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.     

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.     

Stereochemical analysis of 3,4-methylenedioxymethamphetamine and its main metabolites by gas chromatography/mass spectrometry

3,4-Methylenedioxymethamphetamine (MDMA, ecstasy) is consumed as the racemate but some metabolic steps are enantioselective. In addition, chiral properties are preserved during MDMA biotransformation. A quantitative analytical methodology using gas chromatography/mass spectrometry (GC/MS) to determine enantioselective disposition in the body of MDMA and its main metabolites including 3,4-methylenedioxyamphetamine (MDA), 4-hydroxy-3-methoxymethamphetamine (HMMA), and 4-hydroxy-3-methoxyamphetamine (HMA) was developed. Plasma and urine samples were collected from a male volunteer. The analysis of MDMA, MDA, and 4-hydroxy-3-methoxy metabolites by GC/MS required a two-step derivatization procedure. The first step consisted of derivatization of the amine with enantiomerically pure Mosher's reagent ((R)-MTPCl). Triethylamine was used as a base to neutralize hydrochloric acid formed during the reaction allowing quantitative derivatization, which resulted in a substantial improvement in the sensitivity of the method compared with other previously described techniques. Further treatment with ammonium hydroxide was required since both amine and hydroxyl groups underwent derivatization in the reaction. Ammonium hydroxide breaks bonds formed with hydroxyl groups without affecting amine derivatives. The second derivatization step using hexamethyldisilazane was needed for metabolites containing phenol residues. This derivatization method permitted the stereochemically specific study of MDMA and its main monohydroxylated metabolites by GC/MS. A detailed study of the chemical reactions involved in the derivatization steps was indispensable to develop a straightforward, sensitive, and reproducible method for the analysis of the parent drug compound and its metabolites.     

Fast screening of anabolic steroids and other banned doping substances in human urine by gas chromatography/tandem mass spectrometry

A fast and sensitive method for the comprehensive screening of anabolic agents and other banned doping substances using gas chromatography/tandem mass spectrometry (GC/MS/MS) with an external ionization ion trap mass spectrometer is presented. The method takes advantage of the resolving power of MS/MS to eliminate background interferences, thus speeding up the chromatographic analysis. For each compound, different fragmentation reactions were studied and their collision energies optimized to obtain the best sensitivity in terms of their signal-to-noise ratio (S/N). A dramatic reduction in overall analysis time was achieved compared with other common approaches. More than 50 substances could finally be monitored in less than 7.4 min with detection limits (S/N >3) lower than 0.5 ng ml(-1) for most of the compounds with special sensitivity requirements according to the International Olympic Committee (IOC). A validation procedure for qualitative analysis was performed. The selectivity of the method showed that no interfering peaks were observed at the retention time of the analytes. Good intermediate precision, below 25% for most of the compounds, and robustness were observed. The optimized method was successfully applied to analyse more than 100 real human urine samples with optimum sensitivity and specificity rates.     

Directed evolution experiments reveal mutations at cycloartenol synthase residue His477 that dramatically alter catalysis

[reaction: see text] Cycloartenol synthase cyclizes and rearranges oxidosqualene to the protosteryl cation and then specifically deprotonates from C-19. To identify mutants that deprotonate differently, randomly generated mutant cycloartenol synthases were selected in a yeast lanosterol synthase mutant. A novel His477Asn mutant was uncovered that produces 88% lanosterol and 12% parkeol. The His477Gln mutant produces 73% parkeol, 22% lanosterol, and 5% Delta(7)-lanosterol. These are the most accurate lanosterol synthase and parkeol synthase that have been generated by mutagenesis.     

Simple and rapid micellar electrokinetic capillary chromatographic method for simultaneous determination of four antiepileptics in human serum

A very rapid and simple MEKC method was developed for the simultaneous determination of four antiepileptic drugs, ethosuximide (Etho), primidone (Pri), phenytoin (Pht) and carbamazepine (Cbz) in human serum. Sample analysis required only 100 microL of human serum which only needed to be centrifuged, decanted and combined with the running buffer [5.3 mM Na(2)HPO(4)/3.2 mM borax buffer (pH 9.5) containing 55 mM SDS and 3.5% (v/v) acetone]. The analysis was performed in only 10 min into fused-silica capillaries (57 cm total length with 50 microm i.d. and 50 cm to the detector) using the MEKC methodology with diode-array detection at 220 nm. The calibration graphs were established for ethoximide, primidone, phenytoin and carbamazepine between 0 and 20 mg/L. Recoveries were between 85 and 87%. The simplicity of the proposed methodology makes it suitable for routine clinical use, especially for epileptic patients on polytherapy.