Dichotomous Hamiltonians with unbounded entries and solutions of Riccati equations

An operator Riccati equation from systems theory is considered in the case that all entries of the associated Hamiltonian are unbounded. Using a certain dichotomy property of the Hamiltonian and its symmetry with respect to two different indefinite inner products, we prove the existence of nonnegative and nonpositive solutions of the Riccati equation. Moreover, conditions for the boundedness and uniqueness of these solutions are established.

Land system science and sustainable development of the earth system: A global land project perspective

Land systems are the result of human interactions with the natural environment. Understanding the drivers, state, trends and impacts of different land systems on social and natural processes helps to reveal how changes in the land system affect the functioning of the socio-ecological system as a whole and the tradeoff these changes may represent. The Global Land Project has led advances by synthesizing land systems research across different scales and providing concepts to further understand the feedbacks between social-and environmental systems, between urban and rural environments and between distant world regions. Land system science has moved from a focus on observation of change and understanding the drivers of these changes to a focus on using this understanding to design sustainable transformations through stakeholder engagement and through the concept of land governance. As land use can be seen as the largest geo-engineering project in which mankind has engaged, land system science can act as a platform for integration of insights from different disciplines and for translation of knowledge into action.

Fire ecology north and south of the Alps since the last ice age

Wildfires are very rare in central Europe, which is probably why fire effects on vegetation have been neglected by most central European ecologists and palaeoecologists. Presently, reconstructions of fire history and fire ecology are almost absent. We analysed sediment cores from lakes on the Swiss Plateau (Lobsigensee and Soppensee) for pollen and charcoal to investigate the relationship between vegetation and fire. Microscopic charcoal evidence suggests increasing regional fire frequencies during the Neolithic (7350-4150 cal. BP, 5400-2200 BC) and the subsequent prehistoric epochs at Lobsigensee, whereas at Soppensee burnings remained rather rare until modern times. Neolithic peaks of charcoal at 6200 and 5500 cal. BP (4250 and 3550 BC) coincided with declines of pollen of fire-sensitive taxa at both sites (e.g., Ulmus, Tilia, Hedera, Fagus), suggesting synchronous vegetational responses to fire at regional scales. However, correlation analysis between charcoal and pollen for the period 6600-4400 cal. BP (4650-2650 BC) revealed no significant link between fire and vegetation at Soppensee, whereas at Lobsigensee increases of Corylus and decreases of Fagus were related to fire events. Fire impact on vegetation increased during the subsequent epochs at both sites. Correlation analyses of charcoal and pollen data for the period 4250-1150 cal. BP (2300 BC -AD 800) suggest that fires were intentionally set to disrupt forests and to provide open areas for arable and pastoral farming (e.g., significant positive correlations between charcoal and Cerealia, Plantago lanceolata, Asteroideae). These results are compared with southern European records (Lago di Origlio, Lago di Muzzano), which are situated in particularly fire-prone environments. After the Mesolithic period (I1 200-7350 cal. BP, 9250-5400 BC), charcoal influx was higher by an order of magnitude in the south, suggesting more frequent fires. Neolithic fires caused similar though more pronounced responses of vegetation in the south (e.g., expansions of Corylus). Post-Neolithic land-use practices involving (controlled) burning culminated in both regions at about 2550 cal. BP (c. 600 BC). However, fire-caused disappearances of entire forest communities were confined to the southern sites. Such differences in fire effects among the sites are explained by the dissimilar importance of fire as a result of different climatic conditions and cultural activities. Our results imply that the remaining (fire-sensitive) fragments of central European vegetation north of the Alps are especially endangered by increasing fire frequencies resulting from predicted climatic change.

Multiple-Choice Testing in Science and Technology Courses

Wide spread and continuing use of multiple-choice testing in technical subjects is leading to a mindset amongst students which is antithetical with actual use of intellect.

Jewish science and health : text book of Jewish science

by Morris Lichtenstein

Revising the National Ambient Air Quality Standards: The integration of science and policy

Under the Clean Air Act, Congress granted discretionary decision making authority to the Administrator of the Environmental Protection Agency (EPA). This discretionary authority involves setting standards to protect the public's health with an "adequate margin of safety" based on current scientific knowledge. The Administrator of the EPA is usually not a scientist, and for the National Ambient Air Quality Standard (NAAQS) for particulate matter (PM), the Administrator faced the task of revising a standard when several scientific factors were ambiguous. These factors included: (1) no identifiable threshold below which health effects are not manifested, (2) no biological basis to explain the reported associations between particulate matter and adverse health effects, and (3) no consensus among the members of the Clean Air Scientific Advisory Committee (CASAC) as to what an appropriate PM indicator, averaging period, or value would be for the revised standard. ^ This project recommends and demonstrates a tool, integrated assessment (IA), to aid the Administrator in making a public health policy decision in the face of ambiguous scientific factors. IA is an interdisciplinary approach to decision making that has been used to deal with complex issues involving many uncertainties, particularly climate change analyses. Two IA approaches are presented; a rough set analysis by which the expertise of CASAC members can be better utilized, and a flag model for incorporating the views of stakeholders into the standard setting process. ^ The rough set analysis can describe minimal and maximal conditions about the current science pertaining to PM and health effects. Similarly, a flag model can evaluate agreement or lack of agreement by various stakeholder groups to the proposed standard in the PM review process. ^ The use of these IA tools will enable the Administrator to (1) complete the NAAQS review in a manner that is in closer compliance with the Clean Air Act, (2) expand the input from CASAC, (3) take into consideration the views of the stakeholders, and (4) retain discretionary decision making authority. ^