Note on Signature Change and Colombeau Theory

Recent work alludes to various 'controversies' associated with signature change in general relativity and claims to resolve them. As we have argued previously, these are in fact disagreements about the (often unstated) assumptions underlying various possible approaches. We demonstrate that the issue has not been resolved and the choice between approaches remains open.     

Binary group and Chinese postman polyhedra

A new proof of the characterization of the Chinese postman polyhedra is given. In developing this proof, a theorem of Gomory about homomorphic lifting of facets for group polyhedra is generalized to subproblems. Some results for the Chinese postman problem are generalized to binary group problems. In addition, a connection is made between Fulkerson's blocking polyhedra and a blocking pair of binary group problems. A connection is also developed between minors and lifting of facets for group problems.     

Fragmentation pathways of 2,3‐dimethyl‐2,3‐dinitrobutane cations in the gas phase

2,3‐Dimethyl‐2,3‐dinitrobutane (DMNB) is an explosive taggant added to plastic explosives during manufacture making them more susceptible to vapour‐phase detection systems. In this study, the formation and detection of gas‐phase [M+H]⁺, [M+Li]⁺, [M+NH₄]⁺ and [M+Na]⁺ adducts of DMNB was achieved using electrospray ionisation on a triple quadrupole mass spectrometer. The [M+H]⁺ ion abundance was found to have a strong dependence on ion source temperature, decreasing markedly at source temperatures above 50°C. In contrast, the [M+Na]⁺ ion demonstrated increasing ion abundance at source temperatures up to 105°C. The relative susceptibility of DMNB adduct ions toward dissociation was investigated by collision‐induced dissociation. Probable structures of product ions and mechanisms for unimolecular dissociation have been inferred based on fragmentation patterns from tandem mass (MS/MS) spectra of source‐formed ions of normal and isotopically labelled DMNB, and quantum chemical calculations. Both thermal and collisional activation studies suggest that the [M+Na]⁺ adduct ions are significantly more stable toward dissociation than their protonated analogues and, as a consequence, the former provide attractive targets for detection by contemporary rapid screening methods such as desorption electrospray ionisation mass spectrometry. Copyright © 2009 Commonwealth of Australia. Published by John Wiley & Sons, Ltd.     

Phenanthrene removal in unsaturated soils treated by electrokinetics with different surfactants—Triton X-100 and rhamnolipid

In this study, the remediation performance of electrokinetic (EK) technology integrated with different surfactants for removing phenanthrene from unsaturated soils was investigated. A synthetic surfactant (Triton X-100) and a biosurfactant (rhamnolipid) were used to enhance phenanthrene solubility and removal efficiency during EK process. Results indicate that the electro-osmotic flow (EOF) rate in the rhamnolipid system is higher than that in Triton X-100. Using the EK technology for the removal of phenanthrene in the presence of rhamnolipid was more efficient than in the presence of Triton X-100. In addition to the transport mechanism of phenanthrene in EK system, the presence of rhamnolipid may promote microbial growth in the soil–water system and bring about biodegradation of phenanthrene. A diffusion–advection–sorption (DAS) model was solved by MATLAB, based on the linear sorption isotherm at the non-equilibrium condition, which is feasible to simulate the movement of phenanthrene during the EK + Triton X-100 treatment.     

Synthesis of S-linked carbohydrate analogues via a Ferrier reaction

In this work, the synthetic utility of the Ferrier reaction to access S-linked disaccharides and S-linked glycoamino acids has been probed. Significantly, entry to a range of 1,4- and 1,6-S-linked disaccharides has been achieved using glycals derived from glucose and galactose, and sulfur containing coupling partners derived from methyl α-d-glucopyranoside. Access to S-linked glycoamino acids and glycopeptides has also been achieved using protected cysteine and homocysteine coupling partners within the Ferrier reaction. Functionalisation of the Ferrier products, for example, via dihydroxylation using OsO₄ or amino acid coupling, and deprotection of the targets have also been achieved. In this way, entry to materials of interest as mimics of biologically interesting disaccharides and glycopeptides has been realised, including targets derived from rare sugars such as talopyranose and gulopyranose.     

Sample period selection and long-term dependence: New evidence from the Dow Jones index

This study employs the classical and modified rescaled adjusted range statistic (R/S statistic) to investigate the sensitivity of the long-term return anomaly observed on the Dow Jones Industrial Average (DJIA) to sample and method bias. Daily data from 1/1/1970 to 17/3/2004 is used with sub-periods identified based on sign shifts in the mean returns as well as the October 1987 crash. The return series are also filtered to accommodate autoregressive conditional heteroskedastic (ARCH) innovations and short-term dependencies. Hurst exponent and V-statistic values for each of the filtered series for the whole sample and sub-periods are estimated, while polynomial regression techniques are applied to plot the V-statistics. These plots show oscillating cycles of varying lengths. Overall, we find the null hypothesis of no long-term dependence is accepted for the whole sample and every sub-period using the modified rescaled range test, but not necessarily using the classical rescaled adjusted range test. The later test does, however, reveal episodes of both positive and negative dependence over the various sample periods, which have been reported by other researchers.