Heterocyclic fused tropylium ions VII. On the synthesis of 9H-dithieno[2,1 -b:4,5-c′]tropylium fluoborate and 4H-dithieno[1,2-b:4,5-c′]tropylium fluoborate

9H-Dithieno[2,1 -b:4,5-c′]tropylium ion (III) and 4ii-dithieno[1,2-b:4,5-c′]tropylium ion (IV) have been synthesized by ring-closure of 1-(4-carboxy-3-thienyl)-2-(3′-thienyl)ethane (IX) and 1-(4-carboxy-3-thienyl)-2-(2′-thienyl)ethane (XVI), respectively, followed by bromination-debrom-ination to 9H-cyclohepta[2,1-b:4,5-c′] dithiophen-9-one (XI) and 4H-cyclohepta[1,2-b:4,5-c′]-dithiophen-4-one (XVIII), and finally by reduction and hydride transfer. The tropylium ions III and IV were less stable than the [b,b′]-fused isomers previously studied.     

Balancing admission control,speedup, and waiting in service systems

Queueing Systems - Consider a population of customers, each of which needs to decide independently when to arrive to a facility that provides a service during a fixed period of time, say a day....