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.

Bubbling transition to spatial mode excitation in an extended dynamical system

We investigated the transition to spatio-temporal chaos in spatially extended nonlinear dynamical systems possessing an invariant subspace with a low-dimensional attractor. When the latter is chaotic and the subspace is transversely stable we have a spatially homogeneous state only. The onset of spatio-temporal chaos, i.e. the excitation of spatially inhomogeneous modes, occur through the loss of transversal stability of some unstable periodic orbit embedded in the chaotic attractor lying in the invariant subspace. This is a bubbling transition, since there is a switching between spatially homogeneous and nonhomogeneous states with statistical properties of on-off intermittency. Hence the onset of spatio-temporal chaos depends critically both on the existence of a chaotic attractor in the invariant subspace and its being transversely stable or unstable. (C) 2008 Elsevier B.V. All rights reserved.

Suppressing grazing chaos in impacting system by structural nonlinearity

In this note we investigate the influence of structural nonlinearity of a simple cantilever beam impacting system on its dynamic responses close to grazing incidence by a means of numerical simulation. To obtain a clear picture of this effect we considered two systems exhibiting impacting motion, where the primary stiffness is either linear (piecewise linear system) or nonlinear (piecewise nonlinear system). Two systems were studied by constructing bifurcation diagrams, basins of attractions, Lyapunov exponents and parameter plots. In our analysis we focused on the grazing transitions from no impact to impact motion. We observed that the dynamic responses of these two similar systems are qualitatively different around the grazing transitions. For the piecewise linear system, we identified on the parameter space a considerable region with chaotic behaviour, while for the piecewise nonlinear system we found just periodic attractors. We postulate that the structural nonlinearity of the cantilever impacting beam suppresses chaos near grazing. (C) 2007 Elsevier Ltd. All rights reserved.

Reentrant quantum Hall effect in bilayer system at high filling factors

We report on the measurements of the quantum Hall effect states in double quantum well structures at the filling factors v = 4N + 1 and 4N + 3, where N is the Landau index number, in the presence of the in-plane magnetic field. The quantum Hall states at these filling factors vanish and reappear several times. Repeated reentrance of the transport gap occurs due to the periodic vanishing of the tunneling amplitude in the presence of the in-plane field. When the gap vanishes, the transport becomes anisotropic. The anisotropy persist at half-odd filling factors, when bilayer quantum Hall states are recovered with increase of the tilt angle. (C) 2007 Elsevier B.V. All rights reserved.

TRANSPORT IN A BILAYER SYSTEM AT HIGH LANDAU FILLING FACTOR

We have studied Shubnikov de Haas oscillations and the quantum Hall effect in GaAs-double well structures in tilted magnetic fields. We found strong magnetoresistance oscillations as a function of an in-plane magnetic field B(parallel to) at nu = 4N + 3 and nu = 4N + 1 filling factors. At low perpendicular magnetic field B(perpendicular to), the amplitude of the conventional Shubnikov-de Haas (SdH) oscillations also exhibits B(parallel to)-periodic dependence at fixed values of B(perpendicular to). We interpret the observed oscillations as a manifestation of the interference between cyclotron orbits in different quantum wells.

STABILITY ANALYSIS WITH APPLICATIONS OF A TWO-DIMENSIONAL DYNAMICAL SYSTEM ARISING FROM A STOCHASTIC MODEL FOR AN ASSET MARKET

We analyze the stability properties of equilibrium solutions and periodicity of orbits in a two-dimensional dynamical system whose orbits mimic the evolution of the price of an asset and the excess demand for that asset. The construction of the system is grounded upon a heterogeneous interacting agent model for a single risky asset market. An advantage of this construction procedure is that the resulting dynamical system becomes a macroscopic market model which mirrors the market quantities and qualities that would typically be taken into account solely at the microscopic level of modeling. The system`s parameters correspond to: (a) the proportion of speculators in a market; (b) the traders` speculative trend; (c) the degree of heterogeneity of idiosyncratic evaluations of the market agents with respect to the asset`s fundamental value; and (d) the strength of the feedback of the population excess demand on the asset price update increment. This correspondence allows us to employ our results in order to infer plausible causes for the emergence of price and demand fluctuations in a real asset market. The employment of dynamical systems for studying evolution of stochastic models of socio-economic phenomena is quite usual in the area of heterogeneous interacting agent models. However, in the vast majority of the cases present in the literature, these dynamical systems are one-dimensional. Our work is among the few in the area that construct and study analytically a two-dimensional dynamical system and apply it for explanation of socio-economic phenomena.

Stability and Hopf bifurcation in an hexagonal governor system

In this paper we study the Lyapunov stability and the Hopf bifurcation in a system coupling an hexagonal centrifugal governor with a steam engine. Here are given sufficient conditions for the stability of the equilibrium state and of the bifurcating periodic orbit. These conditions are expressed in terms of the physical parameters of the system, and hold for parameters outside a variety of codimension two. (C) 2007 Elsevier Ltd. All rights reserved.

Microbial distribution in the root canal system after periapical lesion induction using different methods

The aim of this study was to evaluate the microbial distribution in the root canal system after periapical lesion induction in dogs' teeth using different methods. Fifty-two root canals were assigned to 4 groups (n=13). Groups I and II: root canals were exposed to the oral cavity for 180 days; groups III and IV: root canals were exposed for 7 days and then the coronal openings were sealed for 53 days. The root apices of groups I and III were perforated, while those of groups II and IV remained intact. After the experimental periods, the animals were euthanized and the anatomic pieces containing the roots were processed and stained with the Brown & Brenn method to assess the presence and distribution of microorganisms. The incidence of microorganisms at different sites of the roots and periapical lesions was analyzed statistically by the chi-square test at 5% significance level. All groups presented microorganisms in the entire root canal system. A larger number of microorganisms was observed on the root canal walls, apical delta and dentinal tubules (p<0.05), followed by cementum and cemental resorption areas. In spite of the different periods of exposure to the oral environment, the methods used for induction of periapical periodontitis yielded similar distribution of microorganisms in the root canal system.

Influence of sodium hypochlorite and edta on the microtensile bond strength of a self-etching adhesive system

Chemical substances used during biomechanical preparation of root canals can alter the composition of dentin surface and affect the interaction with restorative materials. OBJECTIVE: The purpose of this study was to evaluate the microtensile bond strength (µTBS) of a self-etching adhesive system to dentin irrigated with sodium hypochlorite (NaOCl) and ethylenediaminetetraacetic acid (EDTA). MATERIAL AND METHODS: Thirty human third molars were sectioned 3 mm below the occlusal surface, polished with 600- to 1200-grit silicon carbide papers, and randomly divided into 3 groups: G1 (control): no irrigating solution; G2: 1% NaOCl; and G3: 1% NaOCl followed by the application of 17% EDTA. The specimens received the self-etching adhesive system (XENO III - Dentsply), restored with microhybrid composite resin (Z250 - 3M ESPE), sectioned and trimmed to create 4 hourglass-shaped slabs of each tooth. The slabs were tested in microtensile strength in a universal testing machine (Emic DL 2000) at a crosshead speed of 0.5 mm/min until fracture. The results were analyzed statistically by ANOVA and Newman-Keuls test. RESULTS: Mean µTBS values and standard deviations in MPa were: G1 = 11.89 ± 4.22; G2 = 19.41 ± 5.32; G3 = 11.34 ± 4.73. 1% NaOCl increased the adhesive resistance significantly (p<0.001/F=22.5763). The application of 1% NaOCl/17% EDTA resulted in statistically similar µTBS to the control group. CONCLUSIONS: None of the irrigants affected negatively the µTBS of XENO III to dentin. The use of 1% NaOCl alone resulted in higher bond strength than the other treatments. The combination of 1% NaOCl and 17% EDTA produced similar bond strength to that of untreated dentin.

Do the origins of primary teeth affect the bond strength of a self-etching adhesive system to dentin?

The aim of this in vitro study was to evaluate the tensile bond strength of a self-etching adhesive system to three different dentinal substrates. Primary molar teeth that had been recently exfoliated (RE), with unknown time of exfoliation (UT), and extracted due to prolonged retention (PR) were used for this investigation. Ten primary molar teeth of each group were cut in the middle following the mesio-distal direction, creating a total of twenty specimens per group. The specimens were included in acrylic resin and had a flat dentin surface exposed. The self-etching adhesive system was applied to this surface and a 3-millimeter high cone with diameter of 2 mm in the adhesion area was constructed using composite resin. The specimens were stored in distilled water at 37ºC for 24 hours. Fifteen specimens of each substrate were used for the tensile bond test (n = 15) and 5 had the interface analyzed by scanning electron microscopy (SEM). The data was examined by one-way ANOVA and presented no significant differences between groups (p = 0.5787). The mean values obtained for RE, UT and PR were 18.39 ± 9.70, 19.41 ± 7.80, and 23.30 ± 9.37 MPa, respectively. Any dentinal substrates of primary teeth studied are safe for tensile bond strength tests with adhesive systems.

Effectiveness of sealing active proximal caries lesions with an adhesive system: 1-year clinical evaluation

The objective of this study was to evaluate the effectiveness of a therapeutic sealant to arrest non-cavitated proximal carious lesion progression. The study population comprised 44 adolescents who had bitewing radiographs taken for caries diagnosis. Non-cavitated lesions extending up to half of dentin thickness were included in the sample. In the experimental group (n = 33), the proximal caries-lesion surfaces were sealed with an adhesive (OptiBond Solo, Kerr) after tooth separation. The control group (n = 11) received no treatment, except for oral hygiene instructions including use of dental floss. Follow-up radiographs were taken after one year and were analyzed in comparison with baseline radiographs. In a blind study setting, visual readings were performed by two examiners, blinded to whether the examined radiograph was baseline or follow-up, and whether it concerned a test or control lesion. The efficacy of sealing treatment was evaluated by the McNemar test (0.05). About 22% of the sealed lesions showed reduction, 61% showed no change and 16% showed progression. For the control lesions, the corresponding values were 27%, 36% and 36% respectively. The number of lesions that showed reduction and no changes were merged and therefore 83.3% of the sealed lesions and 63.6% of the control lesions were considered clinically successful. No statistical significance was detected (p > 0.05). In the course of 1 year, sealing proximal caries lesions was not shown to be superior to lesion monitoring.

Renin angiotensin system and cardiac hypertrophy after sinoaortic denervation in rats

OBJECTIVE: The aim of this study was to evaluate the role of angiotensin I, II and 1-7 on left ventricular hypertrophy of Wistar and spontaneously hypertensive rats submitted to sinoaortic denervation. METHODS: Ten weeks after sinoaortic denervation, hemodynamic and morphofunctional parameters were analyzed, and the left ventricle was dissected for biochemical analyses. RESULTS: Hypertensive groups (controls and denervated) showed an increase on mean blood pressure compared with normotensive ones (controls and denervated). Blood pressure variability was higher in denervated groups than in their respective controls. Left ventricular mass and collagen content were increased in the normotensive denervated and in both spontaneously hypertensive groups compared with Wistar controls. Both hypertensive groups presented a higher concentration of angiotensin II than Wistar controls, whereas angiotensin 1-7 concentration was decreased in the hypertensive denervated group in relation to the Wistar groups. There was no difference in angiotensin I concentration among groups. CONCLUSION: Our results suggest that not only blood pressure variability and reduced baroreflex sensitivity but also elevated levels of angiotensin II and a reduced concentration of angiotensin 1-7 may contribute to the development of left ventricular hypertrophy. These data indicate that baroreflex dysfunction associated with changes in the renin angiotensin system may be predictive factors of left ventricular hypertrophy and cardiac failure.

Genetic evaluation of the mating system in the blue-and-yellow macaw (Ara ararauna, Aves, Psittacidae) by DNA fingerprinting

More than 90% of birds are socially monogamous, although genetic studies indicate that many are often not sexually monogamous. In the present study, DNA fingerprinting was used to estimate the genetic relationships between nestlings belonging to the same broods to evaluate the mating system in the socially monogamous macaw, Ara ararauna. We found that in 10 of 11 broods investigated, the nestlings showed genetic similarity levels congruent with values expected among full-sibs, suggesting that they shared the same parents. However, in one brood, the low genetic similarity observed between nestlings could be a result of intraspecific brood parasitism, intraspecific nest competition or extra-pair paternity. These results, along with available behavioral and life-history data, imply that the blue-and-yellow macaw is not only socially, but also genetically monogamous. However, the occurrence of eventual cases of extra-pair paternity cannot be excluded.

Hemodynamic, morphometric and autonomic patterns in hypertensive rats - renin-angiotensin system modulation

BACKGROUND: Spontaneously hypertensive rats develop left ventricular hypertrophy, increased blood pressure and blood pressure variability, which are important determinants of heart damage, like the activation of renin-angiotensin system. AIMS: To investigate the effects of the time-course of hypertension over 1) hemodynamic and autonomic patterns (blood pressure; blood pressure variability; heart rate); 2) left ventricular hypertrophy; and 3) local and systemic Renin-angiotensin system of the spontaneously hypertensive rats. METHODS: Male spontaneously hypertensive rats were randomized into two groups: young (n=13) and adult (n=12). Hemodynamic signals (blood pressure, heart rate), blood pressure variability (BPV) and spectral analysis of the autonomic components of blood pressure were analyzed. LEFT ventricular hypertrophy was measured by the ratio of LV mass to body weight (mg/g), by myocyte diameter (μm) and by relative fibrosis area (RFA, %). ACE and ACE2 activities were measured by fluorometry (UF/min), and plasma renin activity (PRA) was assessed by a radioimmunoassay (ng/mL/h). Cardiac gene expressions of Agt, Ace and Ace2 were quantified by RT-PCR (AU). RESULTS: The time-course of hypertension in spontaneously hypertensive rats increased BPV and reduced the alpha index in adult spontaneously hypertensive rats. Adult rats showed increases in left ventricular hypertrophy and in RFA. Compared to young spontaneously hypertensive rats, adult spontaneously hypertensive rats had lower cardiac ACE and ACE2 activities, and high levels of PRA. No change was observed in gene expression of Renin-angiotensin system components. CONCLUSIONS: The observed autonomic dysfunction and modulation of Renin-angiotensin system activity are contributing factors to end-organ damage in hypertension and could be interacting. Our findings suggest that the management of hypertensive disease must start before blood pressure reaches the highest stable levels and the consequent established end-organ damage is reached.