hence motivation to acquire the resource. These assessments of potential costs and benefits are also predicted to influence escalated fight behaviour. This is examined in shell exchange contests of hermit crabs in which we establish an information asymmetry about a particularly poor quality shell. The poor shell was created by gluing sand to the interior whereas control shells lacked sand and the low value of the poor shell could not be accurately assessed by the opponent. Crabs in the poor shell showed changes in the use of pre-fight displays, apparently to increase the chances of swapping shells. When the fights escalated, crabs in poor shells fought harder if they took the role of attacker but gave up quickly if in the defender role. These tactics appear to be adaptive but do not result in a major shift in the roles taken or outcome. We thus link resource assessment with pre-fight displays, the roles taken, tactics used during escalation and the outcome of these contests.

Interaction of High Intensity Picosecond Laser Pulses with Large Pre-formed Plasmas

The interaction of short (1-2 ps) laser pulses with solid targets at irradiances of over 1016 Wcm~2 , in the presence of a substantial prepulse has been investigated. High absorption of laser energy is found even at high angles of incidence, with evidence for a resonance absorption peak being found for S, P, and circular polarizations. It is considered that this may be a result of refraction and beam filamentation, which causes loss of distinct polarization. Measurements of hard X-ray emission (~ 100 keV) confirm a resonance absorption type peak at 45-50°, again for all three cases. Typically, 5-15% of the incident light is back-reflected by stimulated Brillouin scatter, with spatially resolved spectra showing evidence of beam hot-spots at high intensity. The possibility that filamentation and refraction of the beam can explain the lack of polarization dependence in the absorption and hard X-ray emission data is discussed.

Nature as historical protagonist: environment and society in pre-industrial England

This article compares chronologies reconstructed from historical records of prices, wages, grain harvests, and population with corresponding chronologies of growing conditions and climatic variations derived from dendrochronology and Greenland ice-cores. It demonstrates that in pre-industrial, and especially late medieval, England, short-term environmental shocks and more enduring shifts in environmental conditions (sometimes acting in concert with biological agencies) exercised a powerful influence upon the balance struck between population and available resources via their effects upon the reproduction, health and life expectancy of humans, crops, and livestock. Prevailing socio-economic conditions and institutions, in turn, shaped society's susceptibility to these environmental shocks and shifts.