Splitting of separatrices in Hamiltonian systems and symplectic maps

Poincar\'e, Melnikov and Arnol'd introduced the standard method for measuring the splitting of separatrices of Hamiltonian systems. It is based on the study of the zeros of the so-called Melnikov integral, a vectorial function for three or more degrees of freedom, that gives the first-order behavior. In the most interesting cases, it turns out that the splitting is exponentially small with respect of the parameter of the perturbation, and that means that the remainder has to be bounded very carefully. The mechanism for obtaining rigorously this exponentially small splitting for the one and a half degrees of freedom Hamiltonians is reviewed, and the main ideas for its generalization to more degrees of freedom are presented. Concerning symplectic maps, the Melnikov function is not an integral anymore, but an infinite sum. Nevertheless, for meromorphic perturbations of $2D$-area preserving maps, the Melnikov function turns out to be an elliptic function, and moreover can be evaluated via residues. Furthermore, general results on non-integrability can be provided. For instance, the elliptic billiard turns out to be non-integrable when perturbed by any non-trivial entire perturbation. For more degrees of freedom, using variational arguments, the Melnikov vectorial function for a symplectic map can be deduced from a scalar function (the Melnikov potential), and the splitting of separatrices associated to hyperbolic points can also be easily detected in several situations, for instance for generalized standard maps

Stability of the phase motion in race-track microtrons

We model the phase oscillations of electrons in race-track microtrons by means of an area preserving map with a fixed point at the origin, which represents the synchronous trajectory of a reference particle in the beam. We study the nonlinear stability of the origin in terms of the synchronous phase —the phase of the synchronous particle at the injection. We estimate the size and shape of the stability domain around the origin, whose main connected component is enclosed by an invariant curve. We describe the evolution of the stability domain as the synchronous phase varies. We also clarify the role of the stable and unstable invariant curves of some hyperbolic (fixed or periodic) points.Peer ReviewedPostprint (author's final draft

What are the determinants of investment in environmental R&D?

To face the challenges posed by climate change, environmental R&D and innovation are critical factors if we hope to cut emissions; yet, investment in environmental R&D remains below the social optimum. The aim of this paper is to analyse the determinants of investment in environmental innovation and to detect the differences, if any, with the determinants of investment in general innovation. In addition, this paper examines the relationship between environmental innovation R&D expenditure and a range of policy instruments, including environmental regulation and other policy measures including R&D subsidies and environmental taxes. The empirical analysis is carried out for 22 manufacturing sectors in Spain for the period 2008-2013. To overcome problems of data availability, we construct a comprehensive database from different surveys. The main implications from our results are (1). Managerial strategy appears as a relevant driver of environmental R&D investments. (2) The establishment of a policy mix between environmental, energy and technological regulatory measures is recommended. (3) The promotion of self-regulation through actions that encourage companies to follow a policy that affects their energy efficiency and is environmentally friendly

New N-pyrazole, P-phosphine hybrid ligands and their reactivity towards Pd(II): X-ray crystal structures of complexes with [PdCl2(N,P)] core

Two new N-pyrazole, P-phosphine hybrids ligands: 1-[2-(diphenylphosphanyl)methyl]-3,5-dimethylpyrazole (LP1) and 1-[2-(diphenylphosphanyl)propyl]-3,5-dimethylpyrazole (LP3) are presented. The reaction of these two ligands and two other ligands reported in the literature: 1-[2-(diphenylphosphanyl)ethyl]-3,5-dimethylpyrazole (LP2) and 1-[2-(diphenylphosphanyl)ethyl]-3,5-diphenylpyrazole (LP4) with [PdCl2(CH3CN)2] yield [PdCl2(LP)] (LP = LP1 (1), LP2 (2), LP3 (3) and LP4 (4)) complexes. All complexes are fully characterised by analytical and spectroscopic methods and the resolution of the crystal structure of complexes 2 and 3 by single crystal X-ray diffraction is also presented. In these complexes the ligands are coordinated to Pd(II) via κ2(N,P) forming metallocycles of six (2) and seven (3) members and finish their coordination with two cis-chlorine atoms. Finally, complex 2 is studied in the palladium-catalysed C-C coupling reaction, being active even for aryl chlorides substrates

Tissue-specific effects of central leptin on the expression of genes involved in lipid metabolism in liver and white adipose tissue

Copyright (2007) The Endocrine Society .The paper can be found at the following URL on the website http://endo.endojournals.org

El territoi d'Emporion i les seves dades paleoambientals

Se aportan nuevos datos que provienen de un sondeo efectuado en las marismas del Arnpurdán (Girona). En resumen, la época ibérica se caracteriza por un aprovechamiento sostenibie de los recursos naturales y ia romana por potenciar más ei cultivo de/ oiivo que el de los cereales; ia triada cereai/oiivo/viña es más típica de los períodos medievales y posteriores. Predomina en ia zona un paisaje de ralos aicornocaies y encinares mixtos, con pocos pinos, determinado por un clima mediterráneo templado con escasas precipitaciones.New data are presented frorn a core takan frorn the wetiands of the Emporda (Girona). in summary, the iberian period is characterised by sustainable use of natural resources, whiie the Roman period shows more intensive cuitivation of olives than of cereals; the triad cereal/ olive/ vine is typicai of the medieval and iater periods. The predorninant landscape NI the area supported cork oak and other mixed species, with few pines, typical of a temperate Mediterranean ciirnate with iittle precipitation

CATÁLOGO DE LOS BRIÓFITOS DE LA PROVINCIA DE MURCIA (SURESTE DE ESPAÑA)

A check-list of the bryophytes of Murcia province is provided. Bryophyte diversity in Murcia consists of 200 taxa (74 genera) of mosses and 32 taxa (20 genera) of liverworts. Pseudocrossidium obtusulum is reported as new to the Iberian Peninsula. A total of 30 taxa are new record from Murcia: Acaulon casasianum, Astomum levieri, Bryoerythrophyllum recurvirostrum, Crossidium laevipilum, Entosthodon convexus, Grimmia dissimulata, Gymnostomum lanceolatum, Hedwigia ciliata, Orthotrichum affine, O. pumilum, O. scanicum, O. schimperi, O. striatum, O. tenellum, O. tortidontium, O. vittii, Philonotis fontana, Pleuridium acuminatum, Pohlia cruda, Pterygoneurum subsessile, Rhynchostegiella tenella, Schistidium crassipilum, Schistidium singarense, Syntrichia virescens, Tortula canescens, T. mucronifolia, Weissia brachycarpa, W. condensa var. armata, Athalamia hyalina, and Jungermannia atrovirens. Thirty eight taxa (33 mosses and 5 liverworts) are excluded from the checklist or represent doubtful reports for Murcia.Se realiza un catalogo de los briofitos de la provincia de Murcia. La diversidad briofitica de Murcia se estima en 200 taxones (74 generos) de musgos y 32 taxones de hepaticas (20 generos). Pseudocrossidium obtusulum se cita por primera vez en la Peninsula Iberica. Un total de 30 taxones son novedades para la provincia de Murcia: Acaulon casasianum, Astomum levieri, Bryoerythrophyllum recurvirostrum, Crossidium laevipilum, Entosthodon convexus, Grimmia dissimulata, Gymnostomum lanceolatum, Hedwigia ciliata, Orthotrichum affine, O. pumilum, O. scanicum, O. schimperi, O. striatum, O. tenellum, O. tortidontium, O. vittii, Philonotis fontana, Pleuridium acuminatum, Pohlia cruda, Pterygoneurum subsessile, Rhynchostegiella tenella, Schistidium crassipilum, Schistidium singarense, Syntrichia virescens, Tortula canescens, T. mucronifolia, Weissia brachycarpa, W. condensa var. armata, Athalamia hyalina y Jungermannia atrovirens. Treinta y ocho taxones (33 musgos y 5 hepaticas) se han excluido del catalogo de la provincia o se citan como dudosos

Generation of Molecular Diversity from Amino Acids. A Source for the Discovery of New TRP Channel Modulators

Trabajo presentado en el IV RECI: New Horizons in Ion Channel Research, celebrado en Cuenca (España) del 12 al 13 de febrero de 2013.Ion channels are central and challenging targets in medicinal chemistry but, because of the scarce structural knowledge, rational approaches to ion channel modulators are still rare. Moreover, the multimodal activation of some channels, like TRPs, complicates still more the scenario for rational discovery programs. Due to these facts, most strategies directed to identify ion channel modulators rely on the screening of peptide and small-molecule libraries. In this context, we have been involved in the development of synthetic pathways for the generation of diverse, chiral, highly functionalized linear and heterocyclic scaffolds from amino acids, and in the production of discrete libraries from them. The screening of these libraries on different TRP channels has allowed the discovery of some innovative hits that have progressed to hit-to-lead optimization programs. This communication will deal with the synthesis, structural characterization, and biological evaluation of a collection of β,γ–diaminoester derivatives that display significant activity at TRPV1, TRPM8 and TRPA1 channels. Compound RGM04-7, a selective.Supported by MICINN grants: Consolider-Ingenio 2010 (CSD2008-00005 and CSD2006-00015), SAF2009-09323 and BFU2009-08346, and the Generalitat Valenciana (PROMETEO/2010/046)

N′-[5-(4-Nitro­phen­yl)furan-2-yl­methyl­idene]-N,N-diphenyl­hydrazine

The title compound, C23H17N3O3, has an E configuration with respect to the C=N bond. The dihedral angle between the two phenyl rings bonded to the hydrazine group is 86.45 (13)°. The furan ring makes dihedral angles of 3.4 (2) and 7.06 (13)°, respectively, with the methyl­idenehydrazine C=N—N plane and the benzene ring