What is the nature of polyacetylene neutral and anionic chains HC(2n)H and HC(2n)H(-) (n = 6-12) that have recently been observed?

The optimized geometries, adiabatic electron affinities, and IR-active vibrational frequencies have been predicted for the long linear carbon chains HC(2n)H. The B3LYP density functional combined with the DZP basis set was used in this theoretical study. The computed physical properties are discussed. The predicted electron affinities form a remarkably regular sequence: 1.78 (HC(12)H), 2.08 (HC(14)H), 2.32 (HC(16)H), 2.53 (HC(18)H), 2.69 (HC(20)H), 2.83 (HC(22)H), and 2.95 eV (HC(24)H). The predicted structures display an alternating triple and very short single bond pattern, with the degree of bond alternation significantly less for the radical anions.     

Recurrence and transience for random walks with stationary increments

Summary Let S _n = ₁+...+ _n , n1, be the partial sums of stationary, dependent random variables in ^m . The probability space can be partitioned into I _t I _r , where I _t = {S _n} and I _r ={each S _n is limit point of (S _n)_n1}. This result follows from the inclusion{S _n > for n>0}I _t a.s., which is obtained by using Kac's inequality.     

O(2) symmetric connections in an SU(2) Yang-Mills theory

The general O(2) symmetric Yang-Mills equations are derived. An ansatz for O(2) symmetric merons is presented and it is shown that any connection in this ansatz will have SU(2) topological charge density which is a sum of delta functions at points in a plane with weights ± 1/2. It is shown that any connection in this ansatz will beC away from these points.National Science Foundation Pre-doctoral FellowSupported in part by the National Science Foundation under Grant PHY 77-18762     

Carbophilic 3‐Component Cascades: Access to Complex Bioactive Cyclopropyl Diindolylmethanes

Naturally occurring indole‐3‐carbinol and 3,3‐diindolylmethane show bioactivity in a number of disparate disease areas, including cancer, prompting substantial synthetic analogue activity. We describe a new approach to highly functionalised derivatives that starts from allene gas and proceeds via the combination of a three‐component Pd⁰‐catalysed cascade with a one‐pot, three‐component carbophilic Pt^II cascade linked to a stereoselective acid‐catalysed Mannich–Michael reaction that generates complex cyclopropyl diindolylmethanes which show selective activity against prostate cancer cell lines.     

A decision support tool for Public Rights of Way officers based on the Analytic Hierarchy Process

Local Government Authorities (LGA) in England and Wales have statutory responsibility for the maintenance of Public Rights of Way (PROW), such as pathways and byways open to non-motorised traffic. The departments responsible have to compete for budgets and justify their expenditure in terms of councils’ priorities, such as well-being and environment. A need was identified for a simple decision support tool to provide a consistent and transparent framework for assessing the range of possible social and economic benefits from expenditure on PROW. The tool uses the Analytic Hierarchy Process to elicit weights forming the links from path attributes to users and usage to benefits, with a final stage to combine the benefits according to LGA priorities. It was successfully tested through case studies, where improving signage was generally found to be the most cost effective option, giving moderate benefits at low cost, whereas improving the physical conditions of the surface gave greater benefits at relatively high cost.