Asymptotic stability, concentration, and oscillation in harmonic map heat-flow, Landau-Lifshitz, and Schroedinger maps on R^2

We consider the Landau-Lifshitz equations of ferromagnetism (including the harmonic map heat-flow and Schroedinger flow as special cases) for degree m equivariant maps from R^2 to S^2. If m \geq 3, we prove that near-minimal energy solutions converge to a harmonic map as t goes to infinity (asymptotic stability), extending previous work down to degree m = 3. Due to slow spatial decay of the harmonic map components, a new approach is needed for m=3, involving (among other tools) a "normal form" for the parameter dynamics, and the 2D radial double-endpoint Strichartz estimate for Schroedinger operators with sufficiently repulsive potentials (which may be of some independent interest). When m=2 this asymptotic stability may fail: in the case of heat-flow with a further symmetry restriction, we show that more exotic asymptotics are possible, including infinite-time concentration (blow-up), and even "eternal oscillation".Comment: 34 page

On uniqueness of tangent cones for Einstein manifolds

We show that for any Ricci-flat manifold with Euclidean volume growth the tangent cone at infinity is unique if one tangent cone has a smooth cross-section. Similarly, for any noncollapsing limit of Einstein manifolds with uniformly bounded Einstein constants, we show that local tangent cones are unique if one tangent cone has a smooth cross-section

The harmonic map heat flow from surfaces

SIGLEAvailable from British Library Document Supply Centre-DSC:DXN011327 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

Characterisation of a human skin equivalent model to study the effects of ultraviolet B radiation on keratinocytes

The incidences of skin cancers resulting from chronic ultraviolet radiation (UVR) exposure are on the incline both in Australia and globally. Hence, the cellular and molecular pathways associated with UVR-induced photocarcinogenesis urgently need to be elucidated, in order to develop more robust preventative and treatment strategies against skin cancers. In vitro investigations into the effects of UVR (in particular the highly-mutagenic UVB wavelength) have, to date, mainly involved the use of cell culture and animal models. However, these models possess biological disparities to native skin, which to some extent have limited their relevance to the in vivo situation. To address this, we characterised a 3-dimensional, tissue-engineered human skin equivalent (HSE) model (consisting of primary human keratinocytes cultured on a dermal-derived scaffold) as a representation of a more physiologically-relevant platform to study keratinocyte responses to UVB. Significantly, we demonstrate that this model retains several important epidermal properties of native skin. Moreover, UVB-irradiation of the HSE constructs was shown to induce key markers of photodamage in the HSE keratinocytes, including the formation of cyclobutane pyrimidine dimers, the activation of apoptotic pathways, the accumulation of p53 and the secretion of inflammatory cytokines. Importantly, we also demonstrate that the UVB-exposed HSE constructs retain the capacity for epidermal repair and regeneration following photodamage. Together, our results demonstrate the potential of this skin equivalent model as a tool to study various aspects of the acute responses of human keratinocytes to UVB radiation damage

Avaliação do efeito de sopas desidratadas ricas em fibras na redução do colesteroal sangüíneo em ratos Evaluation of the cholesterol-lowering efect of high-fiber dehydrated soup in rats

Neste estudo foi avaliado o efeito de quatro formulações dietéticas ricas em fibra solúvel na redução de colesterol sangüíneo em ratos. As formulações foram preparadas com farinha de soja desengordurada, farelo de aveia, cebola desidratada, fibra de soja, condimentos e aromas. Duas das formulações continham feijão preto FP(+) e FP(-), nos níveis de 40 e 30%, respectivamente. As outras duas continham feijão vermelho FV(+) e FV(-), nesses mesmos teores. Foram utilizados seis grupos de oito ratos machos, com peso médio inicial de 200g. O grupo Padrão recebeu dieta basal. O grupo Controle recebeu dieta de composição semelhante à Padrão, porém, acrescida de 1% de colesterol cristalino e 0,1% de ácido cólico. As demais dietas foram semelhantes ao grupo Controle, substituídas pelas formulações FV(+), FP(+), FV(-) e FP(-), de modo a fornecerem 7,4% de fibra total da dieta. Ratos alimentados com dieta do grupo Controle apresentaram aumento significativo dos níveis de colesterol sérico, peso dos fígados, colesterol e lipídio total das fezes e dos fígados, em relação ao grupo recebendo dieta Padrão. As dietas FV(+), FP(+), FV(-) e FP(-), não diferiram entre si quanto ao efeito nos níveis de lipídios séricos e glicose, no peso e lipídio total dos fígados e no peso, umidade e nitrogênio das fezes. No entanto, reduziram significativamente os níveis sangüíneos de colesterol total em 29,0%, os níveis de HDL - colesterol em 34,0%, o peso dos fígados em 11,7% e o colesterol do fígado em 9,0% em relação à dieta Controle. As dietas de feijão vermelho proporcionaram maior redução de colesterol no fígado e maior excreção de lipídio e colesterol nas fezes comparadas com as de feijão preto.<br>The effect of 4 high fiber dietary formulas on reducing blood cholesterol levels in rats was evaluated in the present study. The products were formulated with defatted soy flour, oat bran, dehydrated onion, soy fiber and spices. Two of them contained black beans, FP(+) or FP(-), at 40 or 30%, respectively. The other two contained red beans, FV(+) or FV(-), at the same levels. Six groups of 8 male rats, with initial body weight of about 200g, were used. The Standard group received a basal diet. The Control group received a similar diet, but it was added 1% of cholesterol and 0.1% of cholic acid. The other diets were similar to the Control one, substituted for the formulas FV(+), FP(+), FV(-) and FP(-) to provide 7.4% of total dietary fiber. Rats fed on Control diet showed a significant increase in their blood cholesterol levels, liver weight and fecal and liver cholesterol and total lipid, in relation to the Standard group. There was no significant difference among the diets FV(+), FP(+), FV(-) and FP(-) in terms of blood levels of cholesterol, triglycerides and glucose, liver weight, liver total lipids, fecal weight and moisture and the output of nitrogen. All the formulas reduced blood cholesterol levels by 29%, HDL-cholesterol by 34%, liver weigth by 11.7% and liver cholesterol by 9%, in comparison with the Control diet. The diets containing red beans showed higher reductions of cholesterol in the rat liver and higheroutput of total lipids and cholesterol than the black bean diets