Sobolev Spaces with only Trivial Isometries

We will give some conditions for Sobolev spaces on bounded Lipschitz domains to admit only trivial isometries.     

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.     

Disordered ground states for classical discrete-state problems in one dimension

It is known that one-dimensional lattice problems with a discrete, finite set of states per site generically have periodic ground states (GSs). We consider slightly less generic cases, in which the Hamiltonian is constrained by either spin (S) or spatial (I) inversion symmetry (or both). We show that such constraints give rise to the possibility ofdisordered GSs over a finite fraction of the coupling-parameter space—that is, without invoking any nongeneric fine tuning of coupling constants, beyond that arising from symmetry. We find that such disordered GSs can arise for many values of the number of statesk at each site and the ranger of the interaction. The Ising (k=2) case is the least prone to disorder:I symmetry allows for disordered GSs (without fine tuning) only forr5, whileS symmetry never gives rise to disordered GSs.     

Ultraviolet protection factors for clothing: an intercomparison of measurement systems

In recent years the need to standardize measurement protocols for quantifying the degree of ultraviolet radiation (UVR) protection provided by clothing has led to the introduction of a number of standards around the world. To date, these standards have specified spectral measurements of UVR transmission by clothing and fabrics. Development of a standard test method has become an important part of the testing process, and this article presents results from an intercomparison involving 10 independent testing laboratories and 11 different UVR transmission measurement instruments. In addition to comparing the measured ultraviolet protection factors (UPF), this intercomparison also incorporates detailed scan results from all 10 laboratories and highlights differences in performance of the various instruments in different wavelength regions. Careful examination of these differences can indicate where changes to the systems could be made to allow improvements both in equipment performance and in agreement of the final results. The variability in the measurements of UPF in this study suggest that the protection categories in standards may need to be broadened.     

An experimental and theoretical study of competitive adsorption at the n-heptane/water interface

A model to calculate the interfacial concentration of competing surface active species in a two-phase oil/water system was developed. To enable the calculation of the surface excess of 2-hydroxy-5-nonylacetophenone oxime (HNAPO, active ingredient of LIX 84) in the presence of surfactants competing for interfacial area, an interfacial adsorption competition model was derived for noninteracting surface active species in a n-heptane/aqueous system, assuming ideal enthalpy and entropy of mixing. The model was found to be valid for HNAPO in the presence of sodium dodecyl sulfate (SDS) or dodecyldimethyl(3-sulfopropyl)ammonium (DDSA). In the case of dodecyltrimethylammonium chloride (DTAC) or octa(ethylene glycol) mono-n-dodecyl ether (C12E8) as the competing surfactants with HNAPO, the predicted surface excess values from the model fit less favorably. The difference was shown to not be due to nonideal entropy of mixing.     

Comparison of capillary electrophoresis with traditional methods to analyse bovine whey proteins

The separation of the four major whey proteins by sodium dodecyl sulphate (SDS)-capillary gel electrophoresis (CGE) is described. Whilst commercially purified whey proteins could be analysed using the recommended protocol, the more complex nature of an acid whey and a reconstituted whey protein concentrate (WPC) powder necessitated considerable refinement of the CGE sample buffer. Individual whey proteins in the acid whey and WPC samples were then also separated and quantitated using capillary zone electrophoresis, polyacrylamide gel electrophoresis (PAGE) and HPLC methods and the results were compared. The values obtained for -lactalbumin (-Lac) and β-lactoglobulin (β-Lg) were consistent throughout the various methods, although size-exclusion HPLC, SDS-PAGE and SDS-CGE could not separate the two β-Lg variants or the glycosylated form of -Lac from the β-Lg. There was considerable variation in the values for the bovine serum albumin and immunoglobulin determined by the different methods and it was concluded that none of the methods could satisfactorily quantitate all four whey proteins.     

Electroactive conducting polymers for corrosion control

There is an intensive effort underway to develop new corrosion control coatings for structural metals. In part, this effort has been motivated by the desire to replace chromium(VI)-containing coatings currently used for corrosion control of iron and aluminum alloys. Cr(VI) has been shown to be hazardous to the environmental and to human health, and its use in many countries will be sharply curtailed in the coming years. Electroactive conducting polymers (ECPs) represent a class of interesting materials currently being explored for use in corrosion control coating systems, possibly as a replacement for Cr(VI)-based coatings. The electroactivity and the electronic conductivity (or semiconductivity) of ECPs set them apart from traditional organic coatings. As with chromate, interesting and potentially beneficial interactions of ECPs with active metal alloys such as steel and aluminum are anticipated, with concomitant alteration of their corrosion behavior. A review of this active research area will be presented in two parts. Here in Part 1, a general introduction to the topic of corrosion control by ECPs will be presented, including an overview of corrosion and its control by traditional methods, an introduction to ECPs and their properties, and a discussion of the processing issues surrounding the use of ECPs as coatings. Part 1 also includes a review of the literature on the use of ECPs as coatings (or components of coatings) on non-ferrous active metals, principally aluminum and aluminum alloys, although some work on zinc, copper, silver, titanium and silicon will also be described. In Part 2 of this review (to be published in the next issue of this journal), the rather extensive literature on the use of ECPs for the corrosion control of ferrous alloys (steels) will be reviewed. Electronic Publication     

Organisational linkages and O.R. projects

An empirical study of a group of O.R. projects in presented with particular attention being paid to organisational interactions. The results are derived from detailed investigations of O.R. projects in which both the managers(s) and O.R. practitioner(s) were interviewed. This initial exploration has indicated a variety of organisational forms, and revealed the importance of non-formal processes that often take place.     

Designing routes to minimize fleet operating costs

A route-planner must try to schedule the delivaries by a fleet of vehicles such that customer requirements are met and management objectives are satisfied. In most cases, the number of feasible arrangements is legion, and calculations relating to individual vehicle loads, mileages, delivery times, etc. are tedious, allowing only a small fraction of possible route plans to be established and compared. The problem presents an ideal opportunity for computer application, not least to ensure that solutions are timely and error free.Several algorithms have been developed to improve the quality of vehicle routes, but in practice only those that rely on simple selection rules have found widespread acceptance, due to the innate complexity of the calculations that follow from a more rigorous approach and to the great variety of customer, vehicle, and operational characteristics that distinguish transport systems and which must be accomodated.The method presented here is based upon the well-known ‘savings’ criterion, but avoids many of its deficiencies by employing a random selection mode and producing (efficiently) a large sample of schedules from which to choose the most suitable. In particular, this allows greater flexibility in defining management objectives, and has led to substantial reductions in both fleet sizes and distances travelled, compared to published results, for a set of nine test cases each involving more than 200 customer locations.