On the width of an orientation of a tree

There are 2 ^n-1 ways in which a tree on n vertices can be oriented. Each of these can be regarded as the (Hasse) diagram of a partially ordered set. The maximal and minimal widths of these posets are determined. The maximal width depends on the bipartition of the tree as a bipartite graph and it can be determined in time O(n). The minimal width is one of [/2] or [/2]+1, where is the number of leaves of the tree. An algorithm of execution time O(n + ² log ) to construct the minimal width orientation is given.This research was partially funded by the National Science and Engineering Research Council of Canada under Grant Number A4219.     

Construction of multiporphyrin arrays using ruthenium and rhodium coordination to phosphines

The synthesis of linear multiporphyrin arrays with mono- and bisphosphine-substituted porphyrins as ligand donors and ruthenium(II) or rhodium(III) porphyrins as ligand acceptors is described. With appropriate amounts of the building blocks mixed, linear dimeric and trimeric arrays have been synthesized and analyzed by (1)H NMR and (31)P NMR spectroscopy. The Ru/Rh acceptor porphyrins can be located either at the periphery or in the center of the array. Likewise, the monophosphine porphyrins can be positioned at the periphery, thus allowing a high degree of freedom in the overall composition of the arrays. This way, both donor and acceptor porphyrins can act as chain extenders or terminators. One of the trimeric complexes with two nickel and one ruthenium porphyrin has also been analyzed by X-ray crystallography. Attempts have also been made to synthesize higher order arrays by mixing appropriate amounts of the porphyrins; however, from the NMR data it cannot be concluded if monodisperse five, seven, or nine porphyrin arrays are present or if the solutions are composed of a statistical mixture of smaller and larger arrays.     

ABS blends with phenoxy: morphology,thermal, mechanical and rheological properties

Blends of ABS (acrylonitrile–butadiene–styrene) with phenoxy(poly(hydroxyether bisphenol A)) were prepared using a Branender single screw extruder. Scanning and transmission electron micrographs (SEM, TEM) showed a typical two-phase morphology; particle-in-matrix (90/10) (ABS/phenoxy by weight), 70/30, 10/90), island/sea (30/70) and co-continuous (50/50) morphologies. The glass transition temperature (T_g) of SAN was almost unchanged in the blends, while the T_g of phenoxy increased by about 5 °C in the blends. The synergistic effect of tensile modulus and strength was noted in ABS-rich blends, where a drastic drop of ductility was seen, and the results were interpreted in terms of rubber particle migration form SAN to phenoxy phase, which was visualized by TEM. Melt viscosity showed yield in ABS-rich blends, and generally followed the log additivity.     

Surface-enhanced Raman study of organic sulfides adsorbed on silver

The surface-enhanced Raman scatterings of dimethyl sulfide, diethyl sulfide and dimethyl disulfide have been investigated in silver sol. The dimethyl disulfide molecule decomposes on silver to the corresponding mercaptide implying facile cleavage of its S---S bond. The C---S bond in dialkyl monosulfide appears not to cleave on silver. For diethyl sulfide, the C₂ conformation seems to be favorable on silver than other conformations.