The lower central and derived series of the braid groups of the projective plane

In this paper, we determine the lower central and derived series for the braid groups of the projective plane. We are motivated in part by the study of Fadell-Neuwirth short exact sequences, but the problem is interesting in its own right. The n-string braid groups B(n)(RP(2)) of the projective plane RP(2) were originally studied by Van Buskirk during the 1960s. and are of particular interest due to the fact that they have torsion. The group B(1)(RP(2)) (resp. B(2)(RP(2))) is isomorphic to the cyclic group Z(2) of order 2 (resp. the generalised quaternion group of order 16) and hence their lower central and derived series are known. If n > 2, we first prove that the lower central series of B(n)(RP(2)) is constant from the commutator subgroup onwards. We observe that Gamma(2)(B(3)(RP(2))) is isomorphic to (F(3) X Q(8)) X Z(3), where F(k) denotes the free group of rank k, and Q(8) denotes the quaternion group of order 8, and that Gamma(2)(B(4)(RP(2))) is an extension of an index 2 subgroup K of P(4)(RP(2)) by Z(2) circle plus Z(2). As for the derived series of B(n)(RP(2)), we show that for all n >= 5, it is constant from the derived subgroup onwards. The group B(n)(RP(2)) being finite and soluble for n <= 2, the critical cases are n = 3, 4. We are able to determine completely the derived series of B(3)(RP(2)). The subgroups (B(3)(RP(2)))((1)), (B(3)(RP(2)))((2)) and (B(3)(RP(2)))((3)) are isomorphic respectively to (F(3) x Q(8)) x Z(3), F(3) X Q(8) and F(9) X Z(2), and we compute the derived series quotients of these groups. From (B(3)(RP(2)))((4)) onwards, the derived series of B(3)(RP(2)), as well as its successive derived series quotients, coincide with those of F(9). We analyse the derived series of B(4)(RP(2)) and its quotients up to (B(4)(RP(2)))((4)), and we show that (B(4)(RP(2)))((4)) is a semi-direct product of F(129) by F(17). Finally, we give a presentation of Gamma(2)(B(n)(RP(2))). (C) 2011 Elsevier Inc. All rights reserved.

Desingularization of singular Riemannian foliation

Let F be a singular Riemannian foliation on a compact Riemannian manifold M. By successive blow-ups along the strata of F we construct a regular Riemannian foliation (F) over cap on a compact Riemannian manifold (M) over cap and a desingularization map (rho) over cap : (M) over cap -> M that projects leaves of (F) over cap into leaves of F. This result generalizes a previous result due to Molino for the particular case of a singular Riemannian foliation whose leaves were the closure of leaves of a regular Riemannian foliation. We also prove that, if the leaves of F are compact, then, for each small epsilon > 0, we can find (M) over cap and (F) over cap so that the desingularization map induces an epsilon-isometry between M/F and (M) over cap/(F) over cap. This implies in particular that the space of leaves M/F is a Gromov-Hausdorff limit of a sequence of Riemannian orbifolds {((M) over cap (n)/(F) over cap (n))}.

In vitro evaluation of Cu and Fe bioavailability in cashew nuts by off-line coupled SEC-UV and SIMAAS

In this work Cu and Fe bioavailability in cashew nuts was evaluated using in vitro method. Extractions with simulated gastric and intestinal fluids and dialysis procedures were applied for this purpose. The proteins separation and quantification were performed by size exclusion chromatography (SEC) coupled on-line to ultra-violet (UV) and off-line to simultaneous multielement atomic absorption spectrometry (SIMAAS). The SEC-UV and SIMAAS profiles of the protein fractions obtained by alkaline extraction (NaOH) and precipitation with HCl indicated the presence of high and low molecular weight species in the range between >75 kDa and 9.3 kDa. Almost 83% of Cu and 78% of Fe were extracted during cashew nut digestion and 90% of both elements were dialyzed. With these results it is possible to assume that 75% of Cu and 70% of Fe present in cashew nut could be bioavailable. The SEC-UV and SIMAAS chromatographic profiles obtained after in vitro gastrointestinal digestion reveal that Cu and Fe not dialyzed can be associated to a compound of 9.2 kDa. (C) 2010 Elsevier B.V. All rights reserved.

Fast batch injection analysis of H(2)O(2) using an array of Pt-modified gold microelectrodes obtained from split electronic chips

A fast and robust analytical method for amperometric determination of hydrogen peroxide (H(2)O(2)) based on batch injection analysis (BIA) on an array of gold microelectrodes modified with platinum is proposed. The gold microelectrode array (n = 14) was obtained from electronic chips developed for surface mounted device technology (SMD), whose size offers advantages to adapt them in batch cells. The effect of the dispensing rate, volume injected, distance between the platinum microelectrodes and the pipette tip, as well as the volume of solution in the cell on the analytical response were evaluated. The method allows the H(2)O(2) amperometric determination in the concentration range from 0.8 mu mol L(-1) to 100 mu mol L(-1). The analytical frequency can attain 300 determinations per hour and the detection limit was estimated in 0.34 mu mol L(-1) (3 sigma). The anodic current peaks obtained after a series of 23 successive injections of 50 mu L of 25 mu mol L(-1) H(2)O(2) showed an RSD < 0.9%. To ensure the good selectivity to detect H(2)O(2), its determination was performed in a differential mode, with selective destruction of the H(2)O(2) with catalase in 10 mmol L(-1) phosphate buffer solution. Practical application of the analytical procedure involved H(2)O(2) determination in rainwater of Sao Paulo City. A comparison of the results obtained by the proposed ampermetric method with another one which combines flow injection analysis (FIA) with spectrophotometric detection showed good agreement. (C) 2011 Elsevier B.V. All rights reserved.

Flow injection analysis using carbon film resistor electrodes for amperometric determination of ambroxol

Flow injection analysis (FIA) using a carbon film sensor for amperometric detection was explored for ambroxol analysis in pharmaceutical formulations. The specially designed flow cell designed in the lab generated sharp and reproducible current peaks, with a wide linear dynamic range from 5 x 10(-7) to 3.5 x 10(-4) mol L-1, in 0.1 mol L-1 sulfuric acid electrolyte, as well as high sensitivity, 0.110 A mol(-1) L cm(-2) at the optimized flow rate. A detection limit of 7.6 x 10(-8) mol L-1 and a sampling frequency of 50 determinations per hour were achieved, employing injected volumes of 100 mu L and a flow rate of 2.0 mL min(-1). The repeatability, expressed as R.S.D. for successive and alternated injections of 6.0 x 10(-6) and 6.0 x 10(-5) mol L-1 ambroxol solutions, was 3.0 and 1.5%, respectively, without any noticeable memory effect between injections. The proposed method was applied to the analysis of ambroxol in pharmaceutical samples and the results obtained were compared with UV spectrophotometric and acid-base titrimetric methods. Good agreement between the results utilizing the three methods and the labeled values was achieved, corroborating the good performance of the proposed electrochemical methodology for ambroxol analysis. (C) 2008 Elsevier B.V. All rights reserved.

Solvation in Pure Liquids: What Can Be Learned from the Use of Pairs of Indicators?

The solvation of six solvatochromic probes in a large number of solvents (33-68) was examined at 25 degrees C. The probes employed were the following: 2,6-diphenyl-4-(2,4,6-triphenylpyridinium-1-yl) phenolate (RB); 4-[(E)2-(1-methylpyridinium-4-yl)ethenyl] phenolate, MePM; 1-methylquinolinium-8-olate, QB; 2-bromo-4-[(E)-2-(1-methylpyridinium-4-yl)ethenyl] phenolate, MePMBr, 2,6-dichloro-4-(2,4,6-triphenyl pyridinium-1-yl) phenolate (WB); and 2,6-dibromo-4-[(E)-2-(1-methylpyridinium-4-yl)ethenyl] phenolate, MePMBr(2), respectively. Of these, MePMBr is a novel compound. They can be grouped in three pairs, each with similar pK(a) in water but with different molecular properties, for example, lipophilicity and dipole moment. These pairs are formed by RB and MePM; QB and MePMBr; WB and MePMBr(2), respectively. Theoretical calculations were carried out in order to calculate their physicochemical properties including bond lengths, dihedral angles, dipole moments, and wavelength of absorption of the intramolecular charge-transfer band in four solvents, water, methanol, acetone, and DMSO, respectively. The data calculated were in excellent agreement with available experimental data, for example, bond length and dihedral angles. This gives credence to the use of the calculated properties in explaining the solvatochromic behaviors observed. The dependence of an empirical solvent polarity scale E(T)(probe) in kcal/mol on the physicochemical properties of the solvent (acidity, basicity, and dipolarity/polarizability) and those of the probes (pK(a), and dipole moment) was analyzed by using known multiparameter solvation equations. For each pair of probes, values of E(T)(probe) (for example, E(T)(MePM) versus E(T)(RB)) were found to be linearly correlated with correlation coefficients, r, between 0.9548 and 0.9860. For the mercyanine series, the values of E(T)(probe) also correlated linearly, with (r) of 0.9772 (MePMBr versus MePM) and 0.9919 (MePMBr(2) versus MePM). The response of each pair of probes (of similar pK(a)) to solvent acidity is the same, provided that solute-solvent hydrogen-bonding is not seriously affected by steric crowding (as in case of RB). We show, for the first time, that the response to solvent dipolarity/polarizability is linearly correlated to the dipole moment of the probes. The successive introduction of bromine atoms in MePM (to give MePMBr, then MePMBr(2)) leads to the following linear decrease: pK(a) in water, length of the phenolate oxygen-carbon bond, length of the central ethylenic bond, susceptibility to solvent acidity, and susceptibility to solvent dipolarity/polarizability. Thus studying the solvation of probes whose molecular structures are varied systematically produces a wealth of information on the effect of solute structure on its solvation. The results of solvation of the present probes were employed in order to test the goodness of fit of two independent sets of solvent solvatochromic parameters.

Quantification of N-acetylcysteine in pharmaceuticals using cobalt phthalocyanine modified graphite electrodes

Flow injection analysis (FIA) with amperometric detection was employed for the quantification of N-acetylcysteine (NAC) in pharmaceutical formulations, utilizing an ordinary pyrolytic graphite (OPG) electrode modified with cobalt phthalocyanine (CoPc). Cyclic voltammetry was used in preliminary studies to establish the best conditions for NAC analysis. In FIA-amperometric experiments the OPG-CoPc electrode exhibited sharp and reproducible current peaks over a wide linear working range (5.0 x 10(-5)-1.0 x 10(-3) mol L(-1)) in 0.1 mol L(-1) NaOH solution. High sensitivity (130 mA mol(-1) cm(2)) and a low detection limit (9.0 x 10(-7) mol L(-1)) were achieved using the sensor. The repeatability (R.S.D.%) for 13 successive flow injections of a solution containing 5.0 x 10(-4) mol L(-1) NAC was 1.1%. The new procedure was applied in analyses of commercial pharmaceutical products and the results were in excellent agreement with those obtained using the official titrimetric method. The proposed amperometric method is highly suitable for quality control analyses of NAC in pharmaceuticals since it is rapid, precise and requires much less work than the recommended titrimetric method. (C) 2010 Elsevier B.V. All rights reserved.

Development of a new stir bar sorptive extraction coating and its application for the determination of six pesticides in sugarcane juice

In this article, a novel polydimethylsiloxane/activated carbon (PDMS-ACB) material is proposed as a new polymeric phase for stir bar sorptive extraction (SBSE). The PDMS-ACB stir bar, assembled using a simple Teflon (R)/glass capillary mold, demonstrated remarkable stability and resistance to organic solvents for more than 150 extractions. The SBSE bar has a diameter of 2.36 mm and a length of 2.2 cm and is prepared to contain 92 mu L of polymer coating. This new PDMS-ACB bar was evaluated for its ability to determine the quantity of pesticides in sugarcane juice samples by performing liquid desorption (LD) in 200 mu L of ethyl acetate and analyzing the solvent through gas chromatography coupled with mass spectrometry (GC-MS). A fractional factorial design was used to evaluate the main parameters involved in the extraction procedure. Then, a central composite design with a star configuration was used to optimize the significant extraction parameters. The method used demonstrated a limit of quantification (LOQ) of 0.5-40 mu g/L, depending on the analyte detected; the amount of recovery varied from 0.18 to 49.50%, and the intraday precision ranged from 0.072 to 8.40%. The method was used in the analysis of real sugarcane juice samples commercially available in local markets.

THE POTENTIALITIES OF USING A GRAPHITE-SILICONE RUBBER COMPOSITE ELECTRODE IN THE DETERMINATION OF PROPRANOLOL

A graphite silicone-rubber composite electrode (GSR) was used for the determination of propranolol in drug formulation. Cyclic voltammetry (CV) at the GSR presented an irreversible oxidation peak at + 0.8V vs. SCE, in Britton Robinson (B-R) buffer pH 7.4. The quantitative determination was carried out using differential pulse voltammetry (DPV). Under optimized parameters a linear dynamic range from 5.0 to 80.6 mu mol L(-1) with a detection limit of 1.1 mu mol L(-1) was observed. A repeatability of 4.5 +/- 0.1 mu A (n = 10) peak current was found after 10 successive DPV voltammograms of propranolol in the same solution after surface renovations. Using the proposed electrode, propranolol was quantified in a pharmaceutical formulation with results that agreed within 95% confidence level (t-test) with those from an official method.

Polydimethylsiloxane/polypyrrole stir bar sorptive extraction and liquid chromatography (SBSE/LC-UV) analysis of antidepressants in plasma samples

A new polymeric coating consisting of a dual-phase, polydimethylsiloxane (PDMS) and polypyrrole (PPY) was developed for the stir bar sorptive extraction (SBSE) of antidepressants (mirtazapine, citalopram, paroxetine, duloxetine, fluoxetine and sertraline) from plasma samples, followed by liquid chromatography analysis (SBSE/LC-UV). The extractions were based on both adsorption (PPY) and sorption (PDMS) mechanisms. SBSE variables, such as extraction time, temperature, pH of the matrix, and desorption time were optimized, in order to achieve suitable analytical sensitivity in a short time period. The PDMS/PPY coated stir bar showed high extraction efficiency (sensitivity and selectivity) toward the target analytes. The quantification limits (LOQ) of the SBSE/LC-UV method ranged from 20 ng mL(-1) to 50 ng mL(-1), and the linear range was from LOQ to 500 ng mL(-1), with a determination coefficient higher than 0.99. The inter-day precision of the SBSE/LC-UV method presented a variation coefficient lower than 15%. The efficiency of the SBSE/LC-UV method was proved by analysis of plasma samples from elderly depressed patients. (C) 2008 Elsevier B.V. All rights reserved.