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.

A non-autonomous strongly damped wave equation: Existence and continuity of the pullback attractor

In this paper we consider the strongly damped wave equation with time-dependent terms u(tt) - Delta u - gamma(t)Delta u(t) + beta(epsilon)(t)u(t) = f(u), in a bounded domain Omega subset of R(n), under some restrictions on beta(epsilon)(t), gamma(t) and growth restrictions on the nonlinear term f. The function beta(epsilon)(t) depends on a parameter epsilon, beta(epsilon)(t) -> 0. We will prove, under suitable assumptions, local and global well-posedness (using the uniform sectorial operators theory), the existence and regularity of pullback attractors {A(epsilon)(t) : t is an element of R}, uniform bounds for these pullback attractors, characterization of these pullback attractors and their upper and lower semicontinuity at epsilon = 0. (C) 2010 Elsevier Ltd. All rights reserved.

MULTIPLICITY OF POSITIVE SOLUTIONS FOR A CLASS OF NONLINEAR SCHRODINGER EQUATIONS

This paper proves the multiplicity of positive solutions for the following class of quasilinear problems: {-epsilon(p)Delta(p)u+(lambda A(x) + 1)vertical bar u vertical bar(p-2)u = f(u), R(N) u(x)>0 in R(N), where Delta(p) is the p-Laplacian operator, N > p >= 2, lambda and epsilon are positive parameters, A is a nonnegative continuous function and f is a continuous function with subcritical growth. Here, we use variational methods to get multiplicity of positive solutions involving the Lusternick-Schnirelman category of intA(-1)(0) for all sufficiently large lambda and small epsilon.

On the Multiplicity of Orthogonal Geodesics in Riemannian Manifold With Concave Boundary. Applications to Brake Orbits and Homoclinics

Let (M, g) be a complete Riemannian Manifold, Omega subset of M an open subset whose closure is diffeomorphic to an annulus. If partial derivative Omega is smooth and it satisfies a strong concavity assumption, then it is possible to prove that there are at least two geometrically distinct geodesics in (Omega) over bar = Omega boolean OR partial derivative Omega starting orthogonally to one connected component of partial derivative Omega and arriving orthogonally onto the other one. The results given in [6] allow to obtain a proof of the existence of two distinct homoclinic orbits for an autonomous Lagrangian system emanating from a nondegenerate maximum point of the potential energy, and a proof of the existence of two distinct brake orbits for a. class of Hamiltonian systems. Under a further symmetry assumption, it is possible to show the existence of at least dim(M) pairs of geometrically distinct geodesics as above, brake orbits and homoclinics.

Stability and interface properties of thin cellulose ester films adsorbed from acetone and ethyl acetate solutions

Stability and interface properties of cellulose acetate propionate (CAP) and cellulose acetate butyrate (CAB) films adsorbed from acetone or ethyl acetate onto Si wafers have been investigated by means of contact angle measurements and atomic force microscopy (AFM). Surface energy (gamma(total)(S)) values determined for CAP adsorbed from acetone are larger than those from ethyl acetate. In the case of CAB films adsorbed from ethyl acetate and acetone were similar. Dewetting was observed by AFM only for CAP films prepared from ethyl acetate. Positive values of effective Hamaker constant (A(eff)) were found only for CAP prepared from ethyl acetate, corroborating with dewetting phenomena observed by AFM. Oil the contrary, negative values of A(eff) were determined for CAP and CAB prepared from acetone and for CAB prepared from ethyl acetate, Corroborating with experimental observations. Sum frequency generation (SFG) vibrational spectra indicated that CAP and CAB films prepared from ethyl acetate present more alkyl groups oriented perpendicularly to the polymer-air interface than those films prepared from acetone. Such preferential orientation corroborates with macroscopic contact angle measurements. Moreover, SFG spectra showed that acetone hinds strongly to Si wafers, creating a new surface for CAP and CAB films. (C) 2008 Elsevier Inc. All rights reserved.

Surface Activity of the Triflate Ion at the Air/Water Interface and Properties of N,N,N-Trimethyl-N-Dodecylammonium Triflate Aqueous Solutions

The surface activity of salts added to water is Air orders of magnitude lower than that of surfactants. Sodium trifluoromethanesulfonate (NaTf) produced a change in surface tension. with concentration, Delta gamma/Delta c, of -13.2 mN.L/m.mol. This value is ca. 4-fold larger than those of simple salts and that of methanesulfonate. This unexpected surface effect suggested that positively charged micelles containing Tf could exhibit interesting properties. Dodecyltrimethylammonium triflate (DTATf) had a higher Kraft temperature (37 degrees C) and a lower cmc (5 x 10(-3)M) and degree of dissociation (0.11) than the chloride and bromide salts of DTA. Above the Kraft temperature, at a characteristic temperature t(1), the addition of NaTf above 0.05 M. to a DTATf solution induced phase separation. By increasing the temperature of the two-phase system to above t(1), a homogeneous, transparent solution was obtained at a characteristic temperature t(2). These results, together with well-known triflate properties, led us to suggest that the Tf ion pairs With DTA and that the -CF(3) group may be dehydrated in the interfacial region, resulting in new and interesting self-aggregated structures.

Characteristics of thin cellulose ester films spin-coated from acetone and ethyl acetate solutions

Spin-coated films of cellulose acetate (CA), cellulose acetate propionate (CAP), cellulose acetate butyrate (CAB) and carboxymethylcellulose acetate butyrate (CMCAB) have been characterized by ellipsometry, atomic force microscopy (AFM) and contact angle measurements. The films were spin-coated onto silicon wafers, a polar surface. Mean thickness values were determined by means of ellipsometry and AFM as a function of polymer concentration in solutions prepared either in acetone or in ethyl acetate (EA), both are good solvents for the cellulose esters. The results were discussed in the light of solvent evaporation rate and interaction energy between substrate and solvent. The effects of annealing and type of cellulose ester on film thickness, film morphology, surface roughness and surface wettability were also investigated.

Electrocombustion of humic acid and removal of algae from aqueous solutions

This paper reports experiments involving the electrochemical combustion of humic acid (HA) and removal of algae from pond water. An electrochemical flow reactor with a boron-doped diamond film anode was used and constant current experiments were conducted in batch recirculation mode. The mass transfer characteristics of the electrochemical device were determined by voltammetric experiments in the potential region of water stability, followed by a controlled current experiment in the potential region of oxygen evolution. The average mass transfer coefficient was 5.2 x 10(-5) m s(-1). The pond water was then processed to remove HA and algae in the conditions in which the reaction combustion occurred under mass transfer control. To this end, the mass transfer coefficient was used to estimate the initial limiting current density applied in the electrolytic experiments. As expected, all the parameters analyzed here-solution absorbance at 270 nm, total phenol concentration and total organic carbon concentration-decayed according to first-order kinetics. Since the diamond film anode successfully incinerated organic matter, the electrochemical system proved to be predictable and programmable.

Development and Evaluation of a Novel pH Indicator Biodegradable Film Based on Cassava Starch

A pH indicator film based on cassava starch plasticized with sucrose and inverted sugar and incorporated with grape and spinach extracts as pH indicator sources (anthocyanin and chlorophyll) has been developed, and its packaging properties have been assessed. A second-order central composite design (2(2)) with three central points and four star points was used to evaluate the mechanical properties (tensile strength, tensile strength at break, and elongation at break percentage), moisture barrier, and microstructure of the films, and its potential as a pH indicator packaging. The films were prepared by the casting technique and conditioned under controlled conditions (75% relative humidity and 23 degrees C), at least 4 days before the analyses. The materials were exposed to different pH solutions (0, 2, 7, 10, and 14) and their color parameters (L*, a*, b*, and haze) were measured by transmittance. Grape and spinach extracts have affected the material characterization. Film properties (mechanical properties and moisture barrier) were strongly influenced by extract concentration presenting lower results than for the control. Films containing a higher concentration of grape extract presented a greater color change at different pH`s suggesting that anthocyanins are more effective as pH indicators than chlorophyll or the mixture of both extracts. (C) 2010 Wiley Periodicals, Inc. J Appl Polym Sci 120: 1069-1079,2011

Palaeomagnetism, rock magnetism and AMS of the Cabo Magmatic Province, NE Brazil, and the opening of South Atlantic

P>Reconstruction of the South Atlantic opening has long been a matter of debate and several models have been proposed. One problem in tracing properly the Atlantic history arises from the existence of a long interval without geomagnetic reversals, the Cretaceous Normal Superchron, for which ages are difficult to assign. Palaeomagnetism may help in addressing this issue if high-quality palaeomagnetic poles are available for the two drifting continental blocks, and if precise absolute ages are available. In this work we have investigated the Cabo Magmatic Province, northeastern Brazil, recently dated at 102 +/- 1 Ma (zircon fission tracks, Ar39/Ar40). All volcanic and plutonic rocks showed stable thermal and AF demagnetization patterns, and exhibit primary magnetic signatures. AMS data also support a primary origin for the magnetic fabric and is interpreted to be contemporaneous of the rock formation. The obtained pole is located at 335.9 degrees E/87.9 degrees S (N = 24; A(95) = 2.5; K = 138) and satisfies modern quality criteria, resulting in a reference pole for South America at similar to 100 Ma. This new pole also gives an insight to test and discuss the kinematic models currently proposed for the South Atlantic opening during mid-Cretaceous.

Dipeptidyl peptidase IV in the hypothalamus and hippocampus of monosodium glutamate obese and food-deprived rats

Proline-specific dipeptidyl peptidases are emerging as a protease family with important roles in the regulation of signaling by peptide hormones related to energy balance. The treatment of neonatal rats with monosodium glutamate (MSG) is known to produce a selective damage on the arcuate nucleus with development of obesity. This study investigates the relationship among dipeptidyl peptidase IV (DPPIV) hydrolyzing activity, CD26 protein, fasting, and MSG model of obesity in 2 areas of the central nervous system. Dipeptidyl peptidase IV and CD26 were, respectively, evaluated by fluorometry, and enzyme-linked immunosorbent assay and reverse transcriptase polymerase chain reaction in soluble (SF) and membrane-bound (MF) fractions from the hypothalamus and hippocampus of MSG-treated and normal rats, submitted or not to food deprivation (FD). Dipeptidyl peptidase IV in both areas was distinguished kinetically as insensitive (DI) and sensitive (DS) to diprotin A. Compared with the controls, MSG and/or FD decreased the activity of DPPIV-DI in the SF and MF from the hypothalamus, as well as the activity of DPPIV-DS in the SF from the hypothalamus and in the MF from the hippocampus. Monosodium glutamate and/or FD increased the activity of DPPIV-DI in the MF from the hippocampus. The monoclonal protein expression of membrane CD26 by enzyme-linked immunosorbent assay decreased in the hypothalamus and increased in the hippocampus of MSG and/or FD relative to the controls. The existence of DPPIV-like activity with different sensitivities to diprotin A and the identity of insensitive with CD26 were demonstrated for the first time in the central nervous system. Data also demonstrated the involvement of DPPIV-DI/CD26 hydrolyzing activity in the energy balance probably through the regulation of neuropeptide Y and beta-endorphin levels in the hypothalamus and hippocampus. (C) 2011 Elsevier Inc. All rights reserved.

Immunocytochemical characterization of the pregeniculate nucleus and distribution of retinal and neuropeptide Y terminals in the suprachiasmatic nucleus of the Cebus monkey

Circadian rhythms generated by the suprachiasmatic nucleus (SCN) are modulated by photic and non-photic stimuli. In rodents, direct photic stimuli reach the SCN mainly through the retinohypothalamic tract (RHT), whereas indirect photic stimuli are mainly conveyed by the geniculohypothalamic tract (GHT). In rodents, retinal cells form a pathway that reaches the intergeniculate leaflet (IGL) where they establish synapses with neurons that express neuropeptide Y (NPY), hence forming the GHT projecting to the SCN. In contrast to the RHT, which has been well described in primates, data regarding the presence or absence of the IGL and GHT in primates are contradictory. Some studies have suggested that an area of the pregeniculate nucleus (PGN) of primates might be homologous to the IGL of rodents, but additional anatomical and functional studies on primate species are necessary to confirm this hypothesis. Therefore, this study investigated the main histochemical characteristics of the PGN and the possible existence of the GHT in the SCN of the primate Cebus, comparing the distribution of NPY immunoreactivity, serotonin (5-HT) immunoreactivity and retinal terminal fibers in these two structures. The results show that a collection of cell bodies containing NPY and serotonergic immunoreactivity and retinal innervations are present within a zone that might be homologous to the IGL of rodents. The SCN also receives dense retinal innervations and we observed an atypical distribution of NPY- and 5-HT-immunoreactive fibers without regionalization in the ventral part of the nucleus as described for other species. These data may reflect morphological differences in the structures involved in the regulation of circadian rhythms among species and support the hypothesis that the GHT is present in some higher primates (diurnal animals). (C) 2009 Elsevier B.V. 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.

UNIFORM DISSIPATIVENESS, ROBUST SYNCHRONIZATION AND LOCATION OF THE ATTRACTOR OF PARAMETRIZED NONAUTONOMOUS DISCRETE SYSTEMS

In this series of papers, we study issues related to the synchronization of two coupled chaotic discrete systems arising from secured communication. The first part deals with uniform dissipativeness with respect to parameter variation via the Liapunov direct method. We obtain uniform estimates of the global attractor for a general discrete nonautonomous system, that yields a uniform invariance principle in the autonomous case. The Liapunov function is allowed to have positive derivative along solutions of the system inside a bounded set, and this reduces substantially the difficulty of constructing a Liapunov function for a given system. In particular, we develop an approach that incorporates the classical Lagrange multiplier into the Liapunov function method to naturally extend those Liapunov functions from continuous dynamical system to their discretizations, so that the corresponding uniform dispativeness results are valid when the step size of the discretization is small. Applications to the discretized Lorenz system and the discretization of a time-periodic chaotic system are given to illustrate the general results. We also show how to obtain uniform estimation of attractors for parametrized linear stable systems with nonlinear perturbation.

Influence of heavy rare earth ions substitution on microstructure and magnetism of nanocrystalline magnetite

In this work we report results on the influence of heavy rare earth ions substitution on microstructure and magnetism of nanocrystalline magnetite. A series of Fe(2.85)RE(0.15)O(4) (RE = Gd, Dy, Ho, Tm and Yb) samples have been prepared by high energy ball milling. Structure/microstructure investigations of two selected samples Fe(2.85)Gd(0.15)O(4) and Fe(2.85)Tm(0.15)O(4), represent an extension of the previously published results on Fe(3)O(4)/gamma-Fe(2)O(3), Fe(2.85)Y(0.15)O(4) and Fe(2.55)In(0.45)O(4) [Z. Cvejic, S. Rakic, A. Kremenovic, B. Antic, C. Jovalekic. Ph. Colomban, Sol. State Sciences 8 (2006) 908], while magnetic characterization has been done for all the samples. Crystallite/particle size and strain determined by X-ray diffractometry and Transmission electron microscopy (TEM) confirmed the nanostructured nature of the mechanosynthesized materials. X-ray powder diffraction was used to analyze anisotropic line broadening effects through the Rietveld method. The size anisotropy was found to be small while strain anisotropy was large, indicating nonuniform distribution of deffects in the presence of Gd and Tm in the crystal structure. Superparamagnetic(SPM) behavior at room temperature was observed for all samples studied. The Y-substituted Fe(3)O(4) had the largest He and the lowest M(S). We discuss the changes in magnetic properties in relation to their magnetic anisotropy and microstructure. High field irreversibility (H>20kOe) in ZFC/FC magnetization versus temperature indicates the existence of high magnetocrystalline and/or strain induced anisotropy. (C) 2008 Elsevier B.V. All rights reserved.