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.

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.

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.

Measurement of the relative rate of prompt χ c0, χ c1 and χ c2 production at TeV

Prompt production of charmonium χ c0, χ c1 and χ c2 mesons is studied using proton-proton collisions at the LHC at a centre-of-mass energy of TeX TeV. The χ c mesons are identified through their decay to J/ψγ, with J/ψ → μ + μ − using photons that converted in the detector. A data sample, corresponding to an integrated luminosity of 1.0 fb−1 collected by the LHCb detector, is used to measure the relative prompt production rate of χ c1 and χ c2 in the rapidity range 2.0 < y < 4.5 as a function of the J/ψ transverse momentum from 3 to 20 GeV/c. First evidence for χ c0 meson production at a high-energy hadron collider is also presented.

Larock Reaction in the synthesis of heterocyclic compounds

The indole ring is one of the most common features in natural products and small molecules with important bioactivity. Larock reported a new methodology for the synthesis of the indole ring system based on the palladium-catalyzed heteroannulation of 2-iodoaniline and substituted alkyne moieties. This procedure was subsequently extended to the preparation of other nitrogen- and oxygen- containing heterocycles. This is the process of choice for the synthesis of a large number of heterocyclic derivatives, as it provides outstanding regioselectivity and good to excellent yields.

Larock Reaction in the synthesis of heterocyclic compounds

The indole ring is one of the most common features in natural products and small molecules with important bioactivity. Larock reported a new methodology for the synthesis of the indole ring system based on the palladium-catalyzed heteroannulation of 2-iodoaniline and substituted alkyne moieties. This procedure was subsequently extended to the preparation of other nitrogen- and oxygen- containing heterocycles. This is the process of choice for the synthesis of a large number of heterocyclic derivatives, as it provides outstanding regioselectivity and good to excellent yields.