Sobolev Spaces with only Trivial Isometries

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

Polymorphic forms of cilostazol

Two unique conformational polymorphic forms of the compound 6‐[4‐(1‐cyclo­hexyl‐1H‐tetrazol‐5‐yl)­butoxy]‐3,4‐di­hydro­quinolin‐2(1H)‐one (cilostazol), C₂₀H₂₇N₅O₂, have been discovered and characterized using single‐crystal X‐ray structural analysis. A third polymorph also exists, but acceptable crystals could not be obtained. Features of both reported polymorphic structures include a chair conformation of the cyclo­hexyl ring and puckering in the quinolinone ring. The major feature distinguishing the two polymorphic forms is a rotational twisting of the butoxy chain between the tetrazole and quinolinone rings. This difference in conformation influences the intermolecular forces, and hence the packing of the two mol­ecules during crystallization.     

Determination of Interparticle Forces by Colloidal Particle Scattering: A Simulation Study

Preflocculated ferric hydroxide flocs were subjected to either a simple shear flow or a two-dimensional straining flow, and their motion was optically observed. Digital image analysis was applied to extract information on orientation and deformation from the digitized frames. It was found that the simple shear flow led to a rotation of the flocs whose motion can be understood from the behavior of a solid ellipsoid. In the extensional flow, no continuous rotation occurred and flocs were broken apart along the axis of straining. The rupture forces estimated from an ellipsoid model were found to be in the range of 0.1 N/m(2). Copyright 2000 Academic Press.     

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.     

The biosynthesis of quadrone and terrecyclic acid

Feedings of [1-¹³C]- and [1,2-¹³C₂]acetate Aspergillus terreus gave quadrone and terrecyclic acid which were analyzed by ¹³C NMR. The pattern of ¹³C-enrichments and couplings is consistent with the formation of 1 and 2 by cyclization of farnesyl pyrophosphate.     

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.