Minimum cycle cover and Chinese postman problems on mixed graphs with bounded tree-width

Let M = (V, E, A) be a mixed graph with vertex set V, edge set E and arc set A. A cycle cover of M is a family C = {C(1), ... , C(k)} of cycles of M such that each edge/arc of M belongs to at least one cycle in C. The weight of C is Sigma(k)(i=1) vertical bar C(i)vertical bar. The minimum cycle cover problem is the following: given a strongly connected mixed graph M without bridges, find a cycle cover of M with weight as small as possible. The Chinese postman problem is: given a strongly connected mixed graph M, find a minimum length closed walk using all edges and arcs of M. These problems are NP-hard. We show that they can be solved in polynomial time if M has bounded tree-width. (C) 2008 Elsevier B.V. All rights reserved.

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.

Anodic oxidation of wastewater containing the Reactive Orange 16 Dye using heavily boron-doped diamond electrodes

Boron-doped diamond (BDD) films grown on the titanium substrate were used to study the electrochemical degradation of Reactive Orange (RO) 16 Dye. The films were produced by hot filament chemical vapor deposition (HFCVD) technique using two different boron concentrations. The growth parameters were controlled to obtain heavily doped diamond films. They were named as E1 and E2 electrodes, with acceptor concentrations of 4.0 and 8.0 x 10(21) atoms cm(-3), respectively. The boron levels were evaluated from Mott-Schottky plots also corroborated by Raman`s spectra, which characterized the film quality as well as its physical property. Scanning Electron Microscopy showed well-defined microcrystalline grain morphologies with crystal orientation mixtures of (1 1 1) and (1 00). The electrode efficiencies were studied from the advanced oxidation process (AOP) to degrade electrochemically the Reactive Orange 16 azo-dye (RO16). The results were analyzed by UV/VIS spectroscopy, total organic carbon (TOC) and high-performance liquid chromatography (HPLC) techniques. From UV/VIS spectra the highest doped electrode (E2) showed the best efficiency for both, the aromaticity reduction and the azo group fracture. These tendencies were confirmed by the TOC and chromatographic measurements. Besides, the results showed a direct relationship among the BDD morphology, physical property, and its performance during the degradation process. (C) 2011 Elsevier B.V. All rights reserved.