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.     

Incubation period in the 2,2,4,4‐tetramethyl‐1‐piperidinyloxy‐mediated thermal autopolymerization of styrene: Kinetics and simulations

Mechanisms and simulations of the induction period and the initial polymerization stages in the nitroxide‐mediated autopolymerization of styrene are discussed. At 120–125 °C and moderate 2,2,4,4‐tetramethyl‐1‐piperidinyloxy (TEMPO) concentrations (0.02–0.08 M), the main source of radicals is the hydrogen abstraction of the Mayo dimer by TEMPO [with the kinetic constant of hydrogen abstraction (k_h)]. At higher TEMPO concentrations ([N?] > 0.1 M), this reaction is still dominant, but radical generation by the direct attack against styrene by TEMPO, with kinetic constant of addition k_ad, also becomes relevant. From previous experimental data and simulations, initial estimates of k_h ≈ 1 and k_ad ≈ 6 × 10^?7 L mol^?1 s^?1 are obtained at 125 °C. From the induction period to the polymerization regime, there is an abrupt change in the dominant mechanism generating radicals because of the sudden decrease in the nitroxide radicals. Under induction‐period conditions, the simulations confirm the validity of the quasi‐steady‐state assumption (QSSA) for the Mayo dimer in this regime; however, after the induction period, the QSSA for the dimer is not valid, and this brings into question the scientific basis of the well‐known expression k_th[M]³ (where [M] is the monomer concentration and k_th is the kinetic constant of autoinitiation) for the autoinitiation rate in styrene polymerization. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 6962‐6979, 2006     

Über die Reproduzierbarkeit der turbidimetrischen Bestimmung von Phosphorspuren mit Strychninmolybdostickstoff(V)säure

Microchimica Acta - Mit der turbidimetrischen Strychninnitrat-Methode für Phosphorspurenbestimmung nach der Version von Hegedüs und Dvorszky kann man nur dann ausgezeichnete...     

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.     

Determination of the amino acid tryptophan and the biogenic amine tryptamine in foods by the heavy atom induced-room temperature phosphorescence methodology

Very simple and selective methods are presented to determine the amino acid tryptophan (Trp) and the biogenic amine tryptamine (Tryp), both compounds with an indole-type molecular structure by the methodology named Heavy Atom Induced-Room Temperature Phosphorescence (HAI-RTP) which constitutes the first time that HAI-RTP has been used to detect compounds with non-naphthalenic structures in their molecules. Different variables affecting the phosphorescence signal (heavy atom perturber and sodium sulfite concentration) were carefully studied. The analytical curves give a linear dynamic range of 15-100 ng ml(-1) and a detection limit of 4 ng ml(-1) for Trp and 94-400 ng ml(-1) and 28 ng ml(-1) for Tryp. The methods have been successfully applied to the analysis of complex food matrices such as the presence of tryptophan in yoghurt and tryptamine in bottled beer. A single alkaline hydrolysis to release Trp from yoghurt proteins and two methods for extracting Tryp from beer samples are proposed and optimised. A total Trp content of 374 mg of Trp per kg of yoghurt was quantified by the standard addition method of calibration and a recovery of 90% was obtained for 250 ng ml(-1) of Tryp in spiked non-alcoholic beer samples.     

Squaric acid N-hydroxylamides: synthesis, structure, and properties of vinylogous hydroxamic acid analogues

The synthesis of squaric acid N-hydroxylamide esters 5 and amides 6 from dimethyl squarate 2a is described. These derivatives are analogues of the naturally occurring iron(III) chelator hydroxamic acid. On the basis of a comparative reactivity study, a concerted retro-Cope mechanism for the formation of the N-hydroxylamide esters 5 by reaction of dimethyl squarate with hydroxylamines is proposed. A preliminary iron(III) binding study of these hydroxamic acid analogues is presented, demonstrating binding of iron(III) to amides 6 in aqueous solutions, while the esters 5 did not show any sign of metal ion binding. 13C NMR spectroscopic data (chemical shift and spin-lattice relaxation time determination) of these and related derivatives delineate the resonance structures predominant in these molecules. The resonance structures of the derivatives rationalize their spectroscopic data, chemical reactivity, and iron(III) binding properties. Single-crystal X-ray structure analyses of squaric acid N-hydroxylamide ester 5b and squaric acid N-hydroxylamide amide 6c confirm their connectivity and provide structural evidence supporting the spectroscopically derived conclusions. The squaric acid N-hydroxylamides are potentially useful in the construction of chemosensors for iron(III).