We prove exponential decay for the tail of the radius R of the cluster at the origin, for subcritical random-cluster models, under an assumption slightly weaker than that E(R d1) < 1 (here, d is the number of dimensions). Speciically, if E(R d1) < 1 throughout the subcritical phase, then P(R n) exp(n) for some > 0. This implies the exponential decay of the two-point correlation function of subc...

Interferometric observations of the Sunyaev-Zel'dovich Effect (SZE) toward clusters of galaxies provide sensitive cosmological probes. We present results from 1 cm observations (at BIMA and OVRO) of a large, intermediate redshift cluster sample. In addition, we describe a proposed, higher sensitivity array which will enable us to survey large portions of the sky. Simulated observations indicate...

For Fp the field on prime number p > 3 elements, it has been conjectured that there are just p+3 evaluations of the Tutte polynomial in Fp which are computable in polynomial time. In this note it is shown that if p 6≡ −1mod 12 then there are further polynomial-time computable evaluations. 1 Definitions and introduction Let G = (V,E) denote a graph, with loops and parallel edges permitted, and G...

We use a representation of 3-D bodies derived from that used by Lang and Braid [ 3 ] . Body models are b u i l t up from two kinds of p r i m i t i v e s : the half-space H, defined as the set of points and the i defined as the set of points _ Bodies are represented as boolean combinations of sets r e s u l t i n g from transformations of the (perhaps complemented) p r i m i t i v e s by member...