5,780 research outputs found
Hopf algebra of multi-decorated rooted forests, free matching Rota-Baxter algebras and Gr\"obner-Shirshov bases
Recent advances in stochastic PDEs, Hopf algebras of typed trees and integral
equations have inspired the study of algebraic structures with replicating
operations. To understand their algebraic and combinatorial nature, we first
use rooted forests with multiple decoration sets to construct free Hopf
algebras with multiple Hochschild 1-cocycle conditions. Applying the universal
property of the underlying operated algebras and the method of
Gr\"obner-Shirshov bases, we then construct free objects in the category of
matching Rota-Baxter algebras which is a generalization of Rota-Baxter algebras
to allow multiple Rota-Baxter operators. Finally the free matching Rota-Baxter
algebras are equipped with a cocycle Hopf algebra structure.Comment: 27 page
Effects of ultrasound on electrochemical oxidation mechanisms of p-substituted phenols at BDD and PbO2 anodes
The effects of low-frequency (40 kHz) ultrasound are investigated with regard to the effectiveness and mechanisms of electrochemical oxidation of p-substituted phenols (p-nitrophenol, p-hydroxybenzaldehyde, phenol, p-cresol, and p-methoxyphenol) at BDD (boron-doped diamond) and PbO2 anodes. Although ultrasound improved the disappearance rates of p-substituted phenols at both the BDD and PbO2 anodes, the degree of enhancement varied according to the type of p-substituted phenol and type of anode under consideration. At the BDD anode, the % Increase values were in the range 73-83% for p-substituted phenol disappearance and in the range 60-70% for COD removal. However, at the PbO2 anode, the corresponding %Increase values were in the range 50-70% for disappearance of p-substituted phenols and only 5-25% for COD removal, much lower values than obtained at the BDD anode. Further investigations on the influence of ultrasound on the electrochemical oxidation mechanisms at BDD and PbO2 anodes revealed that the different increase extent were due to the specialized electrochemical oxidation mechanisms at these two anodes. The hydroxyl radicals were mainly free at the BDD electrodes with a larger reaction zone, but adsorbed at the PbO2 electrodes with a smaller reaction zone. Therefore, the enhancement due to ultrasound was greater at the BDD anode than at the PbO2 anode. (C) 2010 Elsevier Ltd. All rights reserved.http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000280422800007&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=8e1609b174ce4e31116a60747a720701ElectrochemistrySCI(E)EI21ARTICLE205569-55755
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