Supersolutions for a class of semilinear heat equations

A semilinear heat equation $u_{t}=\Delta u+f(u)$ with nonnegative initial data in a subset of $L^{1}(\Omega)$ is considered under the assumption that $f$ is nonnegative and nondecreasing and $\Omega\subseteq \R^{n}$. A simple technique for proving existence and regularity based on the existence of supersolutions is presented, then a method of construction of local and global supersolutions is proposed. This approach is applied to the model case $f(s)=s^{p}$, $\phi\in L^{q}(\Omega)$: new sufficient conditions for the existence of local and global classical solutions are derived in the critical and subcritical range of parameters. Some possible generalisations of the method to a broader class of equations are discussed.Comment: Expanded version of the previous submission arXiv:1111.0258v1. 14 page

Bridging the theory practice gap: an innovative approach to praxis in professional education

The notion of a ‘theorypractice gap’ in nursing has been the subject of debate for many years and is well documented in the nursing literature (Crane, 1991; Landers, 2000). McCaugherty (1991) explains the ‘gap’ using the symbolobject dichotomy as an analogy, that is the symbol such as a picture or an image is not the same as the actual object. Thus, what is taught in the classroom is not the same as that which is experienced in the clinical environment. Russell (1967) identifies the former as ‘knowledge by description’ and the latter, ‘knowledge by acquaintance’

Lie algebra computations

In the context of prolongation theory, introduced by Wahlquist and Estabrook, computations of a lot of Jacobi identities in (infinite-dimensional) Lie algebras are necessary. These computations can be done (automatically) using ‘symbolic computations’. A package written in REDUCE is demonstrated to give an idea of the chosen approach

Optical Brightener Study of Spruce Creek

Elevated bacteria levels in the Spruce Creek Watershed have led to shellfish bed closures in the Spruce Creek Estuary and impaired waters listings by the State of Maine. Since 2005, the Town of Kittery, Spruce Creek Association and numerous partners have assessed the local waters to attempt to determine the sources of bacteria impairment. Stormwater outfalls and residential septic systems have been identified as potential sources of impairment. To help address these concerns, the Town of Kittery received a grant in 2009 through the Piscataqua Region Estuaries Partnership to further investigate potential bacteria hotspots. Project staff worked with Federal, State and local partners to identify potential hotspots through targeted fecal coliform testing and testing and analysis for optical brighteners. Spring and autumn testing revealed elevated levels of bacteria which has led to immediate repair of a school septic system, and further assessment of a residential neighborhood

One Market, One Money, One Price?

The introduction of the euro was intended to integrate markets within Europe further, after the implementation of the 1992 Single Market Project. We examine the extent to which this objective has been achieved, by examining the degree of price dispersion between countries in the euro zone, compared to a control group of EU countries outside the euro zone. We also establish the role of exchange rate risk in hampering arbitrage by estimating the euro effect for subgroups within the euro zone, utilizing differences among EU countries in participation in the Exchange Rate Mechanism. Our results, in contrast with previous empirical research, suggest robustly that the euro has had a significant integrating effect.

Does skeletal muscle carnitine availability influence fuel selection during exercise?

This is the author accepted manuscript. The final version is available from Cambridge University Press via the DOI in this record.Fat and carbohydrate are the major fuel sources utilised for oxidative, mitochondrial ATP resynthesis during human skeletal muscle contraction. The relative contribution of these two substrates to ATP resynthesis and total energy expenditure during exercise can vary substantially, and is predominantly determined by fuel availability and exercise intensity and duration. For example, the increased ATP demand that occurs with an increase in exercise intensity is met by increases in both fat and carbohydrate oxidation up to an intensity of approximately 60–70 % of maximal oxygen consumption. When exercise intensity increases beyond this workload, skeletal muscle carbohydrate utilisation is accelerated, which results in a reduction and inhibition of the relative and absolute contribution of fat oxidation to total energy expenditure. However, the precise mechanisms regulating muscle fuel selection and underpinning the decline in fat oxidation remain unclear. This brief review will primarily address the theory that a carbohydrate flux-mediated reduction in the availability of muscle carnitine to the mitochondrial enzyme carnitine palmitoyltransferase 1, a rate-limiting step in mitochondrial fat translocation, is a key mechanism for the decline in fat oxidation during high-intensity exercise. This is discussed in relation to recent work in this area investigating fuel metabolism at various exercise intensities and taking advantage of the discovery that skeletal muscle carnitine content can be nutritionally increased in vivo in human subjects