New inequalities from classical Sturm theorems

Inequalities satisfied by the zeros of the solutions of second-order hypergeometric equations are derived through a systematic use of Liouville transformations together with the application of classical Sturm theorems. This systematic study allows us to improve previously known inequalities and to extend their range of validity as well as to discover inequalities which appear to be new. Among other properties obtained, Szegő's bounds on the zeros of Jacobi polynomials for , are completed with results for the rest of parameter values, Grosjean's inequality (J. Approx. Theory 50 (1987) 84) on the zeros of Legendre polynomials is shown to be valid for Jacobi polynomials with |β|1, bounds on ratios of consecutive zeros of Gauss and confluent hypergeometric functions are derived as well as an inequality involving the geometric mean of zeros of Bessel functions.     

On fencing problems

Fencing problems regard the bisection of a convex body in a way that some geometric measures are optimized. We introduce the notion of relative diameter and study bisections of centrally symmetric planar convex bodies, bisections by straight line cuts in general planar convex bodies and also bisections by hyperplane cuts for convex bodies in higher dimensions. In the planar case we obtain the best possible lower bound for the ratio between the relative diameter and the area.     

Stereoselectivity in the intermolecular Pauson-Khand reaction of electron-deficient terminal alkynes

A family of terminal alkyne dicobalthexacarbonyl complexes bearing groups with a range of electron-withdrawing abilities has been synthesized. After submitting these complexes to the intermolecular Pauson-Khand reaction with norbornadiene, electron-deficient substrates afforded up to 26% of the unexpected endo-cyclopentenone.     

Marcinkiewicz–Zygmund inequalities

We study a generalization of the classical Marcinkiewicz–Zygmund inequalities. We relate this problem to the sampling sequences in the Paley–Wiener space and by using this analogy we give sharp necessary and sufficient computable conditions for a family of points to satisfy the Marcinkiewicz–Zygmund inequalities.     

New synthetic “tricks” using old reagents. A mild method for the conversion of RCONHR′ to RCONHR″

N-Alkyl-N-nitrosoamides, RCON(NO)R′, react with primary aliphatic amines (NH₂R″), in refluxing dichloromethane or at room temperature, to give RCONHR″ in 65–98% yields.     

Substituted m-phenylene bridges as strong ferromagnetic couplers for Cu(II)-bridge-Cu(II) magnetic interactions: new perspectives

Based on a combined theoretical-experimental study, we propose that substituted m-phenylene ligands (m-N-Phi-N) can act as tuneable strong ferromagnetic couplers connecting Cu(II) ions; a new complex presenting that bridge with J close to +15 cm(-1) has been suggested and synthesized.     

Electrostatics of phosphatidic acid monolayers: Insights from computer simulations

In this paper, we argue that many of the fascinating electrostatic effects that take place in amphiphilic systems are strongly related to the particular organization of the oxygen atoms within each individual molecule. In particular, we focus on two effects: charge inversion and dielectric overscreening. For that purpose, we present molecular dynamics simulations of phosphatidic acid (DMPA²⁻) in the presence of divalent counterions. Our results show that the many oxygens present in DMPA²⁻ cooperatively create strong binding sites for counterions, which in some cases lead to charge inversion. We also present an analysis of the role of interfacial water and relate our analysis to the phenomenon of dielectric overscreening. Several experimental implications are discussed in the conclusions.     

Theoretical study of alkyl-pi and aryl-pi interactions. Reconciling theory and experiment

Quantum mechanical and quantum mechanical/molecular mechanical calculations in conjunction with continuum solvation models have been used to analyze CH-pi interactions in model systems of aryl- and alkyl-aromatic interactions, as well as in a model folding system designed to study those interactions. High level calculations reproduced accurately the interaction of CH-pi interactions in both alkyl- and aryl-based model systems. Dispersion effects dominate the interaction, but the electrostatics term is also relevant for aryl CH-pi interactions. Theoretical calculations were also used to examine the influence of CH-pi interactions in determining the conformational flexibility of folding models. Finally, a critical comparison of the results obtained from high level calculations on model systems and the experimental data derived for folding models in apolar solvents was carried out, which allowed us to reconcile the apparent discrepancy found between both data.     

SOLVENT EFFECTS ON THE TAUTOMERIZATION OF 5′-DEOXYPYRIDOXAL. A PHOTOPHYSICAL STUDY

Abstract— Absorption and fluorescence spectra of 5′-deoxypyridoxal (DPL) in various pure solvents and mixtures were recorded both at room temperature and over the range10–65°C. The areas under the absorption bands were analyzed to obtain the mole fraction (f_N, f_z) of two tautomers (the zwitterionic, Z, and neutral, N, forms) in the ground state. The following spectral parameters were determined from the fluorescence spectra: Stokes shift (Δv), fluorescence quantum yield of the neutral form (Q_N), fluorescence ratio of the neutral to the zwitterionic form (ø_N/ø_Z) and the rate constant of tautomerization (k₁) from Z to N in the excited state. Some of these parameters (f_N, Δv, Q_N, k₁) were found to depend on the proton donor character of the solvent, whereas others (ø_N/ø_Z) depended on its dipole moment. Thus, the absorption and fluorescence spectra of DPL allow one to obtain information on the polarity and the concentration of –OH groups on its environment.