Lower bounds on blow up solutions of the three-dimensional Navier-Stokes equations in homogeneous Sobolev spaces

Suppose that u(t) is a solution of the three-dimensional Navier-Stokes equations, either on the whole space or with periodic boundary conditions, that has a singularity at time T. In this paper we show that the norm of u(T - t) in the homogeneous Sobolev space (H)over dot(s) must be bounded below by c(s)t(-(2s-1)/4) for 1/2 < s < 5/2 (s not equal 3/2), where c(s) is an absolute constant depending only on s; and by c(s)parallel to u(0)parallel to((5-2s)/5)(L2)t(-2s/5) for s > 5/2. (The result for 1/2 < s < 3/2 follows from well-known lower bounds on blowup in Lp spaces.) We show in particular that the local existence time in (H)over dot(s)(R-3) depends only on the (H)over dot(s)-norm for 1/2 < s < 5/2, s not equal 3/2. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4762841]

Temporary fragmentation of a marginal lake and its effects on zooplankton community structure and organization

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Influência da variação do nível hidrométrico na comunidade fitoplanctônica do Rio Paranapanema e de uma lagoa marginal na zona de desembocadura na Represa de Jurumirim (SP)

Este estudo visou analisar os efeitos da variação do nível hidrométrico na estrutura do fitoplâncton do Rio Paranapanema e de uma lagoa marginal na zona de desembocadura no Reservatório de Jurumirim (SP). As amostragens foram realizadas em duas estações em cada ambiente de julho/2004 a julho/2005. Os maiores valores de riqueza e diversidade foram encontrados na estiagem, enquanto que as maiores densidade e biovolume foram registradas na cheia. A espécie Cryptomonas brasiliensis Castro, C. Bicudo & D. Bicudo (R - estrategista) foi constante ao longo de todo o estudo, sendo dominante, principalmente, no final da estiagem e na enchente, quando os eventos de distúrbios foram mais freqüentes. As diatomáceas foram predominantes quanto à biomassa, representadas, principalmente, por Aulacoseira granulata (Ehrenberg) Simonsem e suas variedades. Conclui-se que, o volume de água acumulada no reservatório à jusante não permite que o pulso hidrológico ocasione um distúrbio que resulte em elevado aumento da diversidade nos ambientes estudados, após a enchente.

Effect of the composite surface sealant application moment on marginal sealing of compactable composite resin restoration

An analysis was carried out to observe whether the application or not of a composite surface sealant (CSS), as well the moment for CSS application were able to reduce marginal microleakage in compactable composite resin restoration. All the preparations were restored with a compactable composite resin. The restored teeth were randomly assessed. G1 (control group): finished and polished; G2: finished, polished, etched and cover with CSS; G3: immediately after the restoration done the CSS was applied, then finished and polished; G4: CSS applied immediately after the restoration was done, the finished and polished, etched, and covered with CSS. The specimens were isolated with nail polish, thermocycled, immersed in aqueous solution of silver nitrate, and followed in a photo developing solution. The microleakage scores obtained from the occlusal and cervical walls were analyzed with the Kruskall-Wallis nonparametric test. No microleakage was found at the enamel margins. Comparing the microleakage scores at dentin/cementum margins (p < 0.05) it was found that G3 (p = 0.0162) and G4 (p = 0.0187) were able to reduce microleakage when compared with group G2. However the results were not statistically different from the control group. The application of CSS was not able to completely eliminate marginal microleakage at the dentin/cementum margins.

On the hardy space H¹ on products of half-spaces

We show that the Hardy space H¹ anal (R2+ x R2+) can be identified with the class of functions f such that f and all its double and partial Hubert transforms Hk f belong to L¹ (R2). A basic tool used in the proof is the bisubharmonicity of |F|q, where F is a vector field that satisfies a generalized conjugate system of Cauchy-Riemann type.