Polar orthogonal representations of real reductive algebraic groups

We prove that a polar orthogonal representation of a real reductive algebraic group has the same closed orbits as the isotropy representation of a pseudo-Riemannian symmetric space. We also develop a partial structural theory of polar orthogonal representations of real reductive algebraic groups which slightly generalizes some results of the structural theory of real reductive Lie algebras. (c) 2008 Elsevier Inc. All rights reserved.

Minimal Lagrangian surfaces in the tangent bundle of a Riemannian surface

Given an oriented Riemannian surface (Sigma, g), its tangent bundle T Sigma enjoys a natural pseudo-Kahler structure, that is the combination of a complex structure 2, a pseudo-metric G with neutral signature and a symplectic structure Omega. We give a local classification of those surfaces of T Sigma which are both Lagrangian with respect to Omega and minimal with respect to G. We first show that if g is non-flat, the only such surfaces are affine normal bundles over geodesics. In the flat case there is, in contrast, a large set of Lagrangian minimal surfaces, which is described explicitly. As an application, we show that motions of surfaces in R(3) or R(1)(3) induce Hamiltonian motions of their normal congruences, which are Lagrangian surfaces in TS(2) or TH(2) respectively. We relate the area of the congruence to a second-order functional F = f root H(2) - K dA on the original surface. (C) 2010 Elsevier B.V. All rights reserved.

Abelian torsion groups with a countably compact group topology

Comfort and Remus [W.W. Comfort, D. Remus, Abelian torsion groups with a pseudo-compact group topology, Forum Math. 6 (3) (1994) 323-337] characterized algebraically the Abelian torsion groups that admit a pseudocompact group topology using the Ulm-Kaplansky invariants. We show, under a condition weaker than the Generalized Continuum Hypothesis, that an Abelian torsion group (of any cardinality) admits a pseudocompact group topology if and only if it admits a countably compact group topology. Dikranjan and Tkachenko [D. Dikranjan. M. Tkachenko, Algebraic structure of small countably compact Abelian groups, Forum Math. 15 (6) (2003) 811-837], and Dikranjan and Shakhmatov [D. Dikranjan. D. Shakhmatov, Forcing hereditarily separable compact-like group topologies on Abelian groups, Topology Appl. 151 (1-3) (2005) 2-54] showed this equivalence for groups of cardinality not greater than 2(c). We also show, from the existence of a selective ultrafilter, that there are countably compact groups without non-trivial convergent sequences of cardinality kappa(omega), for any infinite cardinal kappa. In particular, it is consistent that for every cardinal kappa there are countably compact groups without non-trivial convergent sequences whose weight lambda has countable cofinality and lambda > kappa. (C) 2009 Elsevier B.V. All rights reserved.

Fully electrochemical hyphenated flow system for preconcentration, cleanup, stripping, capillary electrophoresis with stacking and contactless conductivity detection of trace heavy metals

Successful coupling of electrochemical preconcentration (EPC) to capillary electrophoresis (CE) with contactless conductivity detection (C(4)D) is reported for the first time. The EPC-CE interface comprises a dual glassy carbon electrode (GCE) block, a spacer and an upper block with flow inlet and outlet, pseudo-reference electrode and a fitting for the CE silica column, consisting of an orifice perpendicular to the surface of a glassy carbon electrode with a bushing inside to ensure a tight press fit. The end of the capillary in contact with the GCE is slant polished, thus defining a reproducible distance from the electrode surface to the column bore. First results with EPC-CE-C(4)D are very promising, as revealed by enrichment factors of two orders of magnitude for Tl, Cu, Pb and Cd ion peak area signals. Detection limits for 10 min deposition time fall around 20 nmol L(-1) with linear calibration curves over a wide range. Besides preconcentration, easy matrix exchange between accumulation and stripping/injection favors procedures like sample cleanup and optimization of pH, ionic strength and complexing power. This was demonstrated for highly saline samples by using a low conductivity buffer for stripping/injection to improve separation and promote field-enhanced sample stacking during electromigration along the capillary. (C) 2010 Elsevier B.V. All rights reserved.

Degradation and adsorption of AZO RR239 dye in aqueous solution by nanoscale zerovalent iron particles immobilized on sawdust

Carra sawdust pretrated with formaldehyde was used to adsorb RR239 (reactive azo dye) at varying pH and zerovalent iron (ZVI) dosage. Modeling of kinetic results shows that sorption process is best described by the pseudo-second-order model. Batch experiments suggest that the decolorization efficiency was strongly enhanced with the presence of ZVI and low solution pH. The kinetics of dye sorption by mixed sorbent (5 g of sawdust and 180 mg of ZVI) at pH 2.0 was rapid, reaching more than 90% of the total discoloration in three minutes.

The role of oxygen in the interaction of emeraldine base polyaniline with Cu(II) or Fe(III) ions in NMP solution

The influence of molecular oxygen in the interactions of emeraldine base form of polyaniline (EB-PANI) with Fe(III) or Cu(II) ions in 1-methyl-2-pyrrolidinone (NMP) solutions has been investigated by UV-vis-NIR, resonance Raman and electron paramagnetic resonance (EPR) spectroscopies. Through the set of spectroscopic results it was possible to rationalize the role Of O(2) and to construct a scheme of preferential routes occurring in the interaction of EB-PANI with Fe(III) or Cu(II). Solutions of 4.0 mmol L(-1) EB-PANI with 0.8, 2.0 and 20 mmol L(-1) Fe(III) or Cu(II) ions in NMP were investigated and the main observed reactions were EB-PANI oxidation to pernigraniline (PB-PANI) and EB-PANI doping process by pseudo-protonation, or by a two-step redox process. In the presence Of O(2), PB-PANI is observed in all Fe(III)/EB solutions and EB-PANI doping only occurs in solutions with high Fe(III) concentrations through pseudo-protonation. On the other hand, emeraldine salt (ES-PANI) is formed in all Fe(III)/EB solutions under N(2) atmosphere and, in this case, doping occurs both by the pseudo-protonation and two-step redox mechanisms. In all Cu(II)/EB solutions PB-PANI is formed both in the presence and absence of O(2), and only for solutions with high Cu(II) concentrations doping process occurs in a very low degree. The most important result from EPR spectra was providing evidence for redox steps. The determined Cu(II) signal areas under oxygen are higher than under N(2) and, further. the initial metal proportions (1:2:20) are maintained in these spectra, indicating that Cu(I) formed are re-oxidized by O(2) and. so, Cu(II) ions are being recycled. Consistently, for the solutions prepared under nitrogen, the corresponding areas and proportions in the spectra are much lower, confirming that a partial reduction of Cu(II) ions actually occurs. (C) 2009 Elsevier B.V. All rights reserved.

Electrocatalytic behavior of glassy carbon electrodes modified with multiwalled carbon nanotubes and cobalt phthalocyanine for selective analysis of dopamine in presence of ascorbic acid

This work describes the development, electrochemical characterization and utilization of a cobalt phthalocyanine modified carbon nanotube electrode for the quantitative determination of dopamine in 0.2 mol L-1 phosphate buffer contaminated with high concentration of ascorbic acid. The electrode surface was analyzed by cyclic voltammetry and electrochemical impedance spectroscopy which showed a modified surface presenting a charge transfer resistance of 500 Omega, against the 16.46 k Omega value found for the bare glassy carbon surface. A pseudo rate constant value of 5.4 x 10(-4) cm s(-1) for dopamine oxidation was calculated. Voltammetric experiments showed a shift of the peak potential of DA oxidation to less positive value at 390 mV as compared with that of a bare GC electrode at 570 mV. The electrochemical determination of dopamine, in presence of ascorbic acid in concentrations up to 0.1 mol L-1 by differential pulse voltarnmetry, yielded a detection limit as low as 2.56 x 10(-7) mol L-1.