Spaces of idempotent measures of compact metric spaces

We investigate certain geometric properties of the spaces of idempotent measures. In particular, we prove that the space of idempotent measures on an infinite compact metric space is homeomorphic to the Hilbert cube.     

On differential properties for bivariate orthogonal polynomials

In this paper, we consider bivariate orthogonal polynomials associated with a quasi-definite moment functional which satisfies a Pearson-type partial differential equation. For these polynomials differential properties are obtained. In particular, we deduce some structure and orthogonality relations for the successive partial derivatives of the polynomials.      

Asymmetric Synthesis of Fluorinated Isoindolinones through Palladium‐Catalyzed Carbonylative Amination of Enantioenriched Benzylic Carbamates

The asymmetric synthesis of fluorinated isoindolinones has been achieved by a palladium‐catalyzed aminocarbonylation reaction of the corresponding α‐fluoroalkyl o‐iodobenzylamines. A base‐mediated anti β‐hydride elimination process was suggested to explain the partial erosion of the optical purity observed in some cases. This mechanistic rationale enabled the minimization of this partial racemization by fine‐tuning the pK_a of the base.     

Potentiometric Studies on the Equilibria of Flufenamic Acid in Aqueous Solutions and in Two-phase Organic Solvent + Water Systems

In this paper, the flufenamic acid equilibria in aqueous solution and in two-phase organic solvent + aqueous solution are described and presented. The dissociation constants K _a1 and K _a2 were determined in MDM + water mixtures. The Yashuda-Shedlovsky extrapolation procedure has been used to obtain the values of K _a1 and K _a2 in aqueous solutions. The distribution ratio D was measured in the toluene + water system over a wide range of pH by the shaking flask method. Based on the results of potentiometric titrations in two-phase organic solvent (benzene, ethylbenzene, toluene, carbon tetrachloride, chloroform, chlorobenzene, and bromobenzene) + aqueous systems, and using models of single and multistep equilibria, the values of distribution constants K _D and dimerization constants K _dim were calculated. The influences of polarity of the applied solvents and pH of the aqueous phase, on the speciation of the particular forms of flufenamic acid in both phases, were demonstrated.     

Binuclear zinc(II) complexes with the anti-inflammatory compounds salicylaldehyde semicarbazone and salicylaldehyde-4-chlorobenzoyl hydrazone (H2LASSBio-1064)

Complexes [Zn₂(HL¹)₂(CH₃COO)₂] (1) and [Zn₂(L²)₂] (2) were synthesized with salicylaldehyde semicarbazone (H₂L¹) and salicylaldehyde-4-chlorobenzoyl hydrazone (H₂LASSBio-1064, H₂L²), respectively. The crystal structure of (1) was determined. Upon recrystallization of previously prepared [Zn₂(HL²)₂(Cl)₂] (3) in 1:9 DMSO:acetone crystals of [Zn₂(L²)₂(H₂O)₂]·[Zn₂(L²)₂(DMSO)₄] (3a) were obtained. The crystal structure of 3a was also determined. All crystal structures revealed the presence of phenoxo-bridged binuclear zinc(II) complexes.     

A fast and efficient one-pot microwave assisted synthesis of variously di-substituted 1,2,4-oxadiazoles

A one-pot two-step microwave assisted synthesis of variously disubstituted 1,2,4-oxadiazoles from carboxylic acids and amidoximes is reported. This methodology is characterized by short reaction times, is versatile, robust and high-yielding and allows for the preparation of heterocycles with a stereocenter with 100% enantiomeric purity.     

Liquid phase microextraction applications in food analysis

Over the last years, liquid-phase microextraction (LPME) in its different application modes (single drop microextraction, dispersive liquid-liquid microextraction and hollow fiber-LPME) has been increasingly applied for the extraction of both inorganic and organic analytes from different matrices. Its advantages over conventional extraction procedures (simplicity, effectiveness, rapidity and low consumption of organic solvents) has also attracted its application in the complex food analysis field, in which it has clearly provided good and challenging results. A comprehensive review dealing with those articles published since its introduction till the end of March 2011 is presented, offering also a critical vision of the analytical potential of LPME for the analysis of foods.     

Shooting methods for a PT-symmetric periodic eigenvalue problem

We present a rigorous analysis of the performance of some one-step discretization schemes for a class of PT-symmetric singular boundary eigenvalue problem which encompasses a number of different problems whose investigation has been inspired by the 2003 article of Benilov et al. (J Fluid Mech 497:201–224, 2003). These discretization schemes are analyzed as initial value problems rather than as discrete boundary problems, since this is the setting which ties in most naturally with the formulation of the problem which one is forced to adopt due to the presence of an interior singularity. We also devise and analyze a variable step scheme for dealing with the singular points. Numerical results show better agreement between our results and those obtained from small-ϵ asymptotics than has been shown in results presented hitherto.     

Electron correlation third-order contributions to the electric dipole transition amplitudes of rare earth ions in crystals

A complete expression for the f?f transition amplitude defined up to the third order in perturbation theory is presented. The third-order contributions are due to electron correlation inside the rare earth ion and arise from the static and dynamic models. The approach is formulated by means of double perturbation theory and in terms of effective tensor operators expressed by unit tensor operators. The discussion of the relative importance of various kinds of effective operators is based on the numerical results of test ab initio calculations performed within the perturbed function approach for the Pr⁺³ ion.