The fast multipole method (FMM) performs fast approximate kernel summation to a specified tolerance ǫ by using a hierarchical division of the domain, which groups source and receiver points into regions that satisfy local separation and the well-separated pair decomposition properties. While square tilings and quadtrees are commonly used in 2D, we investigate alternative tilings and associated ...

We present an external-memory algorithm to compute a well-separated pair decomposition (WSPD) of a given point set S in Rd in O(sort(N)) I/Os, where N is the number of points in S and sort(N) denotes the I/O-complexity of sorting N items. (Throughout this paper, we assume that the dimension d is fixed). As applications of the WSPD, we show how to compute a linear-size t-spanner for S within the...

Parasitic myomas are those that have become partially or almost completely separated from the uterus and receive their main blood-supply from another source. The etiopathogenesis of parasitic myomas may be separation of peduncululated subserosal myomas that have outgrown their blood supply. More commonly, iatrogenic parasitic myomas may be caused by seeding of myoma fragments following morcella...

Rabbit liver UDP-glucuronyltransferase activity was resolved into two separate fractions on DEAE-cellulose, one containing most of the transferase activity toward oestrone and the other most of the activity toward p-nitrophenol. These two activities were completely separated by rechromatography of each fraction on a second DEAE-cellulose column.

Cu as nearly immiscible components. However, it is well-known that in nanoscale structures the higher contribution of the interfacial energy to the thermodynamic potential can lead to a completely different phase diagram [1]. On the other hand, the electrical conductivity of nanoscale ferromagnetic multilayers separated by nonmagnetic interlayers strongly depends on the magnetic alignment betwe...

Within the framework of Euclidean path integral and mass perturbation theory we compute the Wilson loop of widely separated external charges for the massive Schwinger model. From this result we show for arbitrary order mass perturbation theory that integer external charges are completely screened, whereas for noninteger charges a constant long-range force remains.

We prove under CH that if B is a Boolean algebra of size at most c then there is a subalgebra C of P(ω) containing fin such that C/fin is isomorphic to B and C contains no infinite completely separated set. This is a generalization of a result of Dow.  2001 Elsevier Science B.V. All rights reserved.