GLOBAL WELL-POSEDNESS AND NON-LINEAR STABILITY OF PERIODIC TRAVELING WAVES FOR A SCHRODINGER-BENJAMIN-ONO SYSTEM

The objective of this paper is two-fold: firstly, we develop a local and global (in time) well-posedness theory for a system describing the motion of two fluids with different densities under capillary-gravity waves in a deep water flow (namely, a Schrodinger-Benjamin-Ono system) for low-regularity initial data in both periodic and continuous cases; secondly, a family of new periodic traveling waves for the Schrodinger-Benjamin-Ono system is given: by fixing a minimal period we obtain, via the implicit function theorem, a smooth branch of periodic solutions bifurcating a Jacobian elliptic function called dnoidal, and, moreover, we prove that all these periodic traveling waves are nonlinearly stable by perturbations with the same wavelength.

LOCAL WELL POSEDNESS, ASYMPTOTIC BEHAVIOR AND ASYMPTOTIC BOOTSTRAPPING FOR A CLASS OF SEMILINEAR EVOLUTION EQUATIONS OF THE SECOND ORDER IN TIME

A class of semilinear evolution equations of the second order in time of the form u(tt)+Au+mu Au(t)+Au(tt) = f(u) is considered, where -A is the Dirichlet Laplacian, 92 is a smooth bounded domain in R(N) and f is an element of C(1) (R, R). A local well posedness result is proved in the Banach spaces W(0)(1,p)(Omega)xW(0)(1,P)(Omega) when f satisfies appropriate critical growth conditions. In the Hilbert setting, if f satisfies all additional dissipativeness condition, the nonlinear Semigroup of global solutions is shown to possess a gradient-like attractor. Existence and regularity of the global attractor are also investigated following the unified semigroup approach, bootstrapping and the interpolation-extrapolation techniques.

POSITIVITY PROPERTIES OF THE FOURIER TRANSFORM AND THE STABILITY OF PERIODIC TRAVELLING-WAVE SOLUTIONS

In this paper we establish a method to obtain the stability of periodic travelling-wave solutions for equations of Korteweg-de Vries-type u(t) + u(p)u(x) - Mu(x) = 0, with M being a general pseudodifferential operator and where p >= 1 is an integer. Our approach uses the theory of totally positive operators, the Poisson summation theorem, and the theory of Jacobi elliptic functions. In particular we obtain the stability of a family of periodic travelling waves solutions for the Benjamin Ono equation. The present technique gives a new way to obtain the existence and stability of cnoidal and dnoidal waves solutions associated with the Korteweg-de Vries and modified Korteweg-de Vries equations, respectively. The theory has prospects for the study of periodic travelling-wave solutions of other partial differential equations.

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.

Dynamics of the viscous Cahn-Hilliard equation

We study generalized viscous Cahn-Hilliard problems with nonlinearities satisfying critical growth conditions in W-0(1,p)(Omega), where Omega is a bounded smooth domain in R-n, n >= 3. In the critical growth case, we prove that the problems are locally well posed and obtain a bootstrapping procedure showing that the solutions are classical. For p = 2 and almost critical dissipative nonlinearities we prove global well posedness, existence of global attractors in H-0(1)(Omega) and, uniformly with respect to the viscosity parameter, L-infinity(Omega) bounds for the attractors. Finally, we obtain a result on continuity of regular attractors which shows that, if n = 3, 4, the attractor of the Cahn-Hilliard problem coincides (in a sense to be specified) with the attractor for the corresponding semilinear heat equation. (C) 2008 Elsevier Inc. All rights reserved.

Stability of periodic optical solitons for a nonlinear Schrodinger system

This paper is concerned with the existence and nonlinear stability of periodic travelling-wave solutions for a nonlinear Schrodinger-type system arising in nonlinear optics. We show the existence of smooth curves of periodic solutions depending on the dnoidal-type functions. We prove stability results by perturbations having the same minimal wavelength, and instability behaviour by perturbations of two or more times the minima period. We also establish global well posedness for our system by using Bourgain`s approach.

SOLITON SOLUTIONS TO SYSTEMS OF COUPLED SCHRODINGER EQUATIONS OF HAMILTONIAN TYPE

We study the existence of positive solutions of Hamiltonian-type systems of second-order elliptic PDE in the whole space. The systems depend on a small parameter and involve a potential having a global well structure. We use dual variational methods, a mountain-pass type approach and Fourier analysis to prove positive solutions exist for sufficiently small values of the parameter.

Stability of periodic travelling shallow-water waves determined by Newton`s equation

We study the existence and stability of periodic travelling-wave solutions for generalized Benjamin-Bona-Mahony and Camassa-Holm equations. To prove orbital stability, we use the abstract results of Grillakis-Shatah-Strauss and the Floquet theory for periodic eigenvalue problems.

Cyclic variability of the circumstellar disk of the Be star zeta Tauri II. Testing the 2D global disk oscillation model

Context. About 2/3 of the Be stars present the so-called V/R variations, a phenomenon characterized by the quasi-cyclic variation in the ratio between the violet and red emission peaks of the HI emission lines. These variations are generally explained by global oscillations in the circumstellar disk forming a one-armed spiral density pattern that precesses around the star with a period of a few years. Aims. This paper presents self-consistent models of polarimetric, photometric, spectrophotometric, and interferometric observations of the classical Be star zeta Tauri. The primary goal is to conduct a critical quantitative test of the global oscillation scenario. Methods. Detailed three-dimensional, NLTE radiative transfer calculations were carried out using the radiative transfer code HDUST. The most up-to-date research on Be stars was used as input for the code in order to include a physically realistic description for the central star and the circumstellar disk. The model adopts a rotationally deformed, gravity darkened central star, surrounded by a disk whose unperturbed state is given by a steady-state viscous decretion disk model. It is further assumed that this disk is in vertical hydrostatic equilibrium. Results. By adopting a viscous decretion disk model for zeta Tauri and a rigorous solution of the radiative transfer, a very good fit of the time-average properties of the disk was obtained. This provides strong theoretical evidence that the viscous decretion disk model is the mechanism responsible for disk formation. The global oscillation model successfully fitted spatially resolved VLTI/AMBER observations and the temporal V/R variations in the H alpha and Br gamma lines. This result convincingly demonstrates that the oscillation pattern in the disk is a one-armed spiral. Possible model shortcomings, as well as suggestions for future improvements, are also discussed.

Model for facilities or vendors location in a global scale considering several echelons in the Chain

The facilities location problem for companies with global operations is very complex and not well explored in the literature. This work proposes a MILP model that solves the problem through minimization of the total logistic cost. Main contributions of the model are the pioneer carrying cost calculation, the treatment given to the take-or-pay costs and to the international tax benefits such as drawback and added value taxes in Brazil. The model was successfully applied to a real case of a chemical industry with industrial plants and sales all over the world. The model application recommended a totally new sourcing model for the company.

Reshaping the global agricultural landscape: perspectives from Brazil

This article highlights the main changes observed in Brazilian agriculture and analyzes the connections of the observed changes in global agriculture. My approach to the analysis focuses the main drivers of changes, where institutions play a central role. Three driving forces are are considered: first, the effects of global demand for food, fiber, and energy; second, the sustainability debate; and third, the bio-energy paradigm. Each driver presents both local as well as global effects. The article does not emphasize the impact changes in Brazil had on the global agricultural landscape but argues that the impacts run from local and global changes, which cannot be discussed separately.

Decreased AIRE Expression and Global Thymic Hypofunction in Down Syndrome

The Down syndrome (DS) immune phenotype is characterized by thymus hypotrophy, higher propensity to organ-specific autoimmune disorders, and higher susceptibility to infections, among other features. Considering that AIRE (autoimmune regulator) is located on 21q22.3, we analyzed protein and gene expression in surgically removed thymuses from 14 DS patients with congenital heart defects, who were compared with 42 age-matched controls with heart anomaly as an isolated malformation. Immunohistochemistry revealed 70.48 +/- 49.59 AIRE-positive cells/mm(2) in DS versus 154.70 +/- 61.16 AIRE-positive cells/mm(2) in controls (p < 0.0001), and quantitative PCR as well as DNA microarray data confirmed those results. The number of FOXP3-positive cells/mm(2) was equivalent in both groups. Thymus transcriptome analysis showed 407 genes significantly hypoexpressed in DS, most of which were related, according to network transcriptional analysis (FunNet), to cell division and to immunity. Immune response-related genes included those involved in 1) Ag processing and presentation (HLA-DQB1, HLA-DRB3, CD1A, CD1B, CD1C, ERAP) and 2) thymic T cell differentiation (IL2RG, RAG2, CD3D, CD3E, PRDX2, CDK6) and selection (SH2D1A, CD74). It is noteworthy that relevant AIRE-partner genes, such as TOP2A, LAMNB1, and NUP93, were found hypoexpressed in DNA microarrays and quantitative real-time PCR analyses. These findings on global thymic hypofunction in DS revealed molecular mechanisms underlying DS immune phenotype and strongly suggest that DS immune abnormalities are present since early development, rather than being a consequence of precocious aging, as widely hypothesized. Thus, DS should be considered as a non-monogenic primary immunodeficiency. The Journal of Immunology, 2011, 187: 3422-3430.

Global Analysis of Protein Palmitoylation in African Trypanosomes

Many eukaryotic proteins are posttranslationally modified by the esterification of cysteine thiols to long-chain fatty acids. This modification, protein palmitoylation, is catalyzed by a large family of palmitoyl acyltransferases that share an Asp-His-His-Cys Cys-rich domain but differ in their subcellular localizations and substrate specificities. In Trypanosoma brucei, the flagellated protozoan parasite that causes African sleeping sickness, protein palmitoylation has been observed for a few proteins, but the extent and consequences of this modification are largely unknown. We undertook the present study to investigate T. brucei protein palmitoylation at both the enzyme and substrate levels. Treatment of parasites with an inhibitor of total protein palmitoylation caused potent growth inhibition, yet there was no effect on growth by the separate, selective inhibition of each of the 12 individual T. brucei palmitoyl acyltransferases. This suggested either that T. brucei evolved functional redundancy for the palmitoylation of essential palmitoyl proteins or that palmitoylation of some proteins is catalyzed by a noncanonical transferase. To identify the palmitoylated proteins in T. brucei, we performed acyl biotin exchange chemistry on parasite lysates, followed by streptavidin chromatography, two-dimensional liquid chromatography-tandem mass spectrometry protein identification, and QSpec statistical analysis. A total of 124 palmitoylated proteins were identified, with an estimated false discovery rate of 1.0%. This palmitoyl proteome includes all of the known palmitoyl proteins in procyclic-stage T. brucei as well as several proteins whose homologues are palmitoylated in other organisms. Their sequences demonstrate the variety of substrate motifs that support palmitoylation, and their identities illustrate the range of cellular processes affected by palmitoylation in these important pathogens.

Imipramine enhances cell proliferation and decreases neurodegeneration in the hippocampus after transient global cerebral ischemia in rats

This study was aimed to determine whether imipramine chronic treatment promotes neurogenesis in the dentate gyrus (DG) and interferes with neuronal death in the CA1 subfield of the hippocampus after transient global cerebral ischemia (TGCI) in rats. After TGCI, animals were treated with imipramine (20 mg/kg, i.p.) or saline during 14 days. 5-Bromo-2`-deoxyuridine-5`-monophosphate (BrdU) was injected 24 h after the last imipramine or saline injection to label proliferating cells. In order to confirm the effect of TGCI on neuronal death and cell proliferation, a group of animals was sacrificed 7 days after TGCI. Neurogenesis and neurodegeneration were evaluated by doublecortin (DCX)-immunohistochemistry and Fluoro-Jade C (FJC)- staining, respectively. The rate of cell proliferation increases 7 days but returns to basal levels 14 days after TGCI. There was a significant increase in the number of FJC-positive neurons in the CA1 of animals 7 and 14 days after TGCI. Chronic imipramine treatment increased cell proliferation in the SGZ of DG and reduced the neurodegeneration in the CA] of the hippocampus 14 days after TGCI. Immunohistochemistry for DCX detected an increased number of newly generated neurons in the hippocampal DG 14 days after TGCI, which was not affected by imipramine treatment. Further studies are needed to evaluate whether imipramine treatment for longer time would be able to promote survival of newly generated neurons as well as to improve functional recovery after TGCI. (C) 2009 Elsevier Ireland Ltd. All rights reserved.

Ratios of UV, PAR and NIR components to global solar radiation measured at Botucatu site in Brazil

The relationships between the four radiant fluxes are analyzed based on a 4 year data archive of hourly and daily global ultraviolet (I(UV)), photosynthetically active-PAR (I(PAR)), near infrared (I(NIR)) and broadband global solar radiation (I(G)) collected at Botucatu, Brazil. These data are used to establish both the fractions of spectral components to global solar radiation and the proposed linear regression models. Verification results indicated that the proposed regression models predict accurately the spectral radiant fluxes at least for the Brazilian environment. Finally, results obtained in this analysis agreed well with most published results in the literature. (c) 2010 Elsevier Ltd. All rights reserved.