On weak and strong Peano theorems

We say that the Peano theorem holds for a topological vector space $E$ if, for any continuous mapping $f : {\Bbb R}\times E \to E$ and any $(t(0), x(0))$ is an element of ${\Bbb R}\times E$, the Cauchy problem $\dot x(t) = f(t,x(t))$, $x(t(0)) = x(0)$, has a solution in some neighborhood of $t(0)$. We say that the weak version of Peano theorem holds for $E$ if, for any continuous map $f : {\Bbb R}\times E \to E$, the equation $\dot x(t) = f (t, x(t))$ has a solution on some interval. We construct an example (answering a question posed by S. G. Lobanov) of a Hausdorff locally convex topological vector space E for which the weak version of Peano theorem holds and the Peano theorem fails to hold. We also construct a Hausdorff locally convex topological vector space E for which the Peano theorem holds and any barrel in E is neither compact nor sequentially compact.

Advanced glycation end product (AGE) accumulation on Bruch's membrane: links to age-related RPE dysfunction.

PURPOSE: Advanced glycation end products (AGEs) accumulate during aging and have been observed in postmortem eyes within the retinal pigment epithelium (RPE), Bruch's membrane, and subcellular deposits (drusen). AGEs have been associated with age-related dysfunction of the RPE-in particular with development and progression to age-related macular degeneration (AMD). In the present study the impact of AGEs at the RPE-Bruch's membrane interface was evaluated, to establish how these modifications may contribute to age-related disease. METHODS: AGEs on Bruch's membrane were evaluated using immunohistochemistry. A clinically relevant in vitro model of substrate AGE accumulation was established to mimic Bruch's membrane ageing. Responses of ARPE-19 growing on AGE-modified basement membrane (AGE-BM) for 1 month were investigated by using a microarray approach and validated by quantitative (q)RT-PCR. In addition to identified AGE-related mRNA alterations, lysosomal enzyme activity and lipofuscin accumulation were also studied in ARPE-19 grown on AGE-BM. RESULTS: Autofluorescent and glycolaldehyde-derived AGEs were observed in clinical specimens on Bruch's membrane and choroidal extracellular matrix. In vitro analysis identified a range of dysregulated mRNAs in ARPE-19 exposed to AGE-BM. Altered ARPE-19 degradative enzyme mRNA expression was observed on exposure to AGE-BM. AGE-BM caused a significant reduction in cathepsin-D activity in ARPE-19 (P

Capital substitutability and weak sustainability revisited: The conditions for capital substitution in the presence of risk

The capital approach is frequently used to model sustainability. A development is deemed to be sustainable when capital is not reduced. There are different definitions of sustainability, based on whether or not they allow that different forms of capital may be substituted for each other. A development that allows for the substitution of different forms of capital is called weakly sustainable. This article shows that in a risky world and a risk-averse society even under the assumptions of weak sustainability the circumstances under which different forms of capital may be substituted are limited. This is due to the risk-reducing effect of diversification. Using Modern Portfolio Theory this article shows under which conditions substitution of different forms of capital increases risk for future generations.

The role of the supply chain in developing a 'lagging' region's manufacturing industry. How important are links with suppliers and customers?

This paper investigates the use of supply chains as a source of knowledge transfer to manufacturing businesses in South Yorkshire and the effect this can have on improving economic performance. It also looks at where assistance originates from, what factors influence who gets the assistance, and what the benefits are.

On the weak amenability of β(X)

We investigate the weak amenability of the Banach algebra ß(X) of all bounded linear operators on a Banach space X. Sufficient conditions are given for weak amenability of this and other Banach operator algebras with bounded one-sided approximate identities.

How community ecology links natural mortality, growth, and production of fish populations

Size-spectrum theory is used to show that (i) predation mortality is a decreasing function of individual size and proportional to the consumption rate of predators; (ii) adult natural mortality M is proportional to the von Bertalanffy growth constant K; and (iii) productivity rate P/B is proportional to the asymptotic weight W8 -1/3. The constants of proportionality are specified using individual level parameters related to physiology or prey encounter. The derivations demonstrate how traditional fisheries theory can be connected to community ecology. Implications for the use of models for ecosystem-based fisheries management are discussed.

Netwar Geopolitics: Security, Failed States and Illicit Flows

Recent and emerging security policies and practices claim a mutual vulnerability that closely links human insecurity in failed states with the threat to powerful states from illicit flows. This article first examines this ‘emerging orthodoxy’ of transnational security issues that reinforces the securitisation of poverty and the poor. It then subjects this orthodoxy to theoretical and empirical critique. Theoretically it shows that this orthodoxy is formed as a ‘geopolitical imagination’ that associates and stabilises particular views of weak states and illicit flows in a ‘netwar imagination’ by reasserting and reconfiguring traditional assumptions of the spatiality and nature of threats. A final empirical section, focusing on drug production and nuclear smuggling, argues that those assumptions and their assemblage are a partial, incomplete and often self-referential reading of illicit flows.

The effect of teachers trained in a fundamental movement skills programme on children’s self-perceptions and motor competence

Perceived and actual motor competence are hypothesized to have potential links to children and young people’s physical activity (PA) levels with a potential consequential link to long-term health. In this cross-sectional study, Harter’s (1985, Manual for the Self-perception Profile for Children. Denver, CO: University of Denver) Competency Motivation-based framework was used to explore whether a group of children taught, during curriculum time, by teachers trained in the Fundamental Movement Skills (FMS) programme, scored higher on self-perception and on core motor competencies when compared to children whose teachers had not been so trained. One hundred and seventy seven children aged 7–8 years participated in the study. One hundred and seven were taught by FMS-trained teachers (FMS) and the remaining 70 were taught by teachers not trained in the programme (non-FMS). The Harter Self-Perception Profile for Children assessed athletic competence, scholastic competence, global self-worth and social acceptance. Three core components of motor competence (body management, object control and locomotor skills) were assessed via child observation. The FMS group scored higher on all the self-perception domains (p < 0.05). Statistically significant differences were found between the schools on all of the motor tasks (p < 0.05). The relationships between motor performance and self-perception were generally weak and non-significant. Future research in schools and with teachers should explore the FMS programme’s effect on children’s motor competence via a longitudinal approach.

Effect of weak hydrogen bonding and included solvent on the crystal structure of the square-planar complex trans-Pt{PPh2(C16H15)}(2)Cl-2

Crystallisation of the square-planar complex trans-Pt{PPh2(C16H15)}(2)Cl-2 from dichloromethane-diethyl ether (1:1) affords two different solvates; trans-Pt{PPh2(C16H15)}(2)Cl-2. CH2Cl2 1 and trans-Pt{PPh2(C16H15)}(2)Cl-2. Et2O 2; the CH2Cl2 forms H-bonding interactions with the complex whereas the Et2O participates only in weak van der Waals interactions; these differences arise from the different hydrogen-bonding characteristics of each solvent.

A high C/O ratio and weak thermal inversion in the atmosphere of exoplanet WASP-12b

The carbon-to-oxygen ratio (C/O) in a planet provides critical information about its primordial origins and subsequent evolution. A primordial C/O greater than 0.8 causes a carbide-dominated interior, as opposed to the silicate-dominated composition found on Earth; the atmosphere can also differ from those in the Solar System. The solar C/O is 0.54 (ref. 3). Here we report an analysis of dayside multi-wavelength photometry of the transiting hot-Jupiter WASP-12b (ref. 6) that reveals C/O>=1 in its atmosphere. The atmosphere is abundant in CO. It is depleted in water vapour and enhanced in methane, each by more than two orders of magnitude compared to a solar-abundance chemical-equilibrium model at the expected temperatures. We also find that the extremely irradiated atmosphere (T>2,500K) of WASP-12b lacks a prominent thermal inversion (or stratosphere) and has very efficient day-night energy circulation. The absence of a strong thermal inversion is in stark contrast to theoretical predictions for the most highly irradiated hot-Jupiter atmospheres.