A generalization of Plantholt's theorem

Let K denote the complete graph K_2n+1 with each edge replicated r times and let χ′(G) denote the chromatic index of a multigraph G. A multigraph G is critical if χ′(G) > χ′(G/e) for each edge e of G. Let S be a set of sn – 1 edges of K. We show that, for 0 < s ≦ r, G/S is critical and that χ′ (G/(S ∪{e})) = 2rn + r – s for all e ∈ E(G/S). Plantholt [M. Plantholt, The chromatic index of graphs with a spanning star. J. Graph Theory 5 (1981) 5–13] proved this result in the case when r = 1.     

Extracellular proteolytic processing ofAspergillus awamori GAI into GAII is supported by physico-chemical evidence

The proportion of glucoamylases, GAI and GAII, in the culture supernatant ofAspergillus awamori fermentations depends on the medium C/N ratio in such a way that the transformation of GAI into GAII is favored by the existence of a surplus of the carbon source in the growth medium. This condition also favors the appearance of the proteolytic activity. The authors report the observation that the shift in the isoenzyme proportion was concomitant to the peak of proteolytic activity. A peptide that may have resulted from the continuous degradation of the GAI C-terminal peptide, Gp-1, was isolated by gel filtration and purified by reversephase chromatography. This peptide matched with the region G¹⁴-A³⁴ of the substrate-binding domain of GAI, thus reinforcing the hypothesis of the extracellular proteolytic processing of GAI.     

The chromatic index of graphs of even order with many edges

We show that, for r = 1, 2, a graph G with 2n + 2 (≥6) vertices and maximum degree 2n + 1 - r is of Class 2 if and only if |E(G/v)| > () - rn, where v is a vertex of G of minimum degree, and we make a conjecture for 1 ≤ r ≤ n, of which this result is a special case. For r = 1 this result is due to Plantholt.     

Clarifications of Certain Ambiguities and Failings of?Poisson��s Ratios in Linear Viscoelasticity

Detailed new analytical investigations are presented describing the behavior of Class I, II and III viscoelastic Poisson??s ratios (PR). Their previously demonstrated dependence on stress-time histories, which lead to the inability to consider them as universal viscoelastic material properties and the incapacity to produce a general elastic?Cviscoelastic correspondence principle (EVCP) based, is expanded. A new Class VI PR is analytically derived from the viscoelastic constitutive relations in the Fourier transform (FT) space to achieve the proper FT form of the elastic/viscoelastic correspondence principle, i.e., the elastic-viscoelastic analogy. However, even though this PR Class is a pure universal material property function, it still fails to provide a convenient and useful path to a correspondence principle due to its inopportune constitutive form in real time space vis-à-vis a thermodynamic model with equivalent attributes. Consequently, no general EVCP involving PRs can be formulated. The derived Class VI PRs are equivalent to the defined Class III PRs with 1-D loadings (stresses).     

Common black coatings – reflectance and ageing characteristics in the 0.32–14.3 μm wavelength range

The diffuse and regular reflectances of five optically absorbing coatings frequently used in optical systems, were measured over the 0.32–14.3 μm wavelength range, before and after exposure to heat and intense optical radiation. The measured coatings included Nextel Velvet Black, an anodised coating and NPL Super Black. The anodised coating exhibited substantial variations in its diffuse and regular reflectance values after thermal and simulated solar ageing. Solar and thermal ageing of the Nextel Velvet Black resulted in increases of its reflectance. However, thermal ageing tended to decrease the reflectance of the other paint samples examined. Thermal and solar ageing of the NPL Super Black resulted in only minor changes in its reflectance characteristics. All measurements are traceable to the UK National Standards.     

Speciation and detection of organotins from PVC pipe by micro‐liquid chromatography–electrospray–ion trap mass spectrometry

This paper describes the application of a micro‐liquid chromatography–electrospray–ion trap mass spectrometry (µ‐LC–ES–ITMS) method for separation and detection of organotin compounds leached from potable‐water polyvinyl chloride (PVC) pipe. Dibutyltin (DBT) is added as a heat stabilizer to PVC. DBT was determined in 1 l water samples that had remained static in PVC pipes over several days (totaling 96 h). Other organotin compounds in the leachate were screened for, by using µ‐LC–ES–ITMS. An initial level of approximately 1 µgl^?1 of DBT resulted within 24 h, with a subsequent drop and then a rise in DBT levels over the next 96 h to 0.8 µgl^?1. Published in 2001 by John Wiley & Sons, Ltd.     

Outline and Amalgamated Triple Systems of Even Index

This paper proves that a triangulated graph is an outline triplesystem of even index if and only if it is an amalgamated triplesystem of even index. 2000 Mathematical Subject Classification:primary 05B07; secondary 05C99.