Minimal, rigid foliations by curves on ℂℙ n

We prove the existence of minimal and rigid singular holomorphic foliations by curves on the projective space ℂℙ ⁿ for every dimension n≥2 and every degree d≥2. Precisely, we construct a foliation ℱ which is induced by a homogeneous vector field of degree d, has a finite singular set and all the regular leaves are dense in the whole of ℂℙ ⁿ . Moreover, ℱ satisfies many additional properties expected from chaotic dynamics and is rigid in the following sense: if ℱ is conjugate to another holomorphic foliation by a homeomorphism sufficiently close to the identity, then these foliations are also conjugate by a projective transformation. Finally, all these properties are persistent for small perturbations of ℱ.?This is done by considering pseudo-groups generated on the unit ball 𝔹 ⁿ ⊆ℂ ⁿ by small perturbations of elements in Diff(ℂ ⁿ ,0). Under open conditions on the generators, we prove the existence of many pseudo-flows in their closure (for the C ⁰-topology) acting transitively on the ball. Dynamical features as minimality, ergodicity, positive entropy and rigidity may easily be derived from this approach. Finally, some of these pseudo-groups are realized in the transverse dynamics of polynomial vector fields in ℂℙ ⁿ . Received March 7, 2002 / final version received November 26, 2002?Published online February 7, 2003 Most of this work has been carried out during a visit of the first author to IMPA/RJ and a visit of the second author to the University of Lille 1. We would like to thank these institutes for hospitality and express our gratitude to CNPq-Brazil and CNRS-France for the financial support which made these visits possible. We are also indebted to Paulo Sad, Marcel Nicolau and the referee whose comments helped us to improve on the preliminary version. Finally, the second author has partially conducted this research for the Clay Mathematics Institute.     

Development of an HPLC method with electrochemical detection of femtomoles of 8-oxo-7,8-dihydroguanine and 8-oxo-7,8-dihydro-2'-deoxyguanosine in the presence of uric acid

A selective method based on high performance liquid chromatography with electrochemical detection (HPLC-ECD) was developed to enable simultaneous detection of 8-oxo-7,8-dihydroguanine (8-oxoGua) and 8-oxo-7,8-dihydro-2′-deoxyguanosine (8-oxodGuo), products of DNA oxidative damage, in the presence of uric acid (UA), a strong interferent in their electrochemical detection. The method developed consists of HPLC isocratic elution with amperometric detection on a glassy carbon electrode, enabling a detection limit for 8-oxoGua and 8-oxodGuo lower than 1 nM in standard mixtures. Detection of low concentrations up to 25 nM of 8-oxoGua and 8-oxodGuo in the presence of UA in a 10⁴-fold higher concentration was achieved after one-step solid phase extraction (SPE). The method was tested with urine samples and it was possible to detect and quantify the presence of 8-oxoGua, and to confirm that UA was eliminated after uricase degradation and SPE. The LOD found in urine samples was about 80 nM, a value higher than in standard mixtures, due to the increase of background current in the urine matrix. The results presented here contribute to the development of a methodological approach to simultaneous determination of 8-oxoGua and 8-oxodGuo in urine samples.     

Synthesis, crystal structure, spectroscopic and electrochemical characterization of the dinuclear complex {tetra-μ-[(±)-2-(p-methoxyphenoxy)-propionato-O,O′]bis(aqua)dicopper(II)}

Structural, electrochemical and spectroscopic data of a new dinuclear copper(II) complex with (±)-2-(p-methoxyphenoxy)propionic acid are reported. The complex {tetra-μ-[(±)-2-(p-methoxyphenoxy)propionato-O,O′]-bis(aqua)dicopper(II)} crystallizes in the monoclinic system, space group P2₁/n with a = 14.149(1) ?, b = 7.495(1) ?, c = 19.827(1) ?, β = 90.62(1) and Z = 4. X-ray diffraction data show that the two copper(II) ions are held together through four carboxylate bridges, coordinated as equatorial ligands in square pyramidal geometry. The coordination sphere around each copper ion is completed by two water molecules as axial ligands. Thermogravimetric data are consistent with such results. The ligand has an “L” type shape due to the angle formed by the β-carbon of the propionic chain and the linked p-methoxyphenoxy group. This conformation contributes to the occurrence of a peculiar structure of the complex. The complex retains its dinuclear nature when dissolved in acetonitrile, but it decomposes into the corresponding mononuclear species if dissolved in ethanol, according to the EPR measurements. Further, cyclic voltammograms of the complex in acetonitrile show that the dinuclear species maintains the same structure, in agreement with the EPR data in this solvent. The voltammogram shows two irreversible reduction waves at E _pc = −0.73 and −1.04 V vs. Ag/AgCl assigned to the Cu(II)/Cu(I) and Cu(I)/Cu° redox couples, respectively, and two successive oxidation waves at E _pa =− 0.01 and +1.41 V vs. Ag/AgCl, assigned to the Cu°/Cu(I) and Cu(I)/Cu(II) redox couples, respectively, in addition to the oxidation waves of the carboxylate ligand.     

On-off scheduling schemes for power-constrained electric vehicle charging

In this paper, we study the problem of establishing a dynamic charging schedule of electric vehicles (EVs) at a charging station, assuming that limited power implies that only a limited number of EVs can charge simultaneously. The only control we assume to be available to the charging station is the ability to (at any given time) turn on or off the power supply to any EV, with this tool we want to develop a charging schedule that will satisfy the energy demands of the EVs in their intended deadlines. We propose two distinct approaches to this problem: a discretized time version, based on a greedy-like algorithm, and a continuous time version, based on linear programming. We compare these two approaches and numerically study the improvement they yield in the efficiency of the charging procedure, when applied to simulated data based on real parking data. Finally, we illustrate the flexibility of the models by sketching several possible extensions.     

Evaluation of a Brazilian ion chromatography interlaboratory study

This paper describes a Brazilian interlaboratory program study on anion measurement in synthetic water. The program described is promoted regularly since 2007 and recommended the use of ion chromatography as analytical technique for all participant laboratories. Two samples (X and Y) with different anion (fluoride, chloride, nitrite-N, nitrate-N, sulfate and phosphate-P) concentration levels were twice distributed in 2011. Each sample on each round had the homogeneity, and the stability tested for a period of 15 days. Upon ensuring the homogeneity and stability, the samples were distributed to 39 laboratories located around the country. The aim of this study was to verify the laboratories’ precision and to establish the measurement comparability among Brazilian laboratories that routinely use ion chromatography for water sample analysis. It was also possible to identify the most frequent sources of systematic and random errors for each measured anion, related to the ion chromatography technique. Some specific metrological issues related to the geographical region are discussed.     

Viscosity Mixing Rules for Binary Systems Containing One Ionic Liquid

In this work the applicability of four of the most commonly used viscosity mixing rules to [ionic liquid (IL)+molecular solvent (MS)] systems is assessed. More than one hundred (IL+MS) binary mixtures were selected from the literature to test the viscosity mixing rules proposed by 1) Hind (Hi), 2) Grunberg and Nissan (G–N), 3) Herric (He) and 4) Katti and Chaudhri (K–C). The analyses were performed by estimating the average (absolute or relative) deviations, AADs and ARDs, between the available experimental data and the predicted ideal mixture viscosity values obtained by means of each rule. The interaction terms corresponding to the adjustable parameters inherent to each rule were also calculated and their trends discussed.     

Metabisulfite interference in biosensing and Folin-Ciocalteu analysis of polyphenols

Sodium metabisulfite is one of the forms of sulphurous compounds which are added as preservative in food and beverage processing industries. Its interference with different methods of analysis of polyphenols was investigated in the present work. Studies involved the reaction of metabisulfite at platinum electrodes either at a constant applied potential of +100 mV vs. Ag/AgCl electrode with amperometric detection, or at linear potential sweep in cyclic voltammetry experiments. In a second stage, its effect on the analysis of polyphenols that are oxidised by enzymes was examined by the inhibition that metabisulfite caused on caffeic acid oxidation in the presence of free and immobilized laccase. It was found that immobilized laccase was less inhibited than free laccase. A confirmation of the influence of metabisulfite on the Folin-Ciocalteu analysis was also done.     

Quantification of endocrine disruptors and pesticides in water by gas chromatography–tandem mass spectrometry. Method validation using weighted linear regression schemes

A multi-residue methodology based on a solid phase extraction followed by gas chromatography–tandem mass spectrometry was developed for trace analysis of 32 compounds in water matrices, including estrogens and several pesticides from different chemical families, some of them with endocrine disrupting properties. Matrix standard calibration solutions were prepared by adding known amounts of the analytes to a residue-free sample to compensate matrix-induced chromatographic response enhancement observed for certain pesticides. Validation was done mainly according to the International Conference on Harmonisation recommendations, as well as some European and American validation guidelines with specifications for pesticides analysis and/or GC–MS methodology. As the assumption of homoscedasticity was not met for analytical data, weighted least squares linear regression procedure was applied as a simple and effective way to counteract the greater influence of the greater concentrations on the fitted regression line, improving accuracy at the lower end of the calibration curve. The method was considered validated for 31 compounds after consistent evaluation of the key analytical parameters: specificity, linearity, limit of detection and quantification, range, precision, accuracy, extraction efficiency, stability and robustness.