When is a Riemannian submersion homogeneous?

We study the structure of the most common type of Riemannian submersions, namely those whose fibers are given by the orbits of an isometric group action on a Riemannian manifold. Special emphasis is given to the case where the ambient space has nonnegative curvature. The first author was supported by research grant MTM2004-04794-MEC. Most of this work was done during a visit of the second author to Madrid, financed in part by funds of the aforementioned grant.     

Modelling aesthetic variables in the valuation of paintings: an interval goal programming approach

The economic valuation of works of art is a decisive subject in the general field of valuation. Unlike in other areas of valuation, the explanatory power of the directly observable and quantifiable variables is very low, therefore, aesthetic criteria must be used to obtain valuation models with a greater explanatory power. Frequently, these aesthetic criteria are not always precise, and experts usually express them as an interval of values. This paper describes different valuation models that use the goal programming optimisation method to include explanatory variables of the closing price in the form of intervals of values. We have also modelled the possibility that an expert can determine the relevance of each observation in the formation of the valuation function depending on the degree of precision with which the variables have been defined.     

Coupled-column liquid chromatography method with photochemically induced derivatization for the direct determination of benzoylureas in vegetables

The coupled-column (LC-LC) system, consisting of a first column packed with internal surface reversed phase (ISRP) (50 x 4.6mm ID) and a Chrompack C18 (100 x 4.6 mm ID) as second column, allowed the simultaneous determination of five benzoylurea insecticides in dichloromethane (CH2Cl2) extracts of vegetable samples without any clean-up step. This system was combined with a photochemically induced fluorescence (PIF) post-column derivatization in order to provide strongly fluorescent photoproducts from the non-fluorescent benzoylureas. Limits of detection ranged from 0.21 to 0.98 microg L(-1) of pesticide (equivalent to 0.14-0.65 microg kg(-1) in vegetable samples) and limits of determination ranged from 4.0 to 10.0 microg L(-1) (equivalent to 2.7-6.7 microg kg(-1)). Linearity of the method was established between 2 and 1800 microg L(-1), depending upon the compound. Validation of the total method was performed by randomly analyzing recoveries of four vegetable samples (aubergine, cucumber, green bean, and tomato) spiked at two levels of concentration (10.0 and 33.3 microg kg(-1)). The combination of the LC-LC system with PIF detection provides a sensitive, selective, and rapid method for the determination of pesticides in vegetable samples at levels lower than the maximum residue levels (MRLs) established for these compounds by Spanish legislation.     

Cellulose microfibrils from banana farming residues: isolation and characterization

Cellulose microfibrils have been prepared from banana rachis using a combination of chemical and mechanical treatments. The morphology and structure of the samples were characterized using transmission electron microscopy, atomic force microscopy, and X-ray diffraction. Fourier-transformed infrared spectroscopy (FTIR) was used to characterize the chemical modifications of the samples after each treatment. Suspensions of bundled or individualized 5-nm-wide microfibrils were obtained after homogenization (PH) whereas an organosolv (PO) treatment resulted in shorter aggregates of parallel cellulose microcrystallites. The sharper rings in the X-ray diffraction pattern of the PO-treated sample suggest a higher crystallinity due to a more efficient removal of hemicelluloses and dissolution of amorphous zones by the acid treatment. Both microfibrils and microcrystals prepared by both methods can be used as reinforcing filler in nanocomposite materials.     

Reactions of a ruthenium(II) arene antitumor complex with cysteine and methionine

The Ru(II) organometallic antitumor complex [(eta(6)-biphenyl)RuCl(en)][PF(6)] (1) reacts slowly with the amino acid L-cysteine (L-CysH(2)) in aqueous solution at 310 K. Reactions were followed over periods of up to 48 h using HPLC, electronic absorption spectroscopy, LC-ESI-MS, and 1D or 2D (1)H and (15)N NMR spectroscopy. Reactions at a 1 mM/2 mM (Ru/L-CysH(2)) ratio were multiphasic in acidic solutions (pH 5.1) and appeared to involve aquation as the first step. Initially, 1:1 adducts involving substitution of Cl by S-bound or O-bound L-CysH(2), [(eta(6)-biphenyl)Ru(S-L-CysH)(en)](+) (4a) and [(eta(6)-biphenyl)Ru(O-L-CysH(2))(en)](2+) (4b) formed, followed by the cystine adduct [(eta(6)-biphenyl)Ru(O-Cys(2)H(2))(en)](2+) (3), and two dinuclear complexes from which half or all of the chelated ethylenediamine had been displaced, [(eta(6)-biphenyl)Ru(H(2)O)(microS,N-L-Cys)Ru(eta(6)-biphenyl)(en)](2+) (5) containing one bridging cysteine, and [(eta(6)-biphenyl)Ru(O,N-L-Cys-S)(S-L-Cys-N)Ru(eta(6)-biphenyl)(H(2)O)] (6) containing two bridging cysteines. The unusual cluster species [(biphenyl)Ru](8) (7a) was also detected by MS and was more prevalent in reactions at higher L-CysH(2) concentrations. Complex 5 was the dominant product at pH 2-5, but overall, only ca. 50% of 1 reacted with L-CysH(2) in these conditions. The reaction between 1 and L-CysH(2) was suppressed in 50 mM triethylammonium acetate solution at pH > 5 or in 100 mM NaCl. Only 27% of complex 1 reacted with L-methionine (L-MetH) at an initial pH of 5.7 after 48 h at 310 K and gave rise to only one adduct [(eta(6)-biphenyl)Ru(S-L-MetH)(en)](2+) (8).     

Three oxo complexes with a tetra­nuclear [Cu4(μ2‐Cl)6(μ4‐O)] unit

The three title compounds, namely 4‐phenyl‐1H‐imidazolium hexa‐μ₂‐chloro‐chloro‐μ₄‐oxo‐tris­(4‐phenyl‐1H‐imidazole‐κN¹)­tetra­copper(II) monohydrate, (C₉H₉N₂)[Cu₄Cl₇O(C₉H₈N₂)₃]·H₂O, hexa‐μ₂‐chloro‐μ₄‐oxo‐tetra­kis­(pyridine N‐oxide‐κO)tetra­copper(II), [Cu₄Cl₆O(C₅H₅NO)₄], and hexa‐μ₂‐chloro‐tetra­kis(2‐methyl‐1H‐imidazole‐κN¹)‐μ₄‐oxo‐tetra­copper(II) methanol trisolvate, [Cu₄Cl₆O(C₄H₆N₂)₄]·3CH₄O, exhibit the same Cu₄OCl₆ framework, where the O atom at the centre of an almost regular tetra­hedron bridges four copper cations at the corners. This group is in turn surrounded by a Cl₆ octa­hedron, leading to a rather globular species. This special arrangement of the Cu^II cations results in a diversity of magnetic behaviours.     

On the reactivity of naphthalene and biphenyl dianions: tying up loose ends concerning an SN2‐ET dichotomy in alkylation reactions

Naphthalene and biphenyl dianions are interesting compounds that can be obtained by double reduction of the corresponding arenes in solution with certain alkali metals. These dianions are highly reactive and rather elusive species with very high laying and highly delocalized electrons. They share many aspects of the reactivity of the alkali metal they originated from and consequently behave primarily as strong electron transfer (ET) reagents. We report here kinetic evidence for a different type of reactivity in their alkylation reactions with alkyl fluorides. By using cyclopropylmethyl fluoride (c‐C₃H₅CH₂F) as a very fast radical probe, we were able to settle that this alkylation does not involve the classical electron transfer reaction followed by radical coupling between diffusing radicals, but supports the alternative S_N2 concerted mechanism, discerning thus this mechanistic S_N2‐ET dichotomy. Copyright © 2015 John Wiley & Sons, Ltd.     

Parallel connections over symmetric spaces

Let M be a simply connected Riemannian symmetric space, with at most one flat direction. We show that every Riemannian (or unitary) vector bundle with parallel curvature over M is an associated vector bundle of a canonical principal bundle, with the connection inherited from the principal bundle. The problem of finding Riemannian (or unitary) vector bundles with parallel curvature then reduces to finding representations of the structure group of the canonical principal bundle.     

Surface free energy of films of alkali-treated cellulose microfibrils from banana rachis

Cellulose microfibrils extracted by various alkaline treatments of vascular bundles from banana rachis were used to elaborate films. The films were comparatively studied to determine changes in polarity induced by various treatments. Atomic force microscopy was used to characterize the surface morphology of the films and transmission electron microscopy was employed to characterize the microfibrils used to elaborate the films. Contact angles were measured to determine surface free energy (SFE) and thermogravimetric analyses were carried out to determine changes in composition of the films. The results showed that the films of cellulose microfibrils prepared by the peroxide alkaline (PA) and peroxide alkaline-hydrochloric acid (PA-HCl) treatments had lower content of non-cellulosic constituents like xylose and had lower SFE than films of microfibrils treated with KOH-5. Furthermore, specimens treated with the most concentrated KOH solution (18 wt%) and sodium chloride presented the highest SFE and polar component.     

Mixed valuation methods: a combined AHP-GP procedure for individual and group multicriteria agricultural valuation

This paper introduces a new assessment method classification, in which a third procedure, mixed valuation, is jointly included with the traditional economic and non-economic methodologies. The paper considers a case of multiple actors (from a previous work by the same authors—Aznar et al. (Estudios de Economía Aplicada, 25(2):389–409, 2007), in which a new technique for multicriteria agriculture valuation (MAVAM) was proposed. The method is specifically designed for situations in which scarce information about the elements being compared (quantified or not) is available. It works in individual and group decision making contexts and attempts to both obtain and incorporate the objective information associated with the tangible aspects of the problem and the subjective knowledge associated with the human factor into the valuation process. It combines two of the most extended multicriteria decision making techniques: the Analytic Hierarchy Process (AHP) and Goal Programming (GP). The first of these enables tangible and intangible information stemming from known elements to be collected by using pairwise comparisons; the second allows the scarce information available and the personal approach to the valuation to be included in the valuation process. The proposed methodology is illustrated by means of its application to a case of individual and group valuation of an agricultural asset in the La Ribera district, Valencia (Spain).