Regularity and relaxed problems of minimizing biharmonic maps into spheres

For n >= 5 and k >= 4, we show that any minimizing biharmonic map from Omega subset of R-n to S-k is smooth off a closed set whose Hausdorff dimension is at most n - 5. When n = 5 and k = 4, for a parameter lambda is an element of [0, 1] we introduce lambda-relaxed energy H-lambda of the Hessian energy for maps in W-2,W-2 (Omega; S-4) so that each minimizer u(lambda) of H-lambda is also a biharmonic map. We also establish the existence and partial regularity of a minimizer of H-lambda for lambda is an element of [0, 1).

Equivalence of the Peleg, Pilosof and Singh-Kulshrestha models for water absorption in food

The similarity between the Peleg, Pilosof –Boquet–Batholomai and Singh–Kulshrestha models was investigated using the hydration behaviours of whey protein concentrate, wheat starch and whey protein isolate at 30 °C in 100% relative humidity. The three models were shown to be mathematically the same within experimental variations, and they yielded parameters that are related. The models, in their linear and original forms, were suitable (r2 > 0.98) in describing the sorption behaviours of the samples, and are sensitive to the length of the sorption segment used in the computation. The whey proteins absorbed more moisture than the wheat starch, and the isolate exhibited a higher sorptive ability than the concentrate.

An evolutionary framework for studies of hibernation and short-term torpor

Data from diverse studies endorse ideas that short term torpor and hibernation are expressions of ancient characters. In evolutionary terms, their basic mechanisms are probably plesiomorphic (= ancestral/primitive) and physiologically similar. This contrasts with the alternate view that they are apomorphic (= derived, specialized), arising independently in many taxa from homeothermic ancestry by numerous apparent convergences. This paper explores some of the implications of accepting the plesiomorphic interpretation. Hibernation is, of course, a complex phenomenon that has undergone variations and refinements in different mammalian lineages. The argument is not that hibernation in total is a plesiomorphic character, but that it is built upon fundamental processes that are. Taking this view provides a framework for research that emphasizes the value of comparative studies, particularly of reptiles and birds. Studies of reptiles, for example, might unravel the mystery about periodic arousals. A plesiomorphic framework also explains the most extreme examples of hibernation as derived specializations from ancestry in which heterothermy is more about energy management than escape from cold. It cautions against using low body temperature (Tb) alone to diagnose torpor, emphasizes the need to distinguish between constitutional eurythermy (plesiomorphic) and constitutional stenothermy (apomorphic), and leads to a parsimonious theory about the evolution of endothermy. The paper proposes that brown adipose tissue (BAT) is apomorphic within eutheria and highlights the conundrum posed by the occurrence of both nonshivering thermogenesis (NST) and rapid arousal from hibernation in noneutherian mammals that lack BAT and uncoupling protein 1 (UCP1). It endorses the likely existence of a different, ancient and widespread mechanism for regulatory NST in mammals.

Relations between physiologic parameters and pulse transit time during loaded breathing

Pulse transit time (PTT) is a non-invasive measure, defined as time taken for the pulse pressure waves to travel from the R-wave of electrocardiogram to a selected peripheral site. Baseline PTT value is known to be influenced by physiologic variables like heart rate (HR), blood pressure (BP) and arterial compliance (AC). However, few quantitative data are available describing the factors which can influence PTT measurements in a child during breathing. The aim of this study was to investigate the effects of changes in breathing efforts on PTT baseline and fluctuations. Two different inspiratory resistive loading (IRL) devices were used to simulate loaded breathing in order to induce these effects. It is known that HR can influence the normative PTT value however the effect of HR variability (HRV) is not well-studied. Two groups of 3 healthy children ( 0.05) HR changes during all test activities. Results showed that HRV is not the sole contributor to PTT variations and suggest that changes in other physiologic parameters are also equally important. Hence, monitoring PTT measurement can be indicative of these associated changes during tidal or increased breathing efforts in healthy children.

Partial regularity of weak solutions of the liquid crystal equilibrium system

For a parameter, we consider the modified relaxed energy of the liquid crystal system. Each minimizer of the modified relaxed energy is a weak solution to the liquid crystal equilibrium system. We prove the partial regularity of minimizers of the modified relaxed energy. We also prove the existence of infinitely many weak solutions for the special boundary value x.

Positive solutions of a Neumann problem with competing critical nonlinearities

We present existence results for a Neumann problem involving critical Sobolev nonlinearities both on the right hand side of the equation and at the boundary condition.. Positive solutions are obtained through constrained minimization on the Nehari manifold. Our approach is based on the concentration 'compactness principle of P. L. Lions and M. Struwe.

Brisbane Airport: An alluvial landscape veiled by marine sediments

At Brisbane Airport, the construction of a diversion channel for Kedron Brook exposed a former beach, low cliff and sand spit, which, with their associated sediments and acid sulfate soils, demonstrate a postglacial high sea-level 1.3 - 1.4 m above present mean sea-level. The beach appears to date from 4000 to 5000 y BP. It varies in level where it lies above soft ground; these variations, and sag depressions that follow buried streamlines, indicate sediment consolidation since withdrawal of the sea from the former shore. Most of the area consists of former estuarine deposits, mangrove and saline marshes, and stranded tidal flats on which acid sulfate soils are widely developed. The modern landforms mostly reproduce subsurface features, to the extent that the surface relief replicates the landscape transgressed by the sea 7000 years ago. A small rise of sea-level possibly to +0.65 m occurred about 2000-3000 years ago. Foredunes near the present shore that are related to a slightly lower level 1000 - 500 years ago (-0.25 m) are currently subject to wave erosion.

Robustness of mathematical models for biological systems

The robustness of mathematical models for biological systems is studied by sensitivity analysis and stochastic simulations. Using a neural network model with three genes as the test problem, we study robustness properties of synthesis and degradation processes. For single parameter robustness, sensitivity analysis techniques are applied for studying parameter variations and stochastic simulations are used for investigating the impact of external noise. Results of sensitivity analysis are consistent with those obtained by stochastic simulations. Stochastic models with external noise can be used for studying the robustness not only to external noise but also to parameter variations. For external noise we also use stochastic models to study the robustness of the function of each gene and that of the system.

Probabilistic cost benefit analysis of generation investment in a deregulated electricity market

A new methodology is proposed for the analysis of generation capacity investment in a deregulated market environment. This methodology proposes to make the investment appraisal using a probabilistic framework. The probabilistic production simulation (PPC) algorithm is used to compute the expected energy generated, taking into account system load variations and plant forced outage rates, while the Monte Carlo approach has been applied to model the electricity price variability seen in a realistic network. The model is able to capture the price and hence the profitability uncertainties for generator companies. Seasonal variation in the electricity prices and the system demand are independently modeled. The method is validated on IEEE RTS system, augmented with realistic market and plant data, by using it to compare the financial viability of several generator investments applying either conventional or directly connected generator (powerformer) technologies. The significance of the results is assessed using several financial risk measures.