In this article, we propose a Partition ofUnity Refinement (PUR)method to improve the local approximations of elliptic boundary value problems in regions of interest. The PUR method only needs to refine the local meshes and hanging nodes generate no difficulty. The mesh qualities such as uniformity or quasi-uniformity are kept. The advantages of the PUR include its effectiveness and relatively ...

The original definition of a topological space given by Hausdorff used neighborhood systems. Lattice-valued maps appear in this context when you identify a topology with a monoid in the Kleisli category of the filter monad on SET. H?hle’s notion of a lattice-valued topology [2] uses the same idea and it’s inspired in the classical lattice-valued topologies. Ltopological spaces are motivated by ...

The Banks Peninsula tree weta, Hemideina ricta Hutton, is the rarest of the seven species of tree weta. Prior to our study it was known from only two locations on Banks Peninsula: Okains Bay (R. Bigelow, formerly Canterbury University, pers. comm.) and in totara (Podocarpus totara (G. Benn ex D. Don.)) logs near Purple Peak (P. Johns, Canterbury University, pers. comm.). The only other publishe...

s — In this paper, we extend the techniques used in Grid-based Monte Carlo applications to Grid-based quasi-Monte Carlo applications. These techniques include an N-out-of-M strategy for efficiently scheduling subtasks on the Grid, lightweight checkpointing for Grid subtask status recovery, a partial result validation scheme to verify the correctness of each individual partial result, and an int...

In this paper, we establish a deterministic error bound for estimating a functional of the solution of the integral transport equation via random walks that improves an earlier result of Chelson generalizing the Koksma-Hlawka inequality for nite dimensional quadrature. We solve such problems by simulation, using sequences that combine pseudorandom and quasirandom elements in the construction of...