Wecken type problems for self-maps of the Klein bottle

We consider various problems regarding roots and coincidence points for maps into the Klein bottle . The root problem where the target is and the domain is a compact surface with non-positive Euler characteristic is studied. Results similar to those when the target is the torus are obtained. The Wecken property for coincidences from to is established, and we also obtain the following 1-parameter result. Families which are coincidence free but any homotopy between and , , creates a coincidence with . This is done for any pair of maps such that the Nielsen coincidence number is zero. Finally, we exhibit one such family where is the constant map and if we allow for homotopies of , then we can find a coincidence free pair of homotopies.

Robust tori-like Lagrangian coherent structures

In general the term "Lagrangian coherent structure" (LCS) is used to make reference about structures whose properties are similar to a time-dependent analog of stable and unstable manifolds from a hyperbolic fixed point in Hamiltonian systems. Recently, the term LCS was used to describe a different type of structure, whose properties are similar to those of invariant tori in certain classes of two-dimensional incompressible flows. A new kind of LCS was obtained. It consists of barriers, called robust tori that block the trajectories in certain regions of the phase space. We used the Double-Gyre Flow system as the model. In this system, the robust tori play the role of a skeleton for the dynamics and block, horizontally, vortices that come from different parts of the phase space. (C) 2012 Elsevier B.V. All rights reserved.

On global linearization of planar involutions

Let phi: a"e(2) -> a"e(2) be an orientation-preserving C (1) involution such that phi(0) = 0. Let Spc(phi) = {Eigenvalues of D phi(p) | p a a"e(2)}. We prove that if Spc(phi) aS, a"e or Spc(phi) a (c) [1, 1 + epsilon) = a... for some epsilon > 0, then phi is globally C (1) conjugate to the linear involution D phi(0) via the conjugacy h = (I + D phi(0)phi)/2,where I: a"e(2) -> a"e(2) is the identity map. Similarly, we prove that if phi is an orientation-reversing C (1) involution such that phi(0) = 0 and Trace (D phi(0)D phi(p) > - 1 for all p a a"e(2), then phi is globally C (1) conjugate to the linear involution D phi(0) via the conjugacy h. Finally, we show that h may fail to be a global linearization of phi if the above conditions are not fulfilled.

Homogeneous structures and rigidity of isoparametric submanifolds in Hilbert space

We study isoparametric submanifolds of rank at least two in a separable Hilbert space, which are known to be homogeneous by the main result in [E. Heintze and X. Liu, Ann. of Math. (2), 149 (1999), 149-181], and with such a submanifold M and a point x in M we associate a canonical homogeneous structure I" (x) (a certain bilinear map defined on a subspace of T (x) M x T (x) M). We prove that I" (x) , together with the second fundamental form alpha (x) , encodes all the information about M, and we deduce from this the rigidity result that M is completely determined by alpha (x) and (Delta alpha) (x) , thereby making such submanifolds accessible to classification. As an essential step, we show that the one-parameter groups of isometries constructed in [E. Heintze and X. Liu, Ann. of Math. (2), 149 (1999), 149-181] to prove their homogeneity induce smooth and hence everywhere defined Killing fields, implying the continuity of I" (this result also seems to close a gap in [U. Christ, J. Differential Geom., 62 (2002), 1-15]). Here an important tool is the introduction of affine root systems of isoparametric submanifolds.

A model of road effect using line integrals and a test of the performance of two new road indices using the distribution of small mammals in an Atlantic Forest landscape

Effects of roads on wildlife and its habitat have been measured using metrics, such as the nearest road distance, road density, and effective mesh size. In this work we introduce two new indices: (1) Integral Road Effect (IRE), which measured the sum effects of points in a road at a fixed point in the forest; and (2) Average Value of the Infinitesimal Road Effect (AVIRE), which measured the average of the effects of roads at this point. IRE is formally defined as the line integral of a special function (the infinitesimal road effect) along the curves that model the roads, whereas AVIRE is the quotient of IRE by the length of the roads. Combining tools of ArcGIS software with a numerical algorithm, we calculated these and other road and habitat cover indices in a sample of points in a human-modified landscape in the Brazilian Atlantic Forest, where data on the abundance of two groups of small mammals (forest specialists and habitat generalists) were collected in the field. We then compared through the Akaike Information Criterion (AIC) a set of candidate regression models to explain the variation in small mammal abundance, including models with our two new road indices (AVIRE and IRE) or models with other road effect indices (nearest road distance, mesh size, and road density), and reference models (containing only habitat indices, or only the intercept without the effect of any variable). Compared to other road effect indices, AVIRE showed the best performance to explain abundance of forest specialist species, whereas the nearest road distance obtained the best performance to generalist species. AVIRE and habitat together were included in the best model for both small mammal groups, that is, higher abundance of specialist and generalist small mammals occurred where there is lower average road effect (less AVIRE) and more habitat. Moreover, AVIRE was not significantly correlated with habitat cover of specialists and generalists differing from the other road effect indices, except mesh size, which allows for separating the effect of roads from the effect of habitat on small mammal communities. We suggest that the proposed indices and GIS procedures could also be useful to describe other spatial ecological phenomena, such as edge effect in habitat fragments. (C) 2012 Elsevier B.V. All rights reserved.

Secondary nontwist phenomena in area-preserving maps

Phenomena as reconnection scenarios, periodic-orbit collisions, and primary shearless tori have been recognized as features of nontwist maps. Recently, these phenomena and secondary shearless tori were analytically predicted for generic maps in the neighborhood of the tripling bifurcation of an elliptic fixed point. In this paper, we apply a numerical procedure to find internal rotation number profiles that highlight the creation of periodic orbits within islands of stability by a saddle-center bifurcation that emerges out a secondary shearless torus. In addition to the analytical predictions, our numerical procedure applied to the twist and nontwist standard maps reveals that the atypical secondary shearless torus occurs not only near a tripling bifurcation of the fixed point but also near a quadrupling bifurcation. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4750040]

Hero's journey in bifurcation diagram

The hero's journey is a narrative structure identified by several authors in comparative studies on folklore and mythology. This storytelling template presents the stages of inner metamorphosis undergone by the protagonist after being called to an adventure. In a simplified version, this journey is divided into three acts separated by two crucial moments. Here we propose a discrete-time dynamical system for representing the protagonist's evolution. The suffering along the journey is taken as the control parameter of this system. The bifurcation diagram exhibits stationary, periodic and chaotic behaviors. In this diagram, there are transition from fixed point to chaos and transition from limit cycle to fixed point. We found that the values of the control parameter corresponding to these two transitions are in quantitative agreement with the two critical moments of the three-act hero's journey identified in 10 movies appearing in the list of the 200 worldwide highest-grossing films. (C) 2011 Elsevier B.V. All rights reserved.

An algorithm for the strip packing problem using collision free region and exact fitting placement

The irregular shape packing problem is approached. The container has a fixed width and an open dimension to be minimized. The proposed algorithm constructively creates the solution using an ordered list of items and a placement heuristic. Simulated annealing is the adopted metaheuristic to solve the optimization problem. A two-level algorithm is used to minimize the open dimension of the container. To ensure feasible layouts, the concept of collision free region is used. A collision free region represents all possible translations for an item to be placed and may be degenerated. For a moving item, the proposed placement heuristic detects the presence of exact fits (when the item is fully constrained by its surroundings) and exact slides (when the item position is constrained in all but one direction). The relevance of these positions is analyzed and a new placement heuristic is proposed. Computational comparisons on benchmark problems show that the proposed algorithm generated highly competitive solutions. Moreover, our algorithm updated some best known results. (C) 2012 Elsevier Ltd. All rights reserved.

The influence of the degree of back-mixing on hydrogen production in an anaerobic fixed-bed reactor

This paper reports on results obtained from experiments carried out in an acidogenic anaerobic reactor aiming at the optimization of hydrogen production by altering the degree of back-mixing. It was hypothesized that there is an optimum operating point that maximizes the hydrogen yield. Experiments were performed in a packed-bed bioreactor by covering a broad range of recycle ratios (R) and the optimum point was obtained for an R value of 0.6. In this operating condition the reactor behaved as 8 continuous stirred-tank reactors in series and the maximum yield was 4.22 mol H-2 mol sucrose(-1). Such optimum point was estimated by deriving a polynomial function fitted to experimental data and it was obtained as the conjugation of three factors related to the various degrees of back-mixing applied to the reactor: mass transfer from the bulk liquid to the biocatalyst, liquid-to-gas mass transfer and the kinetic behavior of irreversible reactions in series. Copyright (C) 2012, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.

Serologic and molecular diagnostic and bioassay in mice for detection of Toxoplasma gondii in free ranges chickens from Pantanal of Mato Grosso do Sul

Holsback L., Pena H.F.J., Ragozo A., Lopes E. G., Gennari S. M. & Soares R. M. 2012. Serologic and molecular diagnostic and bioassay in mice for detection of Toxoplasma gondii in free range chickens from Pantanal of Mato Grosso do Sul. Pesquisa Veterinaria Brasileira 32(8): 721-726. Setor de Veterinaria e Producao Animal, Universidade Estadual do Norte do Parana, Campus Luiz Meneghel, Rodovia BR 369 Km 54, Bandeirantes, PR 86360-000, Brazil. E-mail: lhsfertonani@uenp.edu.br The aim of this study was to investigate the occurrence of Toxoplasma gondii and compare the results obtained in the Modified Agglutination Test (MAT), Polimerase Chain Reaction (PCR) and bioassay in mice. In order to accomplish this, 40 free-range chickens from eight farms in neighboring areas to the Pantanal in Nhecolandia, Mato Grosso do Sul, were euthanized and blood samples, brain and heart were collected. The occurrence of anti-T. gondii antibodies found in chickens was 67.5% (27 samples), considering as a cutoff point the dilution 1:5. Among the samples analyzed, 7 (25.9%) were positive in the dilution 1: 5, 3 (11.1%) in 1: 10, 2 (7.4%) in 1: 20, 3 (11.1%) in 1: 320, 1 (3.7%) in 1: 640, 3 (11.1%) in 1: 1280, 2 (7.4%) in 1: 2560, 4 (14.8%) in 1: 5120 and 2 (7.4%) in 1: 10.240. From the mixture of tissue samples (brain and heart) from the chickens analyzed, 16 (40%) presented electrophoretic bands compatible with T. gondii by PCR (gene B1). In the comparison of techniques, 59.26% positivity in PCR was revealed among animals that were seropositive in MAT (cutoff 1: 5). From 141 inoculated mice, six (4.44%) died of acute toxoplasmosis between 15 and 23 days after inoculation. Surviving mice were sacrificed at 74 days after inoculation, and a total of 28 cysts were found in the brains of 10 distinct groups. From the seropositive hens, 27 bioassays were performed and 11 (40.7%) isolates were obtained. A greater number of isolations happened in mice that were inoculated with tissues from chickens that had high titers for anti-T. gondii antibodies. Chronic infection in mice was observed in nine groups (33.3%) from five different properties. Among the surviving mice, 25.6% were positive for T. gondii in MAT (1: 25). From mice positive in PCR, 87.5% were also positive in MAT. Among the PCR-negative mice, 5.2% were positive for T. gondii in MAT. It can be concluded through this study that the occurrence of infecton by T. gondii in the rural properties studied was high, that PCR directed to gene B1 does not confirm the viability of the parasite, but it can be used as a screening method for the selection of chickens infected by T. gondii, that the animals with titer greater than 10 must be prioritized for the selection of animals for bioassay, since for them, the chances of isolating the parasite are greater and that seroconversion in experimentally infected mice is not a good indicator for isolating the agent.

Mini-implant insertion based on tooth crown references: a guide-free technique

Mini-implant insertion requires accurate surgical technique. This study shows an insertion technique using only tooth crown references; its scientific basis is evaluated radiographically. The sample consisted of 213 inter-radicular septa, evaluated in 53 bitewing radiographs. The proximal contour of adjacent tooth crowns was used to define septum width. The midpoint of the septum width was linked to the interdental contact point to determine septum midline. The distances from septum midline to "mesial and distal teeth were measured to evaluate the septum midline centralization degree in two different septum heights. The difference between mesial and distal distances represented the septum midline deviation degree. The mesial and distal distances were compared by t-tests, and the septum midline deviation was correlated with septum height using Pearson's correlation test. The mesial and distal distances were not statistically different in the midpoint of the septum height, but they were different at the apical septum height. There was a moderate correlation (r = 0.45) between septum midline deviation and septum height. The tooth crown references evaluated on interproximal radiographs determine a high centralization degree of the septum midline on which the insertion site could be defined. The greater centralization degree was observed at the coronal septum area.

Gaussian deconvolution: a useful method for a form-free modeling of scattering data from mono- and multilayered planar systems

A new method for analysis of scattering data from lamellar bilayer systems is presented. The method employs a form-free description of the cross-section structure of the bilayer and the fit is performed directly to the scattering data, introducing also a structure factor when required. The cross-section structure (electron density profile in the case of X-ray scattering) is described by a set of Gaussian functions and the technique is termed Gaussian deconvolution. The coefficients of the Gaussians are optimized using a constrained least-squares routine that induces smoothness of the electron density profile. The optimization is coupled with the point-of-inflection method for determining the optimal weight of the smoothness. With the new approach, it is possible to optimize simultaneously the form factor, structure factor and several other parameters in the model. The applicability of this method is demonstrated by using it in a study of a multilamellar system composed of lecithin bilayers, where the form factor and structure factor are obtained simultaneously, and the obtained results provided new insight into this very well known system.