Strongly damped wave problems: Bootstrapping and regularity of solutions

The aim of the article is to present a unified approach to the existence, uniqueness and regularity of solutions to problems belonging to a class of second order in time semilinear partial differential equations in Banach spaces. Our results are applied next to a number of examples appearing in literature, which fall into the class of strongly damped semilinear wave equations. The present work essentially extends the results on the existence and regularity of solutions to such problems. Previously, these problems have been considered mostly within the Hilbert space setting and with the main part operators being selfadjoint. In this article we present a more general approach, involving sectorial operators in reflexive Banach spaces. (C) 2008 Elsevier Inc. All rights reserved.

Regularity of solutions on the global attractor for a semilinear damped wave equation

We consider attractors A(eta), eta epsilon [0, 1], corresponding to a singularly perturbed damped wave equation u(tt) + 2 eta A(1/2)u(t) + au(t) + Au = f (u) in H-0(1)(Omega) x L-2 (Omega), where Omega is a bounded smooth domain in R-3. For dissipative nonlinearity f epsilon C-2(R, R) satisfying vertical bar f ``(s)vertical bar <= c(1 + vertical bar s vertical bar) with some c > 0, we prove that the family of attractors {A(eta), eta >= 0} is upper semicontinuous at eta = 0 in H1+s (Omega) x H-s (Omega) for any s epsilon (0, 1). For dissipative f epsilon C-3 (R, R) satisfying lim(vertical bar s vertical bar) (->) (infinity) f ``(s)/s = 0 we prove that the attractor A(0) for the damped wave equation u(tt) + au(t) + Au = f (u) (case eta = 0) is bounded in H-4(Omega) x H-3(Omega) and thus is compact in the Holder spaces C2+mu ((Omega) over bar) x C1+mu((Omega) over bar) for every mu epsilon (0, 1/2). As a consequence of the uniform bounds we obtain that the family of attractors {A(eta), eta epsilon [0, 1]} is upper and lower semicontinuous in C2+mu ((Omega) over bar) x C1+mu ((Omega) over bar) for every mu epsilon (0, 1/2). (c) 2007 Elsevier Inc. All rights reserved.

Global analytic regularity for structures of co-rank one

We consider real analytic involutive structures V, of co-rank one, defined on a real analytic paracompact orientable manifold M. To each such structure we associate certain connected subsets of M which we call the level sets of V. We prove that analytic regularity propagates along them. With a further assumption on the level sets of V we characterize the global analytic hypoellipticity of a differential operator naturally associated to V. As an application we study a case of tube structures.

Weak hypergraph regularity and linear hypergraphs

We consider conditions which allow the embedding of linear hypergraphs of fixed size. In particular, we prove that any k-uniform hypergraph H of positive uniform density contains all linear k-uniform hypergraphs of a given size. More precisely, we show that for all integers l >= k >= 2 and every d > 0 there exists Q > 0 for which the following holds: if His a sufficiently large k-uniform hypergraph with the property that the density of H induced on every vertex subset of size on is at least d, then H contains every linear k-uniform hypergraph F with l vertices. The main ingredient in the proof of this result is a counting lemma for linear hypergraphs, which establishes that the straightforward extension of graph epsilon-regularity to hypergraphs suffices for counting linear hypergraphs. We also consider some related problems. (C) 2009 Elsevier Inc. All rights reserved.

On the manifold structure of the set of unparameterized embeddings with low regularity

Given manifolds M and N, with M compact, we study the geometrical structure of the space of embeddings of M into N, having less regularity than C(infinity) quotiented by the group of diffeomorphisms of M.

Approach combining on-line metal exchange and tangential-flow ultrafiltration for in-situ characterization of metal species in humic hydrocolloids

This paper deals with the development and optimization of an analytical procedure using ultrafiltration and a flow-injection system, and its application in in-situ experiments to characterize the lability and availability of metal species in humic-rich hydrocolloids. The on-line system consists of a tangential flow ultrafiltration device equipped with a 3-kDa filtration membrane. The concentration of free ions in the filtrate was determined by atomic-absorption spectrometry, assuming that metals not complexed by aquatic humic substances (AHS) were separated from the complexed species (M-AHS) retained by the membrane. For optimization, exchange experiments using Cu(II) solutions and AHS solutions doped with the metal ions Ni(II), Mn(II), Fe(III), Cd (II), and Zn(II) were carried out to characterize the stability of the metal-AHS complexes. The new procedure was then applied in-situ at a tributary of the Ribeira do Iguape river (Iguape, São Paulo State, Brazil) and evaluated using the ions Fe(III) and Mn(II), which are considered to be essential constituents of aquatic systems. From the exchange between metal-natural organic matter (M-NOM) and the Cu(II) ions it was concluded that Cu(II) concentrations > 485 mu g L(-1) were necessary to obtain maximum exchange of the complexes Mn-NOM and Fe-NOM, corresponding to 100% Mn and 8% Fe. Moreover, the new analytical procedure is simple and opens up new perspectives for understanding the complexation, transport, stability, and lability of metal species in humic-rich aquatic environments.

Tangential microfiltration of orange juice in bench pilot

O objetivo deste trabalho foi introduzir a técnica de microfiltração tangencial (MFT) na produção de suco de laranja. O suco microfiltrado (SMFT) foi comparado química e sensorialmente com um suco pasteurizado (testemunha). Utilizou-se um piloto de MFT munido de quatro membranas (0,1, 0,2, 0,8 e 1,4mm) cerâmicas monotubulares dispostas em série, cada uma delas com superfície de 0,005m². Suco de laranja comercial flash pasteurizado foi usado como produto inicial. O trabalho experimental foi dividido em três fases: a) caracterização do piloto de MFT; b) otimização das condições operacionais; c) produção do SMFT. Na fase de otimização, a membrana de 0,8mm apresentou os melhores fluxos de permeado, seguidas pelas de 1,4, 0,1 e 0,2mm. Para garantir a esterilidade do permeado, a membrana de 0,1mm foi escolhida para a terceira fase do trabalho. Na produção do SMFT, o suco de laranja foi peneirado para separar uma parte de sua polpa, sendo em seguida microfiltrado. Depois, a polpa foi misturada ao retentato e a mistura pasteurizada. O SMFT foi obtido adicionando a mistura pasteurizada ao permeado. O SMFT apresentou teor de sólidos solúveis (°Brix), polpa, pH e acidez titulável semelhante ao suco inicial pasteurizado (testemunha); embora, tenha perdido maior quantidade (28%) de vitamina C. de acordo com os provadores do painel, o suco testemunha apresentou melhores características sensoriais em relação ao SMFT, por apresentar maior intensidade de odor e sabor frutoso.

Demulsification of water/sunflower oil emulsions by a tangential filtration process using chemically impregnated ceramic tubes

A tangential filtration process was implemented in this study using porous ceramic tubes made of alpha-alumina produced by the slip-casting technique. These tubes were sintered at 1450 degrees C and characterized by mercury intrusion porosimetry, which revealed a mean pore size of 0.5 mu m. The tubes were chemically impregnated with a zirconium citrate solution, after which they were calcined and heat treated at temperatures of up to 600 and 900 degrees C to eliminate volatile organic compounds and transform the zirconium citrate into zirconium oxide impregnated in the alumina in the form of nanoparticle agglomerates. The microporous pipes were tested on a microfiltration hydraulic system to analyze their performance in the demulsification of sunflower oil and water mixtures. The fluid-dynamic parameters of Reynolds number and transmembrane pressure were varied in the process. The volume of permeate was analyzed by measuring the Total Organic Carbon concentration (TOC), which indicated 99% of oil phase retention. The emulsified mixture was characterized by optical microscopy, while the morphology and composition of the impregnated microporous tubes were analyzed by scanning electron microscopy (SEM). Quantification of the TOC values for the tube impregnated once at 600 degrees C showed the best demulsification performance, with the concentration on permeate smaller than 10 mg/L. The impregnated tube sintered once at 900 degrees C presented low carbon concentration (smaller than 20 mg/L), has the advantage of presenting the greatest trans-membrane flux in relation to the other microporous tube. (c) 2006 Elsevier B.V. All rights reserved.

Tangential-flow ultrafiltration: a versatile methodology for determination of complexation parameters in refractory organic matter from Brazilian water and soil samples

In this work the copper(II) complexation parameters of aquatic organic matter, aquatic and soil humic substances from Brazilian were determined using a new versatile approach based on a single-stage tangential-flow ultrafiltration (TF-UF) technique (cut-off 1 kDa) and sensitive atomic spectrometry methods. The results regarding the copper(II) complexation capacity and conditional stability constants obtained for humic materials were compared with those obtained using direct potentiometry with a copper-ion-selective electrode. The analytical procedure based on ultrafiltration is a good alternative to determine the complexation parameters in natural organic material from aquatic and soil systems. This approach presents additional advantages such as better sensibility, applicability for multi-element capability, and its possible to be used under natural conditions when compared with the traditional ion-selective electrode.

Use of diffusive gradients in thin films and tangential flow ultrafiltration for fractionation of Al(III) and Cu(II) in organic-rich river waters

Diffusive gradients in thin films (DGT) and tangential-flow ultrafiltration (TF-UF) were combined for fractionation of Al and Cu in river water containing high content of dissolved organic carbon. A procedure based on ultrafiltration data is proposed to determine diffusion coefficients of the analytes in water samples and model solutions containing both free metal (M) and complex (metal - humic substance). Aiming to evaluate the accuracy of the proposed approach, the DGT results were compared with those from a protocol for determination of labile Al and Cu based on solid phase extraction (SPE). Good agreement between data from DGT and SPE were attained for model solutions. For analysis of real organic-rich water samples, differences between DGT and SPE measurements were consistent with the time-scales of the techniques. The concentration of labile Al determined by DGT were lower than the total dissolved concentrations (determined by inductively coupled plasma mass spectrometry) and exceeded the ultrafiltered concentration, indicating that inorganic Al species (species small enough to pass through 1 kDa membrane) were minor species as compared with Al organic complexes. For both Al and Cu, there were species not measured by DGT as they are not sufficiently labile. (C) 2007 Elsevier B.V. All rights reserved.

On the regularity of the pressure field of relaxed solutions to Euler equations with variable density

In this paper we improve the regularity in time of the gradient of the pressure field in the solution of relaxed version of variational formulation proposed by V. I. Arnold and by Y. Brenier, for the incompressible Euler equations with variable density. We obtain that the pressure field is not only a measure, but a function in Lloc2((0,T);BVloc(D)) as an extension of the work of Ambrosio and Figalli (2008) in [1] to the variable density case. © 2013 Elsevier Ltd.

A note on permutation regularity

The existence of a small partition of a combinatorial structure into random-like subparts, a so-called regular partition, has proven to be very useful in the study of extremal problems, and has deep algorithmic consequences. The main result in this direction is the Szemeredi Regularity Lemma in graph theory. In this note, we are concerned with regularity in permutations: we show that every permutation of a sufficiently large set has a regular partition into a small number of intervals. This refines the partition given by Cooper (2006) [10], which required an additional non-interval exceptional class. We also introduce a distance between permutations that plays an important role in the study of convergence of a permutation sequence. (C) 2011 Elsevier B.V. All rights reserved.

Regularity at infinity of real mappings and a Morse-Sard theorem

We prove a new Morse-Sard-type theorem for the asymptotic critical values of semi-algebraic mappings and a new fibration theorem at infinity for C-2 mappings. We show the equivalence of three different types of regularity conditions which have been used in the literature in order to control the asymptotic behaviour of mappings. The central role of our picture is played by the p-regularity and its bridge toward the rho-regularity which implies topological triviality at infinity.