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.

The energetics of lactation in cooperatively breeding meerkats Suricata suricatta

Species may become obligate cooperative breeders when parents are unable to raise their offspring unassisted. We measured the daily energy expenditure of mothers, helpers and offspring during peak lactation in cooperatively breeding meerkats Suricata suricatta using the doubly labelled water technique. Lactating mothers expended more energy per day than allo-lactating subordinate females, non-lactating females or suckling offspring. Metabolizable energy intakes of lactating mothers were calculated from isotope-based estimates of offspring milk energy intake, and were not significantly different from the previously suggested maximal limit for mammals. Allo-lactating females were the only category of animals that lost weight during the period of study, probably because they spent more time babysitting than non-lactating females. Daily energy expenditure (DEE) of lactating mothers increased with litter size but decreased with the number of helpers. Calculations show that for every 10 helpers, even in the absence of allo-lactators, mothers are able to reduce their DEE during peak lactation by an amount equivalent to the energy cost of one pup. These results indicate that helpers have beneficial energetic consequences for lactating mothers in an obligate cooperatively breeding mammal.

The natural plasma testosterone profile of male blue tits during the breeding season and its relation to song output

In male birds, the gonadal hormone testosterone (T) is known to influence territorial and mating behaviour. Plasma levels of T show seasonal fluctuations which vary in relation to mating system and social instability. First, we determined the natural T profile of male blue tits Parus caeruleus during the breeding season. We found that plasma levels of T increased at the onset of nest building. Thus, the increase in circulating T was not associated with territory establishment, nor with the fertile period of the males' mates. In most individuals, T levels dropped to values close to zero during the period of chick feeding. Second, we investigated the relationship between plasma levels of T and male age, size, and singing behaviour. During the mating period, T levels did not differ between 1 yr old and older males and did not correlate with body size or condition. However, song output during the dawn chorus tended to be positively correlated with T levels. Therefore, if high T levels are costly, song output might be an honest indicator of male quality in blue tits. Finally, we show that plasma levels of T are significantly higher during the night than during the day. This pattern has also been observed in captive non-passerine birds, but its functional significance remains unknown.

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.