Integrability of a linear center perturbed by a fourth degree homogeneous polynomial

In this work we study the integrability of a two-dimensional autonomous system in the plane with linear part of center type and non-linear part given by homogeneous polynomials of fourth degree. We give sufficient conditions for integrability in polar coordinates. Finally we establish a conjecture about the independence of the two classes of parameters which appear in the system; if this conjecture is true the integrable cases found will be the only possible ones.

Integrability of a linear center perturbed by a fifth degree homogeneous polynomial

In this work we study the integrability of two-dimensional autonomous system in the plane with linear part of center type and non-linear part given by homogeneous polynomials of fifth degree. We give a simple characterisation for the integrable cases in polar coordinates. Finally we formulate a conjecture about the independence of the two classes of parameters which appear on the system; if this conjecture is true the integrable cases found will be the only possible ones.

Lifetime enhancement of scroll rings by spatiotemporal fluctuations

The dynamics of three-dimensional scroll rings with spatiotemporal random excitability is investigated numerically using the FitzHugh-Nagumo model. Depending on the correlation time and length scales of the fluctuations, the lifetime of the ring filament is enlarged and a resonance effect between the time scale of the scroll ring and the time correlation of the noise is observed. Numerical results are interpreted in terms of a simplified stochastic model derived from the kinematical equations for three-dimensional excitable waves.

Lifetime enhancement of scroll rings by spatiotemporal fluctuations

The dynamics of three-dimensional scroll rings with spatiotemporal random excitability is investigated numerically using the FitzHugh-Nagumo model. Depending on the correlation time and length scales of the fluctuations, the lifetime of the ring filament is enlarged and a resonance effect between the time scale of the scroll ring and the time correlation of the noise is observed. Numerical results are interpreted in terms of a simplified stochastic model derived from the kinematical equations for three-dimensional excitable waves.

Importance of the embedding environment on the strain within small rings in siliceous materials

The effect of the local environment on the energetic strain within small (SiO)N rings (with N=2,3) in silica materials is investigated via periodic model systems employing density functional calculations. Through comparison of the energies of various nonterminated systems containing small rings in strained and relatively unstrained environments, with alpha quartz, we demonstrate how small ring strain is affected by the nature of the embedding environment. We compare our findings with numerous previously reported calculations, often predicting significantly different small-ring strain energies, leading to a critical assessment of methods of calculating accurate localized ring energies. The results have relevance for estimates of the strain-induced response (e.g., chemical, photo, and radio) of small silica rings, and the propensity for them to form in bulk glasses, thin films, and nanoclusters.

The wide synthetic versatility of five membered rings containing phosphorus

The chemistry of cyclopentadiene rings has been widely studied. This review article deals with a similar chemistry of new compounds containing from 1 to 5 phosphorus atoms on the ring substituting the carbon atoms. The neutral rings containing one, two and three phosphorus atoms can be used as building blocks for the synthesis of new organic compounds containing phosphorus. These rings plus the anionic ones also show great potential as ligands in coordination chemistry. The aim of this article is to show how important this new area is and how diverse the chemistry related to a single type of ring can be.

Multicointegration, polynomial cointegration and I(2) cointegration with structural breaks. An application to the sustainability of the US external deficit

In this paper we model the multicointegration relation, allowing for one structural break. Since multicointegration is a particular case of polynomial or I(2) cointegration, our proposal can also be applied in these cases. The paper proposes the use of a residualbased Dickey-Fuller class of statistic that accounts for one known or unknown structural break. Finite sample performance of the proposed statistic is investigated by using Monte Carlo simulations, which reveals that the statistic shows good properties in terms of empirical size and power. We complete the study with an empirical application of the sustainability of the US external deficit. Contrary to existing evidence, the consideration of one structural break leads to conclude in favour of the sustainability of the US external deficit.

Algorithm to determine the intersection curves between bezier surfaces by the solution of multivariable polynomial system and the differential marching method

The determination of the intersection curve between Bézier Surfaces may be seen as the composition of two separated problems: determining initial points and tracing the intersection curve from these points. The Bézier Surface is represented by a parametric function (polynomial with two variables) that maps a point in the tridimensional space from the bidimensional parametric space. In this article, it is proposed an algorithm to determine the initial points of the intersection curve of Bézier Surfaces, based on the solution of polynomial systems with the Projected Polyhedral Method, followed by a method for tracing the intersection curves (Marching Method with differential equations). In order to allow the use of the Projected Polyhedral Method, the equations of the system must be represented in terms of the Bernstein basis, and towards this goal it is proposed a robust and reliable algorithm to exactly transform a multivariable polynomial in terms of power basis to a polynomial written in terms of Bernstein basis .

Computational studies of deformation in stainless steel rings due to torch heating

A support ring of AISI 304L stainless steel that holds vertical, parallel wires arranged in a circle forming a cylinder is studied. The wires are attached to the ring with heat-induced shrinkage. When the ring is heated with a torch the heat affected zone tries to expand while the adjacent cool structure obstructs the expansion causing upsetting. During cooling, the ring shrinks smaller than its original size clamping the wires. The most important requirement for the ring is that it should be as round as possible and the deformations should occur as overall shrinkage in the ring diameter. A three-dimensional nonlinear transient sequential thermo-structural Abaqus model is used together with a Fortran code that enters the heat flux to each affected element. The local and overall deformations in one ring inflicted by the heating are studied with a small amount of inspection on residual stresses. A variety of different cases are chosen to be studied with the model constructed to provide directional knowledge; torch flux with the means of speed, location of the wires, heating location and structural factors. The decrease of heating speed increases heat flux that rises the temperature increasing shrinkage. In a single progressive heating uneven distribution of shrinkage appears to the start/end region that can be partially fixed with using speeded heating’s to strengthen the heating of that region. Location of the wires affect greatly to the caused shrinkage unlike heating location. The ring structure affects also greatly to the shrinkage; smaller diameter, bigger ring height, thinner thickness and greater number of wires increase shrinkage.

Gadolinium increases the vascular reactivity of rat aortic rings

Gadolinium (Gd) blocks intra- and extracellular ATP hydrolysis. We determined whether Gd affects vascular reactivity to contractile responses to phenylephrine (PHE) by blocking aortic ectonucleoside triphosphate diphosphohydrolase (E-NTPDase). Wistar rats of both sexes (260-300 g, 23 females, 7 males) were used. Experiments were performed before and after incubation of aortic rings with 3 µM Gd. Concentration-response curves to PHE (0.1 nM to 0.1 mM) were obtained in the presence and absence of endothelium, after incubation with 100 µM L-NAME, 10 µM losartan, or 10 µM enalaprilat. Gd significantly increased the maximum response (control: 72.3 ± 3.5; Gd: 101.3 ± 6.4%) and sensitivity (control: 6.6 ± 0.1; Gd: 10.5 ± 2.8%) to PHE. To investigate the blockade of E-NTDase activity by Gd, we added 1 mM ATP to the bath. ATP reduced smooth muscle tension and Gd increased its relaxing effect (control: -33.5 ± 4.1; Gd: -47.4 ± 4.1%). Endothelial damage abolished the effect of Gd on the contractile responses to PHE (control: 132.6 ± 8.6; Gd: 122.4 ± 7.1%). L-NAME + Gd in the presence of endothelium reduced PHE contractile responses (control/L-NAME: 151.1 ± 28.8; L-NAME + Gd: 67.9 ± 19% AUC). ATP hydrolysis was reduced after Gd administration, which led to ATP accumulation in the nutrient solution and reduced ADP concentration, while adenosine levels remained the same. Incubation with Gd plus losartan and enalaprilat eliminated the pressor effects of Gd. Gd increased vascular reactivity to PHE regardless of the reduction of E-NTPDase activity and adenosine production. Moreover, the increased reactivity to PHE promoted by Gd was endothelium-dependent, reducing NO bioavailability and involving an increased stimulation of angiotensin-converting enzyme and angiotensin II AT1 receptors.

Particle swarm optimization for two-connected networks with bounded rings

The Two-Connected Network with Bounded Ring (2CNBR) problem is a network design problem addressing the connection of servers to create a survivable network with limited redirections in the event of failures. Particle Swarm Optimization (PSO) is a stochastic population-based optimization technique modeled on the social behaviour of flocking birds or schooling fish. This thesis applies PSO to the 2CNBR problem. As PSO is originally designed to handle a continuous solution space, modification of the algorithm was necessary in order to adapt it for such a highly constrained discrete combinatorial optimization problem. Presented are an indirect transcription scheme for applying PSO to such discrete optimization problems and an oscillating mechanism for averting stagnation.