173 resultados para reversible diffeomorphisms


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In this paper singularly perturbed reversible vector fields defined in R-n without normal hyperbolicity conditions are discussed. The main results give conditions for the existence of infinitely many periodic orbits and heteroclinic cycles converging to singular orbits with respect to the Hausdorff distance.

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We prove that every robustly transitive and every stably ergodic symplectic diffeomorphism on a compact manifold admits a dominated splitting. In fact, these diffeomorphisms are partially hyperbolic. (c) 2005 Elsevier SAS. All rights reserved.

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We investigated the alignment induced on a nematic liquid crystal (LC) by a photo-aligned polymer film with azo-dye side groups. The orientation of the LC molecules can be manipulated in a reversible manner by irradiating the film with polarized light. We analyzed the competition between the orientation induced by the main chain, through rubbing of the film and that induced by the photo-aligned polymer. Anchoring strength for the different processing conditions are reported. The changes in film morphology caused by rubbing or photo-alignment could be captured by atomic force microscopy. The reversibility of the photo-induced alignment and the competition between the two anchoring mechanisms may allow recording and erasing of information in a LC display.

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A simple, cheap and versatile, polyol-mediated fabrication method has been extended to the synthesis of tin oxide nanoparticles on a large scale. Ultrafine SnO2 nanoparticles with crystallite sizes of less than 5 nm were realized by refluxing SnCl2 . 2H(2)O in ethylene glycol at 195 degrees C for 4 h under vigorous stirring in air. The as-prepared SnO2 nanoparticles exhibited enhanced Li-ion storage capability and cyclability, demonstrating a specific capacity of 400 mAh g(-1) beyond 100 cycles. (c) 2006 Elsevier B.V. All rights reserved.

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Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

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In this paper an unprecedent thermo-reversible sol-gel transition for titania nanoparticles dispersed in a solution of p-toluene sulfonic acid (PTSH) in isopropanol is reported. The sol formed by the thermo-hydrolysis at 60 degrees C of titanium tetraisopropoxide (Ti((OPr)-Pr-i)(4)) reversibly changes into a turbid gel upon cooling to room temperature. Turbidimetric measurements performed for samples containing different nominal acidity ratios (A = [PTSH]/[Ti]) have evidenced that the gel transformation temperature increases from 20 to 35 degrees C as the [PTSH]/[Ti] ratio increases from 0.2 to 2.0. SAXS results indicate that the thermo-reversible gelation is associated to a reversible aggregation of a monodisperse set of titania nanoparticles with average gyration radius of approximate to 2 nm. From the different PTSH species evidenced by Raman spectroscopy and TG/DTA of dried gels we proposed that the then-no-reversible gelation in this systems is induced by the formation of a supramolecular network, in which the protonated surface of nanoparticles is interconnected through cooperative hydrogen bonds between -SO3 groups of p-toluene sulfonic acid. (C) 2009 Elsevier Ltd. All rights reserved.

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We find that within the formalism of coadjoint orbits of the infinite dimensional Lie group the Noether procedure leads, for a special class of transformations, to the constant of motion given by the fundamental group one-cocycle S. Use is made of the simplified formula giving the symplectic action in terms of S and the Maurer-Cartan one-form. The area preserving diffeomorphisms on the torus T2=S1⊗S1 constitute an algebra with central extension, given by the Floratos-Iliopoulos cocycle. We apply our general treatment based on the symplectic analysis of coadjoint orbits of Lie groups to write the symplectic action for this model and study its invariance. We find an interesting abelian symmetry structure of this non-linear problem.

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We study the existence of periodic solutions in the neighbourhood of symmetric (partially) elliptic equilibria in purely reversible Hamiltonian vector fields. These are Hamiltonian vector fields with an involutory reversing symmetry R. We contrast the cases where R acts symplectically and anti-symplectically. In case R acts anti-symplectically, generically purely imaginary eigenvalues are isolated, and the equilibrium is contained in a local two-dimensional invariant manifold containing symmetric periodic solutions encircling the equilibrium point. In case R acts symplectically, generically purely imaginary eigenvalues are doubly degenerate, and the equilibrium is contained in two two-dimensional invariant manifolds containing nonsymmetric periodic solutions encircling the equilibrium point. In addition, there exists a three-dimensional invariant surface containing a two-parameter family of symmetric periodic solutions.

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We study non-hyperbolic repellers of diffeomorphisms derived from transitive Anosov diffeomorphisms with unstable dimension 2 through a Hopf bifurcation. Using some recent abstract results about non-uniformly expanding maps with holes, by ourselves and by Dysman, we show that the Hausdorff dimension and the limit capacity (box dimension) of the repeller are strictly less than the dimension of the ambient manifold.

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Antimony based glasses have been investigated for the first time regarding the possibility of holographic data storage using visible lasers sources. Changes in both refractive index and the absorption coefficient were measured using a holographic setup. The modulation of the optical constants is reversible by heat treatment. Bragg gratings were written under visible light of an Ar laser and erased thermally.

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Human respiratory syncytial virus (HRSV) is the major cause of lower respiratory tract infections in children under 5 years of age and the elderly, causing annual disease outbreaks during the fall and winter. Multiple lineages of the HRSVA and HRSVB serotypes co-circulate within a single outbreak and display a strongly temporal pattern of genetic variation, with a replacement of dominant genotypes occurring during consecutive years. In the present study we utilized phylogenetic methods to detect and map sites subject to adaptive evolution in the G protein of HRSVA and HRSVB. A total of 29 and 23 amino acid sites were found to be putatively positively selected in HRSVA and HRSVB, respectively. Several of these sites defined genotypes and lineages within genotypes in both groups, and correlated well with epitopes previously described in group A. Remarkably, 18 of these positively selected tended to revert in time to a previous codon state, producing a flipflop phylogenetic pattern. Such frequent evolutionary reversals in HRSV are indicative of a combination of frequent positive selection, reflecting the changing immune status of the human population, and a limited repertoire of functionally viable amino acids at specific amino acid sites.

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We implement a singularity theory approach, the path formulation, to classify D3-equivariant bifurcation problems of corank 2, with one or two distinguished parameters, and their perturbations. The bifurcation diagrams are identified with sections over paths in the parameter space of a Ba-miniversal unfolding f0 of their cores. Equivalence between paths is given by diffeomorphisms liftable over the projection from the zero-set of F0 onto its unfolding parameter space. We apply our results to degenerate bifurcation of period-3 subharmonics in reversible systems, in particular in the 1:1-resonance.

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Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

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Broad nosed caiman are ectotherm sauropsids that naturally experience long fasting intervals. We have studied the postprandial responses by measuring oxygen consumption using respirometry, the size changes of the duodenum, the distal small intestine, and the liver, using repeated non-invasive ultrasonography, and by investigating structural changes on the level of tissues and cells by using light- and electron microscopy. The caimans showed the same rapid and reversible changes of organ size and identical histological features, down to the ultrastructure level, as previously described for other ectothermic sauropsids. We found a configuration change of the mucosa epithelium from pseudostratified during fasting to single layered during digestion, in association with hypertrophy of enterocytes by loading them with lipid droplets. Similar patterns were also found for the hepatocytes of the liver. By placing the results of our study in comparative relationship and by utilizing the phylogenetic bracket of crocodiles, birds and squamates, we suggest that the observed features are plesiomorphic characters of sauropsids. By extending the comparison to anurans, we suggest that morphological and physiological adjustments to feeding and fasting described here may have been a character of early tetrapods. In conclusion, we suggest that the ability to tolerate long fasting intervals and then swallow a single large meal as described for many sit-an-wait foraging sauropsids is a functional feature that was already present in ancestral tetrapods.

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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)