Analyticity of smooth eigenfunctions and spectral analysis of the Gauss map

We provide a sufficient condition of analyticity of infinitely differentiable eigenfunctions of operators of the form Uf(x) = integral a(x, y) f(b( x, y)) mu(dy) acting on functions f: [u, v] --> C ( evolution operators of one-dimensional dynamical systems and Markov processes have this form). We estimate from below the region of analyticity of the eigenfunctions and apply these results for studying the spectral properties of the Frobenius-Perron operator of the continuous fraction Gauss map. We prove that any infinitely differentiable eigenfunction f of this Frobenius-Perron operator, corresponding to a non-zero eigenvalue admits a (unique) analytic extension to the set C\(-infinity, 1]. Analyzing the spectrum of the Frobenius Perron operator in spaces of smooth functions, we extend significantly the domain of validity of the Mayer and Ropstorff asymptotic formula for the decay of correlations of the Gauss map.

La evolución de destinos turísticos litorales consolidados. Análisis comparado de Balneario Camnoriú (Brasil) y Benidorm (España)

El objetivo de este trabajo consiste en estudiar la evolución de los destinos turísticos litorales consolidados a partir del análisis comparado entre Balneario Camboriú y Benidorm. Se trata de dos destinos localizados en contextos territoriales y turísticos diferentes, en los que se contrastan de manera empírica los indicadores de evolución de los destinos y se vinculan las dinámicas evolutivas con el modelo territorial-turístico resultante en cada destino. El análisis realizado permite contrastar los postulados de los modelos evolutivos clásicos (Butler, 1980) e incorporar los nuevos planteamientos de la geografía económica evolutiva. La investigación delimita cronológicamente los periodos de desarrollo de ambos destinos para identificar los factores con mayor incidencia en la evolución de los mismos. Una evolución marcada, fundamentalmente, por la ubicación geográfica, la planificación y gestión urbanoturística a diferentes escalas, la dependencia de determinados mercados emisores y la influencia de factores macroeconómicos. Un conjunto de factores interrelacionados que dibujan trayectorias dispares para los destinos analizados.

Electroreduction of sulfur dioxide in some room-temperature ionic liquids

The mechanism of sulfur dioxide reduction at a platinum microelectrode was investigated by cyclic voltammetry in several room-temperature ionic liquids (RTILs)-[C(2)mim][NTf2], [C(4)mim][BF4], [C(4)mim][NO3], [C(4)mim][PF6], and [C(6)mim][Cl] where [C(2)mim] is 1-ethyl-3-methylimidazolium, [C(4)mim] is 1-butyl-3-methylimidazolium, [C(6)mim] is 1-hexyl-3-methylimidazolium, and [NTf2] is bis(trifluoromethylsufonyl)imide-with special attention paid to [C(4)mim][NO3] because of the well-defined voltammetry, high solubility, and relatively low diffusion coefficient of SO2 obtained in that ionic liquid. A cathodic peak is observed in all RTILs between -2.0 and -1.0 V versus a silver quasi-reference electrode. In [C(4)mim][NO3], the peak appears at -1.0 V, and potential step chronoamperometry was used to determine that SO2 has a very high solubility of 3100 (+/-450) mM and a diffusion coefficient of 5.0 (+/-0.8) x 10(-10) m(2) s(-1) in that ionic liquid. On the reverse wave, up to four anodic peaks are observed at ca. -0.4, -0.3, -0.2, and 0.2 V in [C(4)mim][NO3]. The cathodic wave is assigned to the reduction of SO2 to its radical anion, SO2-center dot. The peaks at -0.4 and -0.2 V are assigned to the oxidation of unsolvated and solvated SO2-center dot, respectively. The peak appearing at 0.2 V is assigned to the oxidation of either S2O42- or S2O4-center dot. The activation energy for the reduction of SO2 in [C(4)mim][NO3] was measured to be 10 (+/-2) kJ mol(-1) using chronoamperometric data at different temperatures. The stabilizing interaction of the solvent with the reduced species SO2-center dot leads to a different mechanism than that observed in conventional aprotic solvents. The high sensitivity of the system to SO2 also suggests that [C(4)mim][NO3] may be a viable solvent in gas sensing applications.

Efficient heterogeneous asymmetric catalysis of the Mukaiyama aldol reaction by silica- and ionic liquid-supported Lewis acid copper(II) complexes of bis(oxazolines)

Lewis acid complexes based on copper(II) and an imidazolium-tagged bis(oxazoline) have been used to catalyse the asymmetric Mukaiyama aldol reaction between methyl pyruvate and 1-methoxy-1-tri-methylsilyloxypropene under homogeneous and heterogeneous conditions. Although the ees obtained in ionic liquid were similar to those found in dichloromethane, there was a significant rate enhancement in the ionic liquid with reactions typically reaching completion within 2 min compared with only 55% conversion after 60 min in dichloromethane. However, this rate enhancement was offset by lower chemoselectivity in ionic liquids due to the formation of 3-hydroxy-1,3-diphenylbutan-1-one as a by-product. Supporting the catalyst on silica or an imidazolium-modified silica using the ionic liquid or in an ionic liquid-diethyl ether system completely suppressed the formation of this by-product without reducing the enantioselectivity. Although the heterogeneous systems were characterised by a drop in catalytic activity the system could be recycled up to five times without any loss in conversion or ee.

Stabilization of Ti-molecular sieve catalysts used in selective sulfoxidation reactions by ionic liquids

Sulfoxidation reactions of 4,6-dimethyl-2-methylthiopyrimidine have been performed using titanosilicate catalysts in ionic liquids, dioxane and ethanol. The ionic liquid reactions showed superior reactivity compared with molecular solvents. Moreover, on examination of the recycling of the catalyst, a significant increase in the stability of catalyst was found both in terms of recycling activity and leaching of the titanium from the catalyst. The mechanism by which the ionic liquid reduces the solubilisation of the catalysts is explored.

Oxidation of N,N,N ',N '-tetraalkyl-para-phenylenediamines in a series of room temperature ionic liquids incorporating the bis(trifluoromethylsulfonyl)imide anion

The five room temperature ionic liquids: 1-alkyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([CnMIM][N(Tf)(2)], n = 2, 4, 8, 10) and n-hexyltriethylammonium bis(trifluoromethylsulfonyl)imide ([N-6222][N(Tf)(2)]) were investigated as solvents in which to study the electrochemical oxidation of N,N,N',N'-tetramethyl-para-phenylenediamine (TMPD) and N,N,N',N'-tetrabutyl-paraphenylenediamine (TBPD), using 20 mul micro-samples under vacuum conditions. The effect of dissolved atmospheric gases on the accessible electrochemical window was probed and determined to be less significant than seen previously for ionic liquids containing alternative anions. Chronoamperometric transients recorded at a microdisk electrode were analysed via a process of non-linear curve fitting to yield values for the diffusion coefficients of the electroactive species without requiring a knowledge of their initial concentration. Comparison of experimental and simulated cyclic voltammetry was then employed to corroborate these results and allow diffusion coefficients for the electrogenerated species to be estimated. The diffusion coefficients obtained for the neutral compounds in the five ionic liquids via this analysis were, in units of 10(-11) m(2) s(-1), 2.62, 1.87, 1.12, 1.13 and 0.70 for TMPD. and 1.23, 0.80, 0.40, 0.52 and 0.24 for TBPD (listed using the same order for the ionic liquids as stated above). The most significant consequence of changing the cationic component of the ionic liquid was found to be its effect on the solvent viscosity; the diffusion coefficient of each species was found to be approximately inversely proportional to viscosity across the series of ionic liquids, in accordance with Walden's rule. (C) 2003 Elsevier B.V. All rights reserved.

2DRMP: A suite of two-dimensional R-matrix propagation codes

The R-matrix method has proved to be a remarkably stable, robust and efficient technique for solving the close-coupling equations that arise in electron and photon collisions with atoms, ions and molecules. During the last thirty-four years a series of related R-matrix program packages have been published periodically in CPC. These packages are primarily concerned with low-energy scattering where the incident energy is insufficient to ionize the target. In this paper we describe previous term2DRMP,next term a suite of two-dimensional R-matrix propagation programs aimed at creating virtual experiments on high performance and grid architectures to enable the study of electron scattering from H-like atoms and ions at intermediate energies.