Exact colorations of graphs and digraphs

A coloration is an exact regular coloration if whenever two vertices are colored the same they have identically colored neighborhoods. For example, if one of the two vertices that are colored the same is connected to three yellow vertices, two white and red, then the other vertex is as well. Exact regular colorations have been discussed informally in the social network literature. However they have been part of the mathematical literature for some time, though in a different format. We explore this concept in terms of social networks and illustrate some important results taken from the mathematical literature. In addition we show how the concept can be extended to ecological and perfect colorations, and discuss how the CATREGE algorithm can be extended to find the maximal exact regular coloration of a graph.

Ag+- and Zn2+-exchange kinetics and antimicrobial properties of 11 angstrom tobermorites

Ag+- and Zn2+-exchanged zeolites zeolites and clays have been used as coatings and in composites to confer broad-spectrum antimicrobial properties on a range of technical and biomedical materials. 11 angstrom tobermorite is a bioactive layer lattice ion exchanger whose potential as a carrier for Ag+ and Zn2+ ions in antimicrobial formulations has not yet been explored. In view of this, batch Ag+- and Zn2+-exchange kinetics of two structurally distinct synthetic 11 angstrom tobermorites and their subsequent bactericidal action against Staphylococcus aureus and Pseudomonas aeruginosa are reported. During the exchange reactions, Ag+ ions were found to replace labile interlayer cations; whereas, Zn2+ ions also displaced structural Ca2+ ions from the tobermorite lattice. In spite of these different mechanisms, a simple pseudo-second-order model provided a suitable description of both exchange processes (R-2 >= 0.996). The Ag+- and Zn2+-exchanged tobermorite phases exhibited marked bacteriostatic effects against both bacteria, and accordingly, their potential for use as antimicrobial materials for in situ bone tissue regeneration is discussed. (C) 2008 Elsevier Ltd. All rights reserved.

The performance and persistence of exchange-traded funds: evidence for iShares MSCI country-specific ETFs

The aim of this paper is to investigate the performance and persistence of 20 iShares MSCI country-specific exchange-traded funds (ETFs) in comparison with S&P 500 index over the period July 2001 to June 2006. There are several studies analysing mutual funds performance in past years, but very little is known about ETFs. In our analysis the Sharpe, Treynor and Sortino ratios are used as risk-adjusted performance measures. To evaluate performance persistence and therefore if there is any relationship among past performance and future performance, we apply to the Spearman Rank Correlation Coefficient and the Winner-loser Contingency Table. The main findings are at two levels. First, ETFs can beat the U.S. market index based on risk-adjusted performance measures. Second, there is evidence of ETFs performance persistence based on annual return.