On singular perturbations of superlinear elliptic systems

We study the existence, multiplicity and shape of positive solutions of the system −ε²Δu+V(x)u=K(x)g(v), −ε²Δv+V(x)v=H(x)f(u) in RN, as ε→0. The functions f and g are power-like nonlinearities with superlinear and subcritical growth at infinity, and V, H, K are positive and locally Hölder continuous.     

On Jensen-McShane’s inequality

A sequence of inequalities which include McShane’s generalization of Jensen’s inequality for isotonic positive linear functionals and convex functions are proved and compared with results in [3]. As applications some results for the means are pointed out. Moreover, further inequalities of Hölder type are presented.     

Some equivalent problems in set optimization

Given a set-valued optimization problem (P), there is more than one way of defining the solutions associated with it. Depending on the decision maker’s preference, we consider the vector criterion or the set criterion. Both criteria of solution are considered together to solve problem (P) by reducing the feasible set.     

Likelihood stabilization for ill-conditioned vector GARCH models

The likelihood of vector GARCH models is ill-conditioned because of two facts. First, when the series display high correlations, as often happens with financial data, some eigenvalues of the conditional covariance matrix are close to zero. Second, the likelihood function is very flat in the neighborhood of the optimum due to the functional form of the GARCH process. These facts explain the instability of multivariate GARCH estimation procedures. Building on this analysis, we suggest a data transformation which moves the critical eigenvalues far from zero and, therefore, improves the stability of iterative optimization methods. The transformed values are re-scaled principal components, so their interpretation is straightforward. The application of this technique is illustrated by modeling the short-run conditional correlations of four nominal exchange rates.      

Fast 2D NMR ligand screening using Hadamard spectroscopy

Fast 2D NMR-based screening can be achieved using Hadamard encoded spectroscopy to focus on the signals of interest (e.g., enzyme active or ligand recognition sites). By recording a set of Hadamard spectra (a "Hadamard constellation") with relative offsets comparable to the excitation bandwidth, quantitative ligand-induced shifts can be obtained from peak intensities.     

Dihydrogen to dihydride isomerization mechanism in [(C5Me5)FeH2(Ph2PCH2CH2PPh2)]+ through the experimental and theoretical analysis of kinetic isotope effects

The isomerization of complex [Cp*Fe(dppe)(eta2-H2)]+, generated in situ by low-temperature protonation of Cp*Fe(dppe)H with either HBF4 or CF3COOH, to the dihydride tautomer trans-[Cp*Fe(dppe)(H)2]+ is irreversible and follows first-order kinetics in the -10 to +15 degrees C range with Delta H double dagger = 21.6 +/- 0.8 kcal mol(-1) and DeltaS double dagger = 5 +/- 3 eu. The isomerization rate constant is essentially independent of the nature and quantity of a strong acid. Density functional theory (DFT) calculations on various models, including the complete system at both the quantum mechanics/molecular mechanics (QM/MM) and full QM levels, probe the relative importance of steric and electronic effects for the relative stability of the nonclassical and classical isomers and identify two likely isomerization mechanisms: a "direct" pathway involving simultaneous H-H bond breaking and cis-trans isomerization and a "via Cp" pathway involving agostic C5Me5H intermediates. Both pathways are characterized by activation energies in close correspondence with the experimental value (21.3 and 22.2 kcal mol(-1), respectively). Further kinetic studies were carried out for the Cp*Fe(dppe)H + CF3COOD and Cp*Fe(dppe)D + CF3COOD systems at 273 K. The [Cp*Fe(dppe)(eta2-HD)]+ complex establishes a very rapid isotope redistribution equilibrium with the eta2-H2 and eta2-D2 analogues. The equilibrium constant value (K = 3.3 +/- 0.3) indicates a significant equilibrium isotope effect. Simulation of the rate data provides access to the individual isomerization rate constants kHH, kHD, and kDD for the three isotopomers, yielding kinetic isotope effects: kHH/kHD = 1.24 +/- 0.01 and kHD/kDD = 1.58 +/- 0.01 (and, consequently, kHH/kDD = 1.96 +/- 0.02). The analysis of the DFT-calculated frequencies, using the [Cp*Fe(dhpe)H2]+ model system, for the [Cp*Fe(dhpe)(eta2-XY)]+ isotopomers as well as transition states for the "direct" (TSdir) and "via Cp" (TSrot) pathways (X = H, D) allowed the computation of the expected isotope effects. A comparison with the experiment strongly suggests that the mechanism occurs via the "direct" pathway for the present system, although the small difference in the calculated energy barriers suggests that the "via Cp" pathway may be preferred in other cases.     

Two- and three-dimensional networks of gadolinium(III) with dicarboxylate ligands: synthesis, crystal structure, and magnetic properties

Four gadolinium(III) complexes with dicarboxylate ligands of formulas [Gd2(mal)3(H2O)5]n.2nH2O (1), [Gd2(mal)3(H2O)6]n (2), [NaGd(mal)(ox)(H2O)3]n (3), and [Gd2(ox)3(H2O)6]n.2.5nH2O (4) (mal = malonate; ox = oxalate) have been prepared, and their magnetic properties have been investigated as a function of the temperature. The structures of 1-3 have been determined by X-ray diffraction methods. The crystal structure of 4 was already known, and it is made of hexagonal layers of Gd atoms that are bridged by bis-bidentate oxalate. Compound 1 is isostructural with the europium(III) malonate complex [Eu2(mal)3(H2O)5]n.2nH2O,1 whose structure was reported elsewhere. The Gd atoms in 1 define a two-dimensional network where a terminal bidentate and bridging bidentate/bis-monodentate and tris-bidentate coordination modes of malonate occur. Compound 2 has a three-dimensional structure with a structural phase transition at 226 K, which involves a change of the space group from I2/a to Ia. Although its structure at room temperature was already known, that below 226 K was not. Pairs of Gd atoms with a double oxo-carboxylate bridge occur in both phases, and the main differences between both structures deal with the Gd environment and the H-bond pattern. 3 is also a three-dimensional compound, and it was obtained by reacting Gd(III) ions with malonic acid in a silica gel medium. Oxalic acid results as an oxidized product of the malonic acid, and single crystals of the heteroleptic complex were produced. The Gd atoms in 3 are connected through bis-bidentate oxalate and carboxylate-malonate bridges in the anti-anti and anti-syn coordination modes. Compounds 1 and 2 exhibit weak but significant ferromagnetic couplings between the Gd(III) ions through the single (1) and double (2) oxo-carboxylate bridges, whereas antiferromagnetic interactions across the bis-bidentate oxalate account for the overall antiferromagnetic behavior observed in 3 and 4.     

Stabilization of NH tautomers of quinolines by osmium and ruthenium

Complexes OsH2Cl2(PiPr3)2 and RuH2Cl2(PiPr3)2 promote the tautomerization of quinoline and 8-methylquinoline to NH tautomers, which lie about 44 kcal.mol-1 above the usual CH tautomers. The NH tautomers are stabilized by coordination to the metal center and by means of a Cl...HN interaction. As a consequence, the six-coordinate elongated dihydrogen complexes OsCl2{kappa-C2-(HNC9H5R)}(eta2-H2)(PiPr3)2, the five-coordinate derivatives RuCl2{kappa-C2-(HNC9H5R)}(PiPr3)2, and the six-coordinate dihydrogen compounds RuCl2{kappa-C2-(HNC9H5R)}(eta2-H2)(PiPr3)2 (R = H, Me) have been isolated and characterized.     

Combination of mid- and near-infrared spectroscopy for the determination of the quality properties of beers

The combination of infrared (MIR) and near-infrared (NIR) spectroscopy has been employed for the determination of important quality parameters of beers, such as original and real extract and alcohol content. A population of 43 samples obtained from the Spanish market and including different types of beer, was evaluated. For each technique, spectra were obtained in triplicate. In the case of NIR a 1 mm pathlength quartz flow cell was used, whereas attenuated total reflectance measurements were used in MIR. Cluster hierarchical analysis was employed to select calibration and validation data sets. The calibration set was composed of 15 samples, thus leaving 28 for validation. A critical evaluation of the prediction capability of multivariate methods established from the combination of NIR and MIR spectra was made. Partial least squares (PLS) and artificial neural networks (ANN) were evaluated for the treatment of data obtained in each individual technique and the combination of both. Different parameters of each methodology were optimized. A slightly better predictive performance was obtained for NIR-MIR combined spectra, and in all the cases ANN performs better than PLS, which may be interpreted from the existence of some non-linearity in the data. The root-mean-sqare-error of prediction (RMSEP) values obtained for the combined NIR-MIR spectra for the determination of real extract, original extract and ethanol were 0.076% w/w, 0.14% w/w and 0.091% v/v.