We recently noticed an error in our paper, " Local optimization on graphs " , The error is not too serious, in that all of the lemmata, propositions, and theorems are correct as given. However, the divide-and-conquer algorithm in Section 2.1, p. 159, is incomplete. The necessary changes are as follows (all changes are to p. 159): (2) In Steps 1 and 2, " S "… (More)
For the first time, patterned growth of boron nitride nanotubes is achieved by catalytic chemical vapor deposition (CCVD) at 1200 °C using MgO, Ni, or Fe as the catalysts, and an Al 2 O 3 diffusion barrier as underlayer. The as-grown BNNTs are clean, vertically aligned, and have high crystallinity. Near band-edge absorption ∼6.0 eV is detected, without… (More)
Matching 2-lattice polyhedra are a special class of lattice polyhedra that include network ow polyhedra, fractional matching polyhedra, matroid intersection polyhedra, etc. In this paper we develop a polynomial-time extreme point algorithm for ÿnding a maximum cardinality vector in a matching 2-lattice polyhedron.
Two-lattice polyhedra are a special class of lattice polyhedra that include network ow poly-hedra, fractional matching polyhedra, matroid intersection polyhedra, the intersection of two polymatroids, etc. In this paper we show that the maximum sum of components of a vector in a 2-lattice polyhedron is equal to the minimum capacity of a cover for the… (More)