Generation of symmetric periodic orbits by a heteroclinic loop formed by two singular points and their invariant manifolds of dimension 1 and 2 in R3

In this paper we will find a continuous of periodic orbits passing near infinity for a class of polynomial vector fields in R3. We consider polynomial vector fields that are invariant under a symmetry with respect to a plane and that possess a “generalized heteroclinic loop” formed by two singular points e+ and e− at infinity and their invariant manifolds � and . � is an invariant manifold of dimension 1 formed by an orbit going from e− to e+, � is contained in R3 and is transversal to . is an invariant manifold of dimension 2 at infinity. In fact, is the 2–dimensional sphere at infinity in the Poincar´e compactification minus the singular points e+ and e−. The main tool for proving the existence of such periodic orbits is the construction of a Poincar´e map along the generalized heteroclinic loop together with the symmetry with respect to .

Symmetric periodic orbits near heteroclinic loops at infinity for a class of polynomial vector fields

For polynomial vector fields in R3, in general, it is very difficult to detect the existence of an open set of periodic orbits in their phase portraits. Here, we characterize a class of polynomial vector fields of arbitrary even degree having an open set of periodic orbits. The main two tools for proving this result are, first, the existence in the phase portrait of a symmetry with respect to a plane and, second, the existence of two symmetric heteroclinic loops.

Symmetric periodic orbits near a heteroclinic loop in R3 formed by two singular points, a semistable periodic orbit and their invariant manifolds

In this paper we consider C1 vector fields X in R3 having a “generalized heteroclinic loop” L which is topologically homeomorphic to the union of a 2–dimensional sphere S2 and a diameter connecting the north with the south pole. The north pole is an attractor on S2 and a repeller on . The equator of the sphere is a periodic orbit unstable in the north hemisphere and stable in the south one. The full space is topologically homeomorphic to the closed ball having as boundary the sphere S2. We also assume that the flow of X is invariant under a topological straight line symmetry on the equator plane of the ball. For each n ∈ N, by means of a convenient Poincar´e map, we prove the existence of infinitely many symmetric periodic orbits of X near L that gives n turns around L in a period. We also exhibit a class of polynomial vector fields of degree 4 in R3 satisfying this dynamics.

Symmetric periodic orbits near a heteroclinic loop formed by two singular points and their invariant manifolds of dimension 1 and 2

In this paper we consider vector fields in R3 that are invariant under a suitable symmetry and that posses a “generalized heteroclinic loop” L formed by two singular points (e+ and e −) and their invariant manifolds: one of dimension 2 (a sphere minus the points e+ and e −) and one of dimension 1 (the open diameter of the sphere having endpoints e+ and e −). In particular, we analyze the dynamics of the vector field near the heteroclinic loop L by means of a convenient Poincar´e map, and we prove the existence of infinitely many symmetric periodic orbits near L. We also study two families of vector fields satisfying this dynamics. The first one is a class of quadratic polynomial vector fields in R3, and the second one is the charged rhomboidal four body problem.

Aggregate Costs of Gender Gaps in the Labor Market: A Quantitative Estimate

[eng] This paper examines the quantitative effects of gender gaps in entrepreneurship and labor force participation on aggregate productivity and income per capita. We simulate an occupational choice model with heterogeneous agents in entrepreneurial ability, where agents choose to be workers, self-employed or employers. The model assumes that men and women have the same talent distribution, but we impose several frictions on women's opportunities and pay in the labor market. In particular, we restrict the fraction of women participating in the labor market.

Aggregate Costs of Gender Gaps in the Labor Market: A Quantitative Estimate

This paper examines the quantitative effects of gender gaps in entrepreneurship and labor force participation on aggregate productivity and income per capita. We simulate an occupational choice model with heterogeneous agents in entrepreneurial ability, where agents choose to be workers, self-employed or employers. The model assumes that men and women have the same talent distribution, but we impose several frictions on women's opportunities and pay in the labor market. In particular, we restrict the fraction of women participating in the labor market.

Aggregate Costs of Gender Gaps in the Labor Market: A Quantitative Estimate

This paper examines the quantitative effects of gender gaps in entrepreneurship and labor force participation on aggregate productivity and income per capita. We simulate an occupational choice model with heterogeneous agents in entrepreneurial ability, where agents choose to be workers, self-employed or employers. The model assumes that men and women have the same talent distribution, but we impose several frictions on women's opportunities and pay in the labor market. In particular, we restrict the fraction of women participating in the labor market.

Synchronization of symmetric chaotic systems

This paper contains a study of the synchronization by homogeneous nonlinear driving of systems that are symmetric in phase space. The main consequence of this symmetry is the ability of the response to synchronize in more than just one way to the driving systems. These different forms of synchronization are to be understood as generalized synchronization states in which the motions of drive and response are in complete correlation, but the phase space distance between them does not converge to zero. In this case the synchronization phenomenon becomes enriched because there is multistability. As a consequence, there appear multiple basins of attraction and special responses to external noise. It is shown, by means of a computer simulation of various nonlinear systems, that: (i) the decay to the generalized synchronization states is exponential, (ii) the basins of attraction are symmetric, usually complicated, frequently fractal, and robust under the changes in the parameters, and (iii) the effect of external noise is to weaken the synchronization, and in some cases to produce jumps between the various synchronization states available

From symmetric glycerol derivatives to dissymmetric chlorohydrins

The anticipated worldwide increase in biodiesel production will result in an accumulation of glycerol for which there are insufficient conventional uses. The surplus of this by-product has increased rapidly during the last decade, prompting a search for new glycerol applications. We describe here the synthesis of dissymmetric chlorohydrin esters from symmetric 1,3-dichloro-2-propyl esters obtained from glycerol. We studied the influence of two solvents: 1,4-dioxane and 1-butanol and two bases: sodium carbonate and 1-butylimidazole, on the synthesis of dissymmetric chlorohydrin esters. In addition, we studied the influence of other bases (potassium and lithium carbonates) in the reaction using 1,4-dioxane as the solvent. The highest yield was obtained using 1,4-dioxane and sodium carbonate.

Yield mapping, soil fertility and tree gaps in an orange orchard

The current high competition on Citrus industry demands from growers new management technologies for superior efficiency and sustainability. In this context, precision agriculture (PA) has developed techniques based on yield mapping and management systems that recognize field spatial variability, which contribute to increase profitability of commercial crops. Because spatial variability is often not perceived the orange orchards are still managed as uniform and adoption of PA technology on citrus farms is low. Thus, the objective of the present study was to characterize the spatial variability of three factors: fruit yield, soil fertility and occurrence of plant gaps caused by either citrus blight or huanglongbing (HLB) in a commercial Valencia orchard in Brotas, São Paulo State, Brazil. Data from volume, geographic coordinates and representative area of the bags used on harvest were recorded to generate yield points that were then interpolated to produce the yield map. Soil chemical characteristics were studied by analyzing samples collected along planting rows and inter-rows in 24 points distributed in the field. A map of density of tree gaps was produced by georeferencing individual gaps and later by counting the number of gaps within 500 m² cells. Data were submitted to statistical and geostatistical analyses. A t test was used to compare means of soil chemical characteristics between sampling regions. High variation on yield and density of tree gaps was observed from the maps. It was also demonstrated overlapping regions of high density of plant absence and low fruit yield. Soil fertility varied depending on the sampling region in the orchard. The spatial variability found on yield, soil fertility and on disease occurrence demonstrated the importance to adopt site specific nutrient management and disease control as tools to guarantee efficiency of fruit production.

Challenges for the New Century Schools for All and Narrowing Gaps through Transformation Pedagogies

La pedagogia ha tractat la qüestió de gènere i d’educació? I si és el cas, de quina manera? Quins han estat els resultats? Tant el valor de l’educació com el de gènere foren qüestionats i revisats al començament del segle XX. Els resultats d’aquelles reflexions i les batalles lluitades per millorar les condicions, comencen a sentir-se cent anys més tard. Aquest article inclourà primerament una visió general de la situació de la dona en l’educació en l’àmbit mundial. En segon lloc, se centrarà en els enfocaments pedagògics transformacionals que de manera gradual comencen a introduir-se en els sistemes educatius convencionals —també en algunes universitats i programes de traducció—, secundats d’una banda pels principis de democràcia, diàleg, carnaval, experimentació i (socio) constructivisme, i per la neurociència i la psicologia de l’altra. És evident que aquests enfocaments desafien la discriminació i afavoreixen la creació de ponts, no tan sols entre gèneres, sinó també entre etnicitats i classes social

Symmetric or asymmetric gasoline prices? A meta-analysis approach

The analysis of price asymmetries in the gasoline market is one of the most studied in the energy economics literature. Nevertheless, the great variability of results makes it very difficult to extract conclusive results on the existence or not of asymmetries. This paper shows through a meta-analysis approach how the industry segment analysed, the quality and quantity of data, the estimator and the model used may explain this heterogeneity of results.

Effect of tow-drop gaps on the damage resistance and tolerance of Variable-Stiffness Panels

This paper presents an experimental study of the effects of tow-drop gaps in Variable Stiffness Panels under drop-weight impact events. Two different configurations, with and without ply-staggering, have been manufactured by Automated Fibre Placement and compared with their baseline counterpart without defects. For the study of damage resistance, three levels of low velocity impact energy are generated with a drop-weight tower. The damage area is analysed by means of ultrasonic inspection. Results of the analysed defect configurations indicate that the influence of gap defects is only relevant under small impact energy values. However, in the case of damage tolerance, the residual compressive strength after impact does not present significant differences to that of conventional straight fibre laminates. This indicates that the strength reduction is driven mainly by the damage caused by the impact event rather than by the influence of manufacturing-induced defects

Human Capital and Regional Wage Gaps

This paper uses micro-level data to analyse the effect of human capital on regional wage differentials. The results for the set of Spanish regions confirm that they differ in the endowment of human capital, but also that the return that individuals obtain from it varies sharply across regions. Regional heterogeneity in returns is especially intense in the case of education, particularly when considering its effect on the employability of individuals. These differences in endowment and, especially, in returns to human capital, account for a significant proportion of regional wage gaps.