New types of designs called nested space-filling designs have been proposed for conducting multiple computer experiments with different levels of accuracy. In this article, we develop several approaches to constructing such designs. The development of these methods also leads to the introduction of several new discrete mathematics concepts, including nested orthogonal arrays and nested differen...

We propose an approach for constructing asymmetric nested lattice samples by randomizing asymmetric nested orthogonal arrays. Such designs possess a desirable nested structure and have attractive space-filling properties. Unlike recently developed symmetric nested lattice samples, different axes of asymmetric nested lattice samples can be divided at different scales of fineness. The proposed de...

We show how to build a continuous, one-dimensional index of the points on a triangulated, two-dimensional manifold T . The index is constructed by quickly finding a vertex-adjacent ordering of the triangles (that is, sequential triangles share at least one vertex). Then the space within triangles is indexed with a spacefilling curve oriented so that the lowest point in each triangle is the vert...

In this paper, an algorithm to determine the topology of an algebraic space curve and to compute a certified G rational parametric approximation of the algebraic space curve is given by extending the local generic position method for solving zero dimensional polynomial equation systems to the case of dimension one. By certified, we mean the approximation curve and the original curve have the sa...

‎In the present study‎, ‎we consider a regular curve in Galilean‎ ‎$4$-space $mathbb{G}_{4}$ whose position vector is written as a‎ ‎linear combination of its Frenet vectors‎. ‎We characterize such‎ ‎curves in terms of their curvature functions‎. ‎Further‎, ‎we obtain‎ ‎some results of rectifying‎, ‎constant ratio‎, ‎$T$-constant and‎ ‎$N$-constant curves in $mathbb{G}_{4}$‎.

We prove results showing that the existence of essential maps of surfaces in a manifold M̄ obtained from a 3-manifold M by Dehn filling implies the existence of essential maps of surfaces in M .

In this paper, we classify and describe a method for constructing fractal trees in three dimensions. We explore certain aspects of these trees, such as space-filling and self-contact. 2006 Published by Elsevier Ltd.

Several aspects of managing a sensor network (e.g., motion planning for data mules, serial data fusion and inference) benefit once the network is linearized to a path. The linearization is often achieved by constructing a space filling curve inside the domain. But existing methods cannot handle networks distributed on surfaces of complex topology. This paper presents a novel method for generati...

In this paper we consider the conjecture through the Dehn filling construction. LetM be a compact, connected, orientable, irreducible 3-manifold M such that ∂M is a torus. Recall that a slope on ∂M is the isotopy class of an unoriented, simple, essential loop in ∂M . We use ∆(r1, r2) to denote the distance (i.e. the minimal geometric intersection number) between two slopes r1 and r2 on ∂M and u...

In the context of open distributed systems, the ability to coordinate the agents coupled with the possibility to control the actions they perform is important. As open systems need to be scalable, capabilities may provide the best-fit solution to overcome the problems caused by the loosely controlled coordination of tuple-space systems. Acting as a ‘ticket’, capabilities can be given to the cho...