Generalizations of Pelczynski`s decomposition method for Banach spaces containing a complemented copy of their squares

Suppose that X and Y are Banach spaces isomorphic to complemented subspaces of each other. In 1996, W. T. Gowers solved the Schroeder- Bernstein Problem for Banach spaces by showing that X is not necessarily isomorphic to Y. However, if X-2 is complemented in X with supplement A and Y-2 is complemented in Y with supplement B, that is, { X similar to X-2 circle plus A Y similar to Y-2 circle plus B, then the classical Pelczynski`s decomposition method for Banach spaces shows that X is isomorphic to Y whenever we can assume that A = B = {0}. But unfortunately, this is not always possible. In this paper, we show that it is possible to find all finite relations of isomorphism between A and B which guarantee that X is isomorphic to Y. In order to do this, we say that a quadruple (p, q, r, s) in N is a P-Quadruple for Banach spaces if X is isomorphic to Y whenever the supplements A and B satisfy A(p) circle plus B-q similar to A(r) circle plus B-s . Then we prove that (p, q, r, s) is a P-Quadruple for Banach spaces if and only if p - r = s - q = +/- 1.

Optimization of a method for determination of phenolic acids in exotic fruits by capillary electrophoresis

In this work, the separation of nine phenolic acids (benzoic, caffeic, chlorogenic, p-coumaric, ferulic, gallic, protocatechuic, syringic, and vanillic acid) was approached by a 32 factorial design in electrolytes consisting of sodium tetraborate buffer(STB) in the concentration range of 10-50 mmol L(-1) and methanol in the volume percentage of 5-20%. Derringer`s desirability functions combined globally were tested as response functions. An optimal electrolyte composed by 50 mmol L(-1) tetraborate buffer at pH 9.2, and 7.5% (v/v) methanol allowed baseline resolution of all phenolic acids under investigation in less than 15 min. In order to promote sample clean up, to preconcentrate the phenolic fraction and to release esterified phenolic acids from the fruit matrix, elaborate liquid-liquid extraction procedures followed by alkaline hydrolysis were performed. The proposed methodology was fully validated (linearity from 10.0 to 100 mu g mL(-1), R(2) > 0.999: LOD and LOQ from 1.32 to 3.80 mu g mL(-1) and from 4.01 to 11.5 mu g mL(-1), respectively; intra-day precision better than 2.8% CV for migration time and 5.4% CV for peak area; inter-day precision better than 4.8% CV for migration time and 4.8-11% CV for peak area: recoveries from 81% to 115%) and applied successfully to the evaluation of phenolic contents of abiu-roxo (Chrysophyllum caimito), wild mulberry growing in Brazil (Morus nigra L.) and tree tomato (Cyphomandra betacea). Values in the range of 1.50-47.3 mu g g(-1) were found, with smaller amounts occurring as free phenolic acids. (C) 2009 Elsevier B.V. All rights reserved.

Development of a fast capillary electrophoresis method to determine inorganic cations in biodiesel samples

The aim of this study was to develop a fast capillary electrophoresis method for the determination of inorganic cations (Na(+), K(+), Ca(2+), Mg(2+)) in biodiesel samples, using barium (Ba(2+)) as the internal standard. The running electrolyte was optimized through effective mobility curves in order to select the co-ion and Peakmaster software was used to determine electromigration dispersion and buffer capacity. The optimum background electrolyte was composed of 10 mmol L(-1) imidazole and 40 mmol L(-1) of acetic acid. Separation was conducted in a fused-silica capillary (32 cm total length and 23.5 cm effective length, 50 mu m I.D.), with indirect UV detection at 214 nm. The migration time was only 36 s. In order to obtain the optimized conditions for extraction, a fractional factorial experimental design was used. The variables investigated were biodiesel mass, pH, extractant volume, agitation and sonication time. The optimum conditions were: biodiesel mass of 200 mg, extractant volume of 200 mu L. and agitation of 20 min. The method is characterized by good linearity in the concentration range of 0.5-20 mg kg(-1) (r > 0.999), limit of detection was equal to 0.3 mg kg(-1), inter-day precision was equal to 1.88% and recovery in the range of 88.0-120%. The developed method was successfully applied to the determination of cations in biodiesel samples. (c) 2010 Elsevier B.V. All rights reserved.

Development of a fast capillary electrophoresis method for the determination of propranolol-Total analysis time reduction strategies

The aim of this study was to develop a fast capillary electrophoresis method for the determination of propranolol in pharmaceutical preparations. In the method development the pH and constituents of the background electrolyte were selected using the effective mobility versus pH curves. Benzylamine was used as the internal standard. The background electrolyte was composed of 60 mmol L(-1) tris(hydroxymethyl)aminomethane and 30 mmol L(-1) 2-hydroxyisobutyric acid,at pH 8.1. Separation was conducted in a fused-silica capillary (32 cm total length and 8.5 cm effective length, 50 mu m I.D.) with a short-end injection configuration and direct UV detection at 214 nm. The run time was only 14 s. Three different strategies were studied in order to develop a fast CE method with low total analysis time for propranolol analysis: low flush time (Lflush) 35 runs/h, without flush (Wflush) 52 runs/h, and Invert (switched polarity) 45 runs/h. Since the three strategies developed are statistically equivalent, Mush was selected due to the higher analytical frequency in comparison with the other methods. A few figures of merit of the proposed method include: good linearity (R(2) > 0.9999); limit of detection of 0.5 mg L(-1): inter-day precision better than 1.03% (n = 9) and recovery in the range of 95.1-104.5%. (C) 2009 Elsevier B.V. All rights reserved.

A New Indirect Electroanalytical Method to Monitor the Contamination of Natural Waters with 4-Nitrophenol Using Multiwall Carbon Nanotubes

The electrochemical detection of the hazardous pollutant 4-nitrophenol (4-NP) at low potentials, in order to avoid matrix interferences, is an important research challenge. This study describes the development, electrochemical characterization and utilization of a multiwall carbon nanotube (MWCNT) film electrode for the quantitative determination of 4-NP in natural water. Electrochemical impedence spectroscopy measurements showed that the modified surface exhibits a decrease of ca. 13 times in the charge transfer resistance when compared with a bare glassy carbon (GC) surface. Voltammetric experiments showed the possibility to oxidize a hydroxylamine layer (produced by the electrochemical reduction of 4-NP on the GC/MWNCT surface) in a potential region which is approximately 700 mV less positive than that needed to oxidize 4-NP, thus minimizing the interference of matrix components. The limit of detection for 4-NP obtained using square-wave voltammetry (0.12 mu mol L(-1)) was lower than the value advised by EPA. A natural water sample from a dam located in Sao Carlos (Brazil) was spiked with 4-NP and analyzed by the standard addition method using thee GC/MWCNT electrode, without any further purification step. the recovery procedure yielded a value of 96.5% for such sample, thus confirming the suitability of the developed method to determine 4-NP in natural water samples. The electrochemical determination was compared with that obtained by HPLC with UV-vis detection.

Pt film electrodes prepared by the Pechini method for electrochemical decolourisation of Reactive Orange 16

Electrochemical decolourisation of Reactive Orange 16 was carried out in an electrochemical flow-cell, using as working electrodes a Pt thin film deposited on a Ti substrate (Pt/Ti) prepared by the Pechini method and a pure platinum (Pt) foil. Using the Pt/Ti electrodes better results for dye decolourisation were obtained under milder conditions than those used for pure Pt. For the Pt electrode, colour removal of 93 % (lambda = 493 nm) was obtained after 60 min, at 2.2 V vs. RHE, using 0.017 mol L(-1) NaCl + 0.5 mol L(-1) H(2)SO(4) solution. For the Pt/Ti electrode there was better colour removal, 98%, than for the Pt electrode. Moreover, we used 0.017 mol L(-1) NaCl solution and the applied potential was 1.8 V. Under this condition after 15 min of electrolysis, more than 80% of colour was removed. The rate reaction constant, assuming a first order reaction, was 0.024 min(-1) and 0.069 min(-1), for Pt and Pt/Ti electrodes, respectively.