Fold, transcritical and pitchfork singularities for time-reversible systems

This paper deals with a class of singularly perturbed reversible planar vector fields around the origin where the normal hyperbolicity assumption is not assumed. We exhibit conditions for the existence of infinitely many periodic orbits and hetero-clinic cycles converging to singular orbits with respect to the Hausdorf distance. In addition, generic normal forms of such singularities are presented.

On computing discriminants of subfields of Q(zeta(pr))

The conductor-discriminant formula, namely, the Hasse Theorem, states that if a number field K is fixed by a subgroup H of Gal(Q(zeta(n))/Q), the discriminant of K can be obtained from H by computing the product of the conductors of all characters defined modulo n which are associated to K. By calculating these conductors explicitly, we derive a formula to compute the discriminant of any subfield of Q(zeta(p)r), where p is an odd prime and r is a positive integer. (C) 2002 Elsevier B.V. (USA).

Reversible intermittent flow-injection determination of mercury in sediments and vinasses by cold vapor atomic absorption spectrometry

A reversible intermittent pow-injection procedure is proposed for the automated determination of mercury in sediments and vinasses by cold vapor atomic absorption spectrometry, CVAAS. Solutions of sample and stannous chloride are carried by two air streams and sequentially injected into the generator/separator chamber in a segmented asynchronous merging zone configuration. The intermittent flow in the forward direction carries the mercury vapor through the flow cell, and in the backward direction, if aspirates the the remaining solution from the vessel to waste. We investigated composition and concentration of reagents, pow rates, commutation times, reactor configuration, and conditions for mercury release. The accuracy was checked by mercury determination in a certified sediment and spiked vinasses and river waters. The system handles about 100 samples per hour (0.50-5.00 mu g L-1), consuming ca. 2.5 mL of sample and 50 mg of SnCl2 per determination; Good recoveries (92-103%) were obtained with spiked samples. Results are precise (RSD <3% for 2.5 mu g Hg L-1, n = 12) and in agreement with values for certified reference material at 95% confidence level. (C) 1999 John Wiley & Sons, Inc.

On the dissimilarity between the algorithms for computing the symmetric energy-momentum tensor in ordinary field theory and general relativity

The recipe used to compute the symmetric energy-momentum tensor in the framework of ordinary field theory bears little resemblance to that used in the context of general relativity, if any. We show that if one stal ts fi om the field equations instead of the Lagrangian density, one obtains a unified algorithm for computing the symmetric energy-momentum tensor in the sense that it can be used for both usual field theory and general relativity.

Hopf-zero bifurcations of reversible vector fields

We study the dynamics of a class of reversible vector fields having eigenvalues (0, alphai, -alphai) around their symmetric equilibria. We give a complete list of all normal forms for such vector fields, their versal unfoldings, and the corresponding bifurcation diagrams of the codimensional-one case. We also obtain some important conclusions on the existence of homoclinic and heteroclinic orbits, invariant tori and symmetric periodic orbits.

Singular perturbation problems for time-reversible systems

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.

Competition between anchoring and reversible photo-induced alignment of a nematic liquid crystal

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.

Polyol-mediated synthesis of ultrafine tin oxide nanoparticles for reversible Li-ion storage

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.

Thermo-Reversible Sol-Gel Transition of Surface Modified Titanium Poly Oxo Building Blocks

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

Thermo-reversible sol-gel transition of TiO2 nanoparticles with surface modified by p-toluene sulfonic acid

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.

Algorithm for computing the propagator for higher derivative gravity theories

A simple algorithm for computing the propagator for higher derivative gravity theories based on the Barnes-Rivers operators is presented. The prescription is used, among other things, to obtain the propagator for quadratic gravity in an unconventional gauge. We also find the propagator for both gravity and quadratic gravity in an interesting gauge recently baptized the Einstein gauge [Hitzer and Dehnen, Int. J. Theor. Phys. 36 (1997), 559].

N-methyl-D-aspartate channel and consciousness: From signal coincidence detection to quantum computing

Research on Blindsight, Neglect/Extinction and Phantom limb syndromes, as well as electrical measurements of mammalian brain activity, have suggested the dependence of vivid perception on both incoming sensory information at primary sensory cortex and reentrant information from associative cortex. Coherence between incoming and reentrant signals seems to be a necessary condition for (conscious) perception. General reticular activating system and local electrical synchronization are some of the tools used by the brain to establish coarse coherence at the sensory cortex, upon which biochemical processes are coordinated. Besides electrical synchrony and chemical modulation at the synapse, a central mechanism supporting such a coherence is the N-methyl-D-aspartate channel, working as a 'coincidence detector' for an incoming signal causing the depolarization necessary to remove Mg 2+, and reentrant information releasing the glutamate that finally prompts Ca 2+ entry. We propose that a signal transduction pathway activated by Ca 2+ entry into cortical neurons is in charge of triggering a quantum computational process that accelerates inter-neuronal communication, thus solving systemic conflict and supporting the unity of consciousness. © 2001 Elsevier Science Ltd.

On computing discriminants of subfields of ℚ (ζp r)

The conductor-discriminant formula, namely, the Hasse Theorem, states that if a number field K is fixed by a subgroup H of Gal(ℚ(ζn)/ℚ), the discriminant of K can be obtained from H by computing the product of the conductors of all characters defined modulo n which are associated to K. By calculating these conductors explicitly, we derive a formula to compute the discriminant of any subfield of ℚ(ζpr), where p is an odd rime and r is a positive integer. © 2002 Elsevier Science USA.

Reversible Hamiltonian Liapunov center theorem

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.

Reversible holographic 3D data storage in oxide glasses using visible lasers

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.