Spectral properties of non-local uniformly-elliptic operators

In this paper we consider the spectral properties of a class of non-local uniformly elliptic operators, which arise from the study of non-local uniformly elliptic partial differential equations. Such equations arise naturally in the study of a variety of physical and biological systems with examples ranging from Ohmic heating to population dynamics. The operators studied here are bounded perturbations of linear (local) differential operators, and the non-local perturbation is in the form of an integral term. We study the eigenvalues, the multiplicities of these eigenvalues, and the existence of corresponding positive eigenfunctions. It is shown here that the spectral properties of these non-local operators can differ considerably from those of their local counterpart. However, we show that under suitable hypotheses, there still exists a principal eigenvalue of these operators

Space power technology into the 21st Century

The space power systems of the early 21st century are discussed. The capabilities which are anticipated to evolve from today's state of the art and the technology development programs presently in place or planned for the remainder of the century are emphasized. The power system technologies considered include: solar thermal, nuclear, radioisotope, photovoltaic, thermionic, thermoelectric, and dynamic conversion systems such as the Brayton and Stirling cycles. Energy storage technologies considered include: nickel hydrogen biopolar batteries, advanced high energy rechargeable batteries, regenerative fuel cells, and advanced primary batteries. The present state of the art of these space power and energy technologies is discussed along with their projections, trends and goals. A speculative future mission model is postulated which includes manned orbiting space stations, manned lunar bases, unmanned Earth orbital and interplanetary spacecraft, manned interplanetary missions, military applications, and Earth to space and space to space transportation systems. The various space power/energy system technologies which are anticipated to be operational by the early 21st century are matched to these missions

Self-adjoint boundary-value problems on time-scales

In this paper we consider a second order, Sturm-Liouville-type boundary-value operator of the form $$L u := -[p u^{ abla}]^{Delta} + qu,$$ on an arbitrary, bounded time-scale $mathbb{T}$, for suitable functions $p,q$, together with suitable boundary conditions. We show that, with a suitable choice of domain, this operator can be formulated in the Hilbert space $L^2(mathbb{T}_kappa)$, in such a way that the resulting operator is self-adjoint, with compact resolvent (here, "self-adjoint" means in the standard functional analytic meaning of this term). Previous discussions of operators of this, and similar, form have described them as self-adjoint, but have not demonstrated self-adjointness in the standard functional analytic sense

Interpreting the γ Statistic in Phylogenetic Diversification Rate Studies: A Rate Decrease Does Not Necessarily Indicate an Early Burst

Background Phylogenetic hypotheses are increasingly being used to elucidate historical patterns of diversification rate-variation. Hypothesis testing is often conducted by comparing the observed vector of branching times to a null, pure-birth expectation. A popular method for inferring a decrease in speciation rate, which might suggest an early burst of diversification followed by a decrease in diversification rate is the γ statistic. Methodology Using simulations under varying conditions, I examine the sensitivity of γ to the distribution of the most recent branching times. Using an exploratory data analysis tool for lineages through time plots, tree deviation, I identified trees with a significant γ statistic that do not appear to have the characteristic early accumulation of lineages consistent with an early, rapid rate of cladogenesis. I further investigated the sensitivity of the γ statistic to recent diversification by examining the consequences of failing to simulate the full time interval following the most recent cladogenic event. The power of γ to detect rate decrease at varying times was assessed for simulated trees with an initial high rate of diversification followed by a relatively low rate. Conclusions The γ statistic is extraordinarily sensitive to recent diversification rates, and does not necessarily detect early bursts of diversification. This was true for trees of various sizes and completeness of taxon sampling. The γ statistic had greater power to detect recent diversification rate decreases compared to early bursts of diversification. Caution should be exercised when interpreting the γ statistic as an indication of early, rapid diversification

Equine grass sickness : the geochemical connection

A new study uses the British Geological Survey’s geochemical map to investigate whether minerals in the environment are a factor in this predominantly fatal neurodegenerative disease of horse

Bioaccessibility and human health risk : chromium in Glasgow

The assessment of risk to human health from contaminated land is based on a comparison of predicted human exposure to a contaminant with a Health Criteria Value (HCV) that represents an exposure below which there is thought to be little or no risk to human health. Most assessment tools, such as the Contaminated Land Exposure Assessment Model (CLEA), use estimates of exposure based on intake (consumption rate) rather than on measures of uptake (the amount of contaminant which enters the bloodstream), thus allowing comparison with HCVs, which are also based on intake apposed to uptake. Soil Guideline Values (SGVs) derived using the CLEA model assume that a soil contaminant will be taken up into the body to the same extent as from the medium of exposure used to derive the oral HCV (e.g. soluble salts of Cr(VI)). This is a conservative assumption as contaminants can be tightly bound to other soil components, thus reducing bioavailability (the fraction of a contaminant that can be absorbed by the body)

A complete record from colonization to extinction reveals density dependence and the importance of winter conditions for a population of the silvery blue, Glaucopsyche lygdamus.

Butterflies in the family Lycaenidac are often the focus of conservation efforts. However, our understanding of lycaenid population dynamics has been limited to relatively few examples of long-term monitoring data that have been reported. Here, factors associated with population regulation are investigated using a complete record of a single population of the silvery blue, Glaucopsyche lygdamus Doubleday (Lepidoptera: Lycaenidae). Adults of G. lygdamus were first observed in an annual grassland near Davis, California, in 1982 and were last seen in 2003. Relationships between inter-annual variation in abundance and climatic variables were examined, accounting for density dependent effects. Significant effects of both negative density dependence and climatic variation were detected, particularly precipitation and temperature during winter months. Variation in precipitation, the strongest predictor of abundance, was associated directly and positively with butterfly abundance in the same year. Winter temperatures had a negative effect in the same year, but had a lagged, positive effect on abundance in the subsequent year. Mechanistic hypotheses are posed that include climatic effects mediated through both larval and adult plant resources

Power technologies and the space future

Advancements in space power and energy technologies are critical to serve space development needs and help solve problems on Earth. The availability of low cost power and energy in space will be the hallmark of this advance. Space power will undergo a dramatic change for future space missions. The power systems which have served the U.S. space program so well in the past will not suffice for the missions of the future. This is especially true if the space commercialization is to become a reality. New technologies, and new and different space power architectures and topologies will replace the lower power, low-voltage systems of the past. Efficiencies will be markedly improved, specific powers will be greatly increased, and system lifetimes will be markedly extended. Space power technology is discussed - its past, its current status, and predictions about where it will go in the future. A key problem for power and energy is its cost of affordability. Power must be affordable or it will not serve future needs adequately. This aspect is also specifically addressed

Contamination

Soil contamination occurs when substances are added to soil, resulting in increases in concentrations above background or reference levels. Pollution may follow from contamination when contaminants are present in amounts that are detrimental to soil quality and become harmful to the environment or human health. Contamination can occur via a range of pathways including direct application to land and indirect application from atmospheric deposition. Contamination was identified by SEPA (2001) as a significant threat to soil quality in many parts of Scotland. Towers et al. (2006) identified four principal contamination threats to Scottish soils: acidification; eutrophication; metals; and pesticides. The Scottish Soil Framework (Scottish Government, 2009) set out the potential impact of these threats on the principal soil functions. Severe contamination can lead to “contaminated land” [as defined under Part IIA of the Environmental Protection Act (1990)]. This report does not consider the state and impacts of contaminated land on the wider environment in detail. For further information on contaminated land, see ‘Dealing with Land Contamination in Scotland’ (SEPA, 2009). This chapter considers the causes of soil contamination and their environmental and socio-economic impacts before going on to discuss the status of, and trends in, levels of contaminants in Scotland’s soils