A canonical form for nonderogatory matrices under unitary similarity

A square matrix is nonderogatory if its Jordan blocks have distinct eigenvalues. We give canonical forms for (1) nonderogatory complex matrices up to unitary similarity, and (2) pairs of complex matrices up to similarity, in which one matrix has distinct eigenvalues. The types of these canonical forms are given by undirected and, respectively, directed graphs with no undirected cycles. (C) 2011 Elsevier Inc. All rights reserved.

Evaluation of a carbon paste electrode modified with organofunctionalised SBA-15 nanostructured silica in the simultaneous determination of divalent lead, copper and mercury ions

The performance of a carbon paste electrode (CPE) modified with SBA-15 nanostructured silica organofunctionalised with 2-benzothiazolethiol in the simultaneous determination of Pb(II), Cu(II) and Hg(II) ions in natural water and sugar cane spirit (cachaca) is described. Pb(II), Cu(II) and Hg(II) were pre-concentrated on the surface of the modified electrode by complexing with 2-benzothiazolethiol and reduced at a negative potential (-0.80 V). Then the reduced products were oxidised by DPASV procedure. The fact that three stripping peaks appeared on the voltammograms at the potentials of -0.48 V (Pb2+), -0.03 V (Cu2+) and +0.36 V (Hg2+) in relation to the SCE, demonstrates the possibility of simultaneous determination of Pb2+, Cu2+ and Hg2+. The best results were obtained under the following optimised conditions: 100 mV pulse amplitude, 3 min accumulation time, 25 mV s(-1) scan rate in phosphate solution pH 3.0. Using such parameters, calibration graphs were linear in the concentration ranges of 3.00-70.0 x 10(-7) mol L-1 (Pb2+), 8.00-100.0 X 10(-7) mol L-1 (Cu2+) and 2.00-10.0 x 10(-6) mol L-1 (Hg2+). Detection limits of 4.0 x 10(-8) mol L-1 (Pb2+), 2.0 x 10(-7) mol L-1 (Cu2+) and 4.0 x 10(-7) mol L-1 (Hg2+) were obtained at the signal noise ratio (SNR) of 3. The results indicate that this electrode is sensitive and effective for simultaneous determination of Pb2+, Cu2+ and Hg2+ in the analysed samples. (C) 2008 Published by Elsevier B.V.

Plasticized pectin-based gel electrolytes

Pectin is a natural polymer present in plants and, as all natural polymers has biodegradation properties. Chemically, pectin is a polysaccharide composed of a linear chain of 1 -> 4 linked galacturonic acids, which is esterified with methanol at 80%. The pectin-based gel electrolytes in a transparent film form were obtained by a plasticization process with glycerol and addition of LiClO(4). The films showed good ionic conductivity results, which increased from 10(-5) S/cm for the samples with 37 wt.% of glycerol to 4.7 x 10(-4) S/cm at room temperature for the sample with 68 wt.% of glycerol. The electrochemical behaviors of the samples were studied by electrochemical impedance spectroscopy (EIS), and Nyquist graphs are showed and discussed. The obtained pectin-based samples also presented good adherence to the glass, flexibility, homogeneity (SEM) and transparency (about 70% in the vis) properties. They are good candidates to be applied as gel electrolytes in electrochromic devices. (C) 2009 Elsevier Ltd. All rights reserved.