A critical review of experimental accomplishments in the field of filament-reinforced metal matrix composites Bimonthly progress report

Critical review of experimental accomplishments in filament reinforced metal-matrix composite

An asymptotic formula for the number of non-negative integer matrices with prescribed row and column sums

We count mxn non-negative integer matrices (contingency tables) with prescribed row and column sums (margins). For a wide class of smooth margins we establish a computationally efficient asymptotic formula approximating the number of matrices within a relative error which approaches 0 as m and n grow.Comment: 57 pages, results strengthened, proofs simplified somewha

The number of graphs and a random graph with a given degree sequence

We consider the set of all graphs on n labeled vertices with prescribed degrees D=(d_1, ..., d_n). For a wide class of tame degree sequences D we prove a computationally efficient asymptotic formula approximating the number of graphs within a relative error which approaches 0 as n grows. As a corollary, we prove that the structure of a random graph with a given tame degree sequence D is well described by a certain maximum entropy matrix computed from D. We also establish an asymptotic formula for the number of bipartite graphs with prescribed degrees of vertices, or, equivalently, for the number of 0-1 matrices with prescribed row and column sums.Comment: 52 pages, minor improvement

Kinematics of the Broad Line Region in M81

A new model is presented which explains the origin of the broad emission lines observed in the LINER/Seyfert nucleus of M81 in terms of a steady state spherically symmetric inflow, amounting to 1 x 10^-5 Msun/yr, which is sufficient to explain the luminosity of the AGN. The emitting volume has an outer radius of ~1 pc, making it the largest broad line region yet to be measured, and it contains a total mass of ~ 5 x 10^-2 Msun of dense, ~ 10^8 cm^-3, ionized gas, leading to a very low filling factor of ~ 5 x 10^-9. The fact that the BLR in M81 is so large may explain why the AGN is unable to sustain the ionization seen there. Thus, the AGN in M81 is not simply a scaled down quasar.Comment: Accepted for Publication in ApJ 7/21/0