Darboux transformations for higher-rank Kadomtsev-Petviashvili and Krichever-Novikov equations

It is shown that the action of a special rank 2 or rank 3 Darboux transformation, calledtransference, upon a pair of commuting ordinary differential operators of orders 4 and 6 implements the Abelian sum on their elliptic joint spectrum. A consequence of this is that, under the deformation of these commuting operators by the KP flow, every rank 2 KP solution corresponds to a solution of the Krichever-Novikov (KN) equation, and vice versa, with the transference process providing the correspondence between (2+1) and (1+1) dimensions. For a singular joint spectrum, it is further shown that transference at the singular point produces a correspondence between solutions of the singular KN equation and those of the KdV equation. These correspondences are illustrated by considering examples of a nondecaying rational KdV or Boussinesq solutions and the corresponding rational, singular-KN and rational KP solutions which the transference process generates.     

Experimental and Computational Study of the Thermal Decomposition of 3‐Methyl‐3‐buten‐1‐ol in m‐Xylene Solution

An experimental study of the thermal decomposition of a β‐hydroxy alkene, 3‐methyl‐3‐buten‐1‐ol, in m‐xylene solution, has been carried out at five different temperatures in the range of 513.15–563.15 K. The temperature dependence of the rate constants for the decomposition of this compound in the corresponding Arrhenius equation is given by ln k (s^?1) = (25.65 ± 1.52) ? (17,944 ± 814) (kJ·mol^?1)·T^?1. A computational study has been carried out at the M05–2X/6–31+G(d,p) level of theory to calculate the rate constants and the activation parameters by the classical transition state theory. There is a good agreement between the experimental and calculated rate constants and activation Gibbs energies. The bonding characteristics of reactant, transition state, and products have been investigated by the natural bond orbital analysis, which provides the natural atomic charges and the Wiberg bond indices. Based on the results obtained, the mechanism proposed is a one‐step process proceeding through a six‐membered cyclic transition state, being a concerted and slightly asynchronous process. The results have been compared with those obtained previously by us (Struct Chem 2013, 24, 1811–1816) for the thermal decomposition of 3‐buten‐1‐ol, in m‐xylene solution. We can conclude that in the compound studied in this work, 3‐methyl‐3‐buten‐1‐ol, the effect of substitution at position 3 by a weakly activating CH₃ group is the stabilization of the transition state formed in the reaction and therefore a small increase in the rate of thermal decomposition.     

Structural and Kinetic Aspects of Blood Plasma Protein Adsorption on the Surface of Hydrophobic Polymers

Abstract

Due to the wide use of polymers in medicine, researchers are required to solve a very important problem–to understand the interaction between materials of nonphysiological origin and the surrounding biological liquids, and tissues, particularly blood.     

Pharmaceutical and medical applications of polymer electrolytes

Classic methods of drug delivery have embraced a number of routes into the site of pharmacological action. Modern preference, wherever possible, is for a non-invasive route to minimise the chance of cross infection, especially of the AIDS virus. The skin, which is the largest organ in the human body, is a particularly appealing route as, in the absence of wounds and blemishes, it offers a natural, high-integrity, barrier to the outside world. Skin patches containing active drug that is allowed to diffuse passively across the external skin barrier into the bloodstream now enjoy wide application but a problem is that the rate of egress is often slow. For certain ionic drugs, including local anaesthetics and, more recently, peptides and gene-based, biotechnological engineered pharmaceuticals, it is possible substantially to enhance transdermal transport by iontophoresis. The technique of iontophoresis facilitates the passage of ionic drugs through the skin using an electric current. Ionically conducting polymers (polymer electrolytes) are potential candidates as hosts for drugs to be delivered iontophoretically. Key issues affecting iontophoretic delivery are reviewed in this paper and the potential role of polymer electrolyte materials in iontophoretic devices will be described. Paper presented at the 9th EuroConference on Ionics, Ixia, Rhodes, Greece, Sept. 15–21, 2002.     

Extending the biocatalytic scope of regiocomplementary flavin-dependent halogenase enzymes

Flavin-dependent halogenases are potentially valuable biocatalysts for the regioselective halogenation of aromatic compounds. These enzymes, utilising benign inorganic halides, offer potential advantages over traditional non-enzymatic halogenation chemistry that often lacks regiocontrol and requires deleterious reagents. Here we extend the biocatalytic repertoire of the tryptophan halogenases, demonstrating how these enzymes can halogenate a range of alternative aryl substrates. Using structure guided mutagenesis we also show that it is possible to alter the regioselectivity as well as increase the activity of the halogenases with non-native substrates including anthranilic acid; an important intermediate in the synthesis and biosynthesis of pharmaceuticals and other valuable products.     

Regioselectivity of enzymatic and photochemical single electron transfer promoted carbon-carbon bond fragmentation reactions of tetrameric lignin model compounds

New types of tetrameric lignin model compounds, which contain the common β-O-4 and β-1 structural subunits found in natural lignins, have been prepared and carbon-carbon bond fragmentation reactions of their cation radicals, formed by photochemical (9,10-dicyanoanthracene) and enzymatic (lignin peroxidase) SET-promoted methods, have been explored. The results show that cation radical intermediates generated from the tetrameric model compounds undergo highly regioselective C-C bond cleavage in their β-1 subunits. The outcomes of these processes suggest that, independent of positive charge and odd-electron distributions, cation radicals of lignins formed by SET to excited states of sensitizers or heme-iron centers in enzymes degrade selectively through bond cleavage reactions in β-1 vs β-O-4 moieties. In addition, the findings made in the enzymatic studies demonstrate that the sterically large tetrameric lignin model compounds undergo lignin peroxidase-catalyzed cleavage via a mechanism involving preliminary formation of an enzyme-substrate complex.     

An acoustic resonance technique for finding breaks in gas-filled pipes

An acoustic technique for finding breaks in the wall of a gas-filled pipe has been developed, which is applicable in difficult conditions. A complete pipe is checked from one end in a single rapid measurement by exciting the ‘organ pipe’ resonances of the gas column and using the average spacing between overtones as a measure of the length to the first break. The pipe to be tested may contain valves and sharp bends. Holes smaller than 2 mm² can be detected. An application is described in which the technique was combined with tape recording and computer data processing to provide a means of checking the integrity of over 3000 sampling channels inside a nuclear reactor. Despite the variability of temperature and composition of the gas in this application, defects were located to within 0·4 m in pipes 13 m long.