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]

Thermal behavior of cellulose acetate produced from homogeneous acetylation of bacterial cellulose

Cellulose acetate (CA) is one of the most important cellulose derivatives and its main applications are its use in membranes, films, fibers, plastics and filters. CAs are produced from cellulose sources such as: cotton, sugar cane bagasse, wood and others. One promissory source of cellulose is bacterial cellulose (BC). In this work, CA was produced from the homogeneous acetylation reaction of bacterial cellulose. Degree of substitution (DS) values can be controlled by the acetylation time. The characterization of CA samples showed the formation of a heterogeneous structure for CA samples submitted to a short acetylation time. A more homogeneous structure was produced for samples prepared with a long acetylation time. This fact changes the thermal behavior of the CA samples. Thermal characterization revealed that samples submitted to longer acetylation times display higher crystallinity and thermal stability than samples submitted to a short acetylation time. The observation of these characteristics is important for the production of cellulose acetate from this alternative source. (C) 2008 Elsevier B.V. All rights reserved.

Environmental heterogeneity: Anuran diversity in homogeneous environments

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Anatomia comparada dos limbos cotiledonares e eofilares de dez espécies de Caesalpinioideae (Fabaceae)

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Determination of a point sufficiently close to the asymptote in nonlinear growth functions

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Time-dependent effects of lead on rat reproductive functions

The effects of exposure to lead on endocrine function and the reproductive parameters were studied in pubertal rats treated with 1.0 g l(-1) lead acetate in drinking water for 20 days (subacute group) or 9 months (chronic group) in addition to i.v. injections of lead acetate (0.1 mg 100 g(-1) body wt.) every 10 (subacute group) or 15 days (chronic group). Although basal levels of testosterone were higher both in plasma and in testes of acutely intoxicated animals, the circulating levels of luteinizing hormone (LH) were not affected in either group, nor was the LH-releasing hormone content of the median eminence. The density of [I-125]LH/human chorionic gonadotrophin (hCG) binding sites in testicular homogenates was reduced by saturnism in both groups, concomitant with a significantly increased apparent affinity constant of the hormone-receptor complex. These data can be viewed as the result of a mixture of specific lead toxicity (e.g. at the enzyme level) with other more general actions (e.g. at the level of the hypothalamus-pituitary-testicular axis).

Characterization and catalytic activity of iron(III) mono(4-N-methyl pyridyl)-tris(halophenyl) porphyrins in homogeneous and heterogeneous systems

The synthesis, characterization and catalytic activity of the cationic iron porphyrins Fe[M(4-N-MePy)TDCPP]Cl-2 and Fe[M(4-N-MePy)TFPP]Cl-2 in the epoxidation of (Z)-cyclooctene by PhIO in homogeneous solution and supported on silica gel (SG), imidazole propyl gel (IPG) or SG modified with 2-(4-sulfonatophenyl)ethyl groups (SiSO3) have been accomplished. When supported on IPG, both cationic FeP bind to the support via Fe-imidazole coordination. Fe[M(4-N-MePy)TDCPP]IPG contains a mixture of low-spin bis-coordinated (FeP)-P-III and high-spin mono-coordinated (FeP)-P-III species, whereas Fe[M(4-N-MePy)TFPP]IPG only contains high-spin mono-coordinated (FeP)-P-III. These FePIPG catalysts also contain (FeP)-P-II species, whose presence was confirmed by EPR spectroscopy using NO as a paramagnetic probe. Both cationic FePs coordinate to SG through Fe-O ligation and they are present as high-spin (FeP)-P-III species. The cationic FePs supported on SiSO3- are also high-spin (FeP)-P-III species and they bind to the support via electrostatic interaction between the 4-N-methylpyridyl groups and the SO3- groups present on the matrix. In homogeneous solution, both Fe[M(4-N-MePy)TDCPP]Cl-2 and Fe[M(4-N-MePy)TFPP]Cl-2 have similar catalytic activity to Fe(TDCPP)Cl and Fe(TFPP)Cl, leading to cis-epoxycyclooctane yields of 92%. When supported on inorganic matrices,both FePs lead to epoxide yields comparable to their homogeneous analogues and their anchoring enables catalyst recovery and re-use. Recycling of Fe[M(4-N-MePy)TDCPP]SiSO3- shows that this FeP maintains its activity in a second reaction. (C) 1999 Elsevier B.V. B.V. All rights reserved.

CLASSICAL DISTRIBUTION-FUNCTIONS DERIVED FROM WIGNER DISTRIBUTION-FUNCTIONS

A mapping which relates the Wigner phase-space distribution function associated with a given stationary quantum-mechanical wavefunction to a specific solution of the time-independent Liouville transport equation is obtained. Two examples are studied.

Feedforward neural networks based on PPS-wavelet activation functions

Function approximation is a very important task in environments where computation has to be based on extracting information from data samples in real world processes. Neural networks and wavenets have been recently seen as attractive tools for developing efficient solutions for many real world problems in function approximation. In this paper, it is shown how feedforward neural networks can be built using a different type of activation function referred to as the PPS-wavelet. An algorithm is presented to generate a family of PPS-wavelets that can be used to efficiently construct feedforward networks for function approximation.

Green functions of the Dirac equation with magnetic-solenoid field

Various Green functions of the Dirac equation with a magnetic-solenoid field (the superposition of the Aharonov-Bohm field and a collinear uniform magnetic field) are constructed and studied. The problem is considered in 2+1 and 3+1 dimensions for the natural extension of the Dirac operator (the extension obtained from the solenoid regularization). Representations of the Green functions as proper time integrals are derived. The nonrelativistic limit is considered. For the sake of completeness the Green functions of the Klein-Gordon particles are constructed as well. (C) 2004 American Institute of Physics.

Psychophysical power functions for estimates of area: Effects of age and educational levels

The purpose of the present study was to verify the memory exponents of power function for area in observers of different age and educational levels (elementary school, high school or undergraduate school), using the psychophysics method of magnitude estimation. For the age level I (17 to 30 years old) there was no difference among educational levels, although for the age level II (45 to 60 years old) the differences were significant. Tn the age level II, there was a tendency for greater variability of the responses for lower educational levels. The data obtained for the age level I did not show the same results, although a significant difference among the three educational levels was observed. We call conclude that the mnemonic processes present different results when we observe the answers from observers with different ages. This result leads us to suppose that the motivational factor related to the stimulus used can interact with the mnemonic processes.

Characterization of the porosity developed in a new titania-alumina catalyst support prepared by the sol gel route

Titanium oxide (TiO2) is a good candidate for support of hydrotreating catalysts but has the disadvantage of presenting a low surface area and a poor thermal stability when compared with Al2O3. A mixed TiO2-Al2O3 support was proposed as an alternative that is expected to be free from these drawbacks. The variation during firing of the nanoporous texture of supports composed of TiO2-Al2O3, TiO2 and Al2O3 was studied by small angle X-ray scattering (SAXS). The supports were prepared by the sol-gel route using Ti and Al isopropoxides. We have particularly analyzed the effects of acid and basic hydrolysis on the nanostructural features of catalyst supports fired at different temperatures. The nanopore radius distribution functions were determined from SAXS results assuming a simple model of spherical nanopores embedded in a homogeneous solid matrix. The modal pore radius in both pure TiO2 and pure Al2O3 supports grows from 1.3 to 2.2 nm as the firing temperature increases from 673 to 973 K. on the other hand, the modal pore radius in the mixed TiO2-Al2O3 support remains below 1.2 nm over the same range of firing temperatures. These results demonstrate the good thermal stability of the nanoporous texture of mixed TiO2-Al2O3 supports.

Polar Multiplicities and Euler obstruction of the stable types in weighted homogeneous map germs from C-n to C-3 n >= 3

In this article we show that for corank 1, quasi-homogeneous and finitely determined map germs f : (C-n, 0)-> (C-3, 0), n >= 3 one can obtain formulae for the polar multiplicities defined on the following stable types of f, f(Delta(f) and f(Sigma(n-2,1)(f), in terms of the weights and degrees of f. As a consequence we show how to compute the Euler obstruction of such stable types, also in terms of the weights and degrees of f.

Manganese(III) porphyrins: Catalytic activity and intermediate studies in homogeneous systems

We studied how solvent, stirring method, PhIO/MnP molar ratio, presence of water and axial ligand affect the catalytic activities of Mn(TPP)Cl, Mn(MNPP)Cl, Mn(TDCPP)Cl and Mn(TFPP)Cl in the oxidation of cyclohexane by PhIO. A study of the catalytic intermediates in the reaction between Mn(TPP)Cl or Mn(TDCPP)Cl and PhIO was also carried out by UV-Vis and EPR spectroscopies. The reaction of Mn(TPP)Cl with PhIO showed the formation of a mixture of species Mn-IV(OP+ and Mn-V(O)P as intermediates, which were confirmed by the deconvolution of the UV-Vis spectra. Addition of imidazole as cocatalyst favoured the formation of the intermediate species Mn-V(O)P, evidenced by the UV-Vis band at 408 nm. The corresponding EPR spectra gave evidence that in the presence of imidazole, Mn-IV(OP+ species are formed only in very low amounts. For Mn(TDCPP)Cl the dominating intermediate species is Mn-IV(OP+. Addition of imidazole to halogen-substituted MnP systems does not result in increase of the C-ol yields because very stable bis-imidazole-MnP complexes are formed. Anchoring of such MnP on imidazole propyl gel (IPG) results in better catalytic activity because in this case, the catalyst is mono-coordinated to the support and imidazole favours the formation of the intermediate species Mn-V(O)P.