Advanced microfabrication techniques allow production of experimental systems as narrow as 20 nm for study of electron transport at low temperatures, ~IK. Fine wires in metals, Si-MOS inversion layers, and GaAs modulation-doped heterostructure layers have been studied. Metal rings of diameter ~I ~m have also been studied. New electron interference effects have been discovered in these systems, ...

In this article we resolve the computational complexity of determining the treelength of a graph, thereby solving an open problem of Dourusboure and Gavoille, who introduced this parameter, and asked to determine the complexity of recognizing graphs of bounded treelength [7]. The treelength of a graph G deals with the length of a tree-decomposition. The length of a tree decomposition of G is th...

CLUSTER EXPANSION WITH APPLICATIONS 3 In order to guess the correct form of a, one should consider the left side of the equation above with a(y) ≡ 0. The integral may depend on x; a typical situation is that x is characterized by a length l(x), which is a positive number, so that the left side is roughly proportional to l(x). This suggests to try a(x) = cl(x), and one can then optimize on the v...