Dynamics of a class of ODEs more general than almost periodic

A temporally global solution, if it exists, of a nonautonomous ordinary differential equation need not be periodic, almost periodic or almost automorphic when the forcing term is periodic, almost periodic or almost automorphic, respectively. An alternative class of functions extending periodic and almost periodic functions which has the property that a bounded temporally global solution solution of a nonautonomous ordinary differential equation belongs to this class when the forcing term does is introduced here. Specifically, the class of functions consists of uniformly continuous functions, defined on the real line and taking values in a Banach space, which have pre-compact ranges. Besides periodic and almost periodic functions, this class also includes many nonrecurrent functions. Assuming a hyperbolic structure for the unperturbed linear equation and certain properties for the linear and nonlinear parts, the existence of a special bounded entire solution, as well the existence of stable and unstable manifolds of this solution are established. Moreover, it is shown that this solution and these manifolds inherit the temporal behaviour of the vector field equation. In the stable case it is shown that this special solution is the pullback attractor of the system. A class of infinite dimensional examples involving a linear operator consisting of a time independent part which generates a C(0)-semigroup plus a small time dependent part is presented and applied to systems of coupled heat and beam equations. (C) 2010 Elsevier Ltd. All rights reserved.

Periodic window arising in the parameter space of an impact oscillator

In the bi-dimensional parameter space of an impact-pair system, shrimp-shaped periodic windows are embedded in chaotic regions. We show that a weak periodic forcing generates new periodic windows near the unperturbed one with its shape and periodicity. Thus, the new periodic windows are parameter range extensions for which the controlled periodic oscillations substitute the chaotic oscillations. We identify periodic and chaotic attractors by their largest Lyapunov exponents. (C) 2010 Elsevier B.V. All rights reserved.

Searching for planar signatures in WMAP

We search for planar deviations of statistical isotropy in the Wilkinson Microwave Anisotropy Probe (WMAP) data by applying a recently introduced angular-planar statistics both to full-sky and to masked temperature maps, including in our analysis the effect of the residual foreground contamination and systematics in the foreground removing process as sources of error. We confirm earlier findings that full-sky maps exhibit anomalies at the planar (l) and angular (l) scales (l; l) = (2; 5); (4; 7); and (6; 8), which seem to be due to unremoved foregrounds since this features are present in the full-sky map but not in the masked maps. On the other hand, our test detects slightly anomalous results at the scales (l; l) = (10; 8) and (2; 9) in the masked maps but not in the full-sky one, indicating that the foreground cleaning procedure (used to generate the full-sky map) could not only be creating false anomalies but also hiding existing ones. We also find a significant trace of an anomaly in the full-sky map at the scale (l; l) = (10; 5), which is still present when we consider galactic cuts of 18.3% and 28.4%. As regards the quadrupole (l = 2), we find a coherent over-modulation over the whole celestial sphere, for all full-sky and cut-sky maps. Overall, our results seem to indicate that current CMB maps derived from WMAP data do not show significant signs of anisotropies, as measured by our angular-planar estimator. However, we have detected a curious coherence of planar modulations at angular scales of the order of the galaxy`s plane, which may be an indication of residual contaminations in the full-and cut-sky maps.

Elaboration and optimization of (Y,Er)Al(3)(BO(3))(4) glassy planar waveguides through the sol-gel process

In this work, a sol-gel route was used to prepare Y(0.9)Er(0.1)Al(3)(BO(3))(4) glassy thin films by spin-coating technique looking for the preparation and optimization of planar waveguides for integrated optics. The films were deposited on silica and silicon substrates using stable sols synthesized by the sol-gel process. Deposits with thicknesses ranging between 520 and 720 nm were prepared by a multi-layer process involving heat treatments at different temperatures from glass transition to the film crystallization and using heating rates of 2 degrees C/min. The structural characterization of the layers was performed by using grazing incidence X-ray diffraction and Raman spectroscopy as a function of the heat treatment. Microstructural evolution in terms of annealing temperatures was followed by high resolution scanning electron microscopy and atomic force microscopy. Optical transmission spectra were used to determine the refractive index and the film thicknesses through the envelope method. The optical and guiding properties of the films were studied by m-line spectroscopy. The best films were monomode with 620 nm thickness and a refractive index around 1.664 at 980 nm wavelength. They showed good waveguiding properties with high light-coupling efficiency and low propagation loss at 632.8 and 1550 nm of about 0.88 dB/cm. (C) 2009 Elsevier B.V. All rights reserved.

Er:YAl(3)(BO(3))(4) glassy thin films from polymeric precursor and sol-gel methods: Waveguides for integrated optics

This paper presents the characterization of single-mode waveguides for 980 and 1550 nm wavelengths. High quality planar waveguide structure was fabricated from Y(1-x)Er(x)Al(3)(BO(3))(4) multilayer thin films with x = 0.02, 0.05, 0.1, 0.3, and 0.5, prepared through the polymeric precursor and sol-gel methods using spin-coating. The propagation losses of the planar waveguides varying from 0.63 to 0.88 dB/cm were measured at 632.8 and 1550 nm. The photoluminescence spectra and radiative lifetimes of the Er(3+) (4)I(13/2) energy level were measured in waveguiding geometry. For most samples the photoluminescence decay was single exponential with lifetimes in between 640 mu s and 200 mu s, depending on the erbium concentration and synthesis method. These results indicate that Er doped YAl(3)(BO(3))(4) compounds are promising for low loss waveguides. (C) 2009 Elsevier B.V. All fights reserved.

Erbium and Ytterbium Codoped Titanoniobophosphate Glasses for Ion-Exchange-Based Planar Waveguides

This work presents the optical properties of erbium-doped and erbium/ytterbium codoped Na(2)O-Al(2)O(3)-TiO(2)-Nb(2)O(5)-P(2)O(5) glass systems and also the characterization of planar waveguides obtained by typical thermally assisted Ag+<-> Na+ ion-exchange process. The glass systems allow the preparation of single mode and multimode planar waveguides presenting a strong and relatively broad emission at 1536 nm. The emission signal in the infrared region is intensified for silver-containing samples when compared with free-silver samples. The emission signal intensification may be attributed to a nonplasmonic energy transfer from silver species to Er3+ ions as no bands related to surface plasmon resonance (SPR) of silver nanoparticles were observed.

Metastable Periodic Patterns in Singularly Perturbed Delayed Equations

We consider the scalar delayed differential equation epsilon(x) over dot(t) = -x(t) + f(x(t-1)), where epsilon > 0 and f verifies either df/dx > 0 or df/dx < 0 and some other conditions. We present theorems indicating that a generic initial condition with sign changes generates a solution with a transient time of order exp(c/epsilon), for some c > 0. We call it a metastable solution. During this transient a finite time span of the solution looks like that of a periodic function. It is remarkable that if df/dx > 0 then f must be odd or present some other very special symmetry in order to support metastable solutions, while this condition is absent in the case df/dx < 0. Explicit epsilon-asymptotics for the motion of zeroes of a solution and for the transient time regime are presented.

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.

Periodic geodesics and geometry of compact Lorentzian manifolds with a Killing vector field

We study the geometry and the periodic geodesics of a compact Lorentzian manifold that has a Killing vector field which is timelike somewhere. Using a compactness argument for subgroups of the isometry group, we prove the existence of one timelike non self-intersecting periodic geodesic. If the Killing vector field is nowhere vanishing, then there are at least two distinct periodic geodesics; as a special case, compact stationary manifolds have at least two periodic timelike geodesics. We also discuss some properties of the topology of such manifolds. In particular, we show that a compact manifold M admits a Lorentzian metric with a nowhere vanishing Killing vector field which is timelike somewhere if and only if M admits a smooth circle action without fixed points.

Triply periodic minimal surfaces which converge to the Hoffman-Wohlgemuth example

We get a continuous one-parameter new family of embedded minimal surfaces, of which the period problems are two-dimensional. Moreover, one proves that it has Scherk`s second surface and Hoffman-Wohlgemuth`s example as limit-members.

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.

Improving the Detectability of Sequential Injection Chromatography (SIC): Determination of Triazines by Exploiting Liquid Core Waveguide (LCW) Detection

Coupling a liquid core waveguide cell to a sequential injection chromatograph improved the detection limits for determination of triazine herbicides without compromising peak resolution. Separation of simazine, atrazine, and propazine was achieved in water samples by a 25mm long C18 monolithic column. Detection was made at 238nm using a type II LCW (silica capillary coated with Teflon (R) AF2400) cell with 100cm of optical path length. Detection limits for simazine, atrazine, and propazine were 2.3, 1.9, and 4.5 mu g L-1, respectively. Reduced analysis time and low solvent consumption are other remarkable features of the proposed method.

Fabrication and integration of planar electrodes for contactless conductivity detection on polyester-toner electrophoresis microchips

In this report, we describe the microfabrication and integration of planar electrodes for contactless conductivity detection on polyester-toner (PT) electrophoresis microchips using toner masks. Planar electrodes were fabricated by three simple steps: (i) drawing and laser-printing the electrode geometry on polyester films, (ii) sputtering deposition onto substrates, and (iii) removal of toner layer by a lift-off process. The polyester film with anchored electrodes was integrated to PT electrophoresis microchannels by lamination at 120 degrees C in less than 1 min. The electrodes were designed in an antiparallel configuration with 750 mu m width and 750 gm gap between them. The best results were recorded with a frequency of 400 kHz and 10 V-PP using a sinusoidal wave. The analytical performance of the proposed microchip was evaluated by electrophoretic separation of potassium, sodium and lithium in 150 mu m wide x 6 mu m deep microchannels. Under an electric field of 250 V/cm the analytes were successfully separated in less than 90 s with efficiencies ranging from 7000 to 13 000 plates. The detection limits (S/N = 3) found for K+, Na+, and Li+ were 3.1, 4.3, and 7.2 mu mol/L, respectively. Besides the low-cost and instrumental simplicity, the integrated PT chip eliminates the problem of manual alignment and gluing of the electrodes, permitting more robustness and better reproducibility, therefore, more suitable for mass production of electrophoresis microchips.

Programa preventivo da cárie dentária baseado no controle mecânico da placa bacteriana em crianças, por meio da profilaxia profissional periódica: Resultados após 25 anos de acompanhamento

OBJETIVOS: o objetivo deste trabalho foi verificar a incidência de cárie dentária em um programa de prevenção aplicado durante 25 anos em clínica particular. METODOLOGIA: participaram desse programa 640 crianças de ambos os gêneros, na faixa etária de 3 a 15 anos de idade. O programa foi baseado no controle mecânico da placa bacteriana dentária por meio da profilaxia profissional com jato de bicarbonato de sódio com uma periodicidade mensal. A incidência de cárie foi verificada por meio de exames clínicos durante as sessões de atendimento e radiográficos anualmente. A média de idade das crianças ao ingressarem no programa foi de 7,8 anos. RESULTADOS: antes de ingressar no programa, as crianças apresentaram, em média, 5,3 faces cariadas, enquanto após o programa a média foi de 0,18. A incidência de cáries por ano antes do programa foi de 0,9 faces cariadas e durante o programa de 0,03. O tempo de permanência das crianças no programa foi, em média, de 52,6 meses, e a média de faltas foi de 0,5 falta por ano. Esses resultados demonstram o sucesso do programa, principalmente por ter uma filosofia que procura o equilíbrio da biodiversidade da cavidade bucal, sem o risco de produzir efeitos colaterais indesejáveis. CONCLUSÕES: conclui-se, assim, que esse parece ser o caminho mais curto para resolver o problema da cárie dentária, ou seja, o controle mecânico da placa bacteriana dentária através da profilaxia profissional mensal, pois é um método de prevenção possível de ser aplicado em qualquer criança, independentemente de suas condições psicomotoras e sociais, e que proporciona a melhor relação custo-benefício, além de estar de acordo com os conceitos mais atuais de cárie e de seus fatores etiológicos. Em função da faixa etária das crianças, o programa é de suma importância para clínicas de Odontopediatria e Ortodontia.

Phenology of an agarophyte Gracilaria birdiae Plastino and E.C. Oliveira (Gracilariales, Rhodophyta) in Northeastern Brazil

The reproductive phenology and thallus length of Gracilaria birdiae were studied over a period of 12 months in a natural bed in Northeastern Brazil. Fertile specimens of G. birdiae were observed during the entire study period. Tetrasporophytes were the most common with an annual mean of 80.1±5.6%, followed by cystocarpic plants (9.3±3.4%), male gametophytes (8.3±3.6%) and infertile plants (2.2±3.4%). Only male gametophytes and infertile plants showed a variation in occurrence frequency during the year (p<0.05). With respect to thallus length, a distinct seasonal variation was observed for all reproductive stages (p<0.05), with the highest values recorded during the rainy season (March to August) and the lowest in the dry season (September to February). The results demonstrate that the size of individuals in this population is significantly affected by the periodic changes in the environment caused by rainfall regimes and hydrodynamism.