An abstract is not available for this content so a preview has been provided. Please use the Get access link above information on how to content.

Introduction and remarks. In the theory of r)a-sets three main theorems stand out: that an r/0-set is universal for totally ordered sets of power not exceeding Xa, that any two 7/a-sets of power Na are isomorphic and that 7/a-sets of power Xa exist provided Ka is a regular cardinal number and 2~2i<<> 2t*sS&a. L. Gillman and M. Jerison [6] have shown that a real closed (totally ordered) field wh...

The underlying assumption of Divisible Load Scheduling is that the processors composing the network are obedient, i.e., they do not “cheat” the algorithm. This assumption is unrealistic if the processors are owned by autonomous, self-interested organizations that have no a priori motivation for cooperation and they will manipulate the algorithm if it is beneficial to do so. In this paper we pro...

A group divisible design is resolvable if there exists a partition n = {P,, Pz, . .} of p such that each part Pi is itself a partition of X. In this paper we investigate the existence of resolvable group divisible designs with K = {3}, M a singleton set, and all A. The case where M = { 1) has been solved by Ray-Chaudhuri and Wilson for I = 1, and by Hanani for all h > 1. The case where M is a s...

Recently, the concept of infinitely divisible scaling has attracted much interest. As models of this scaling behavior, Poisson products of Cylindrical Pulses and more general infinitely divisible cascades have been proposed. This paper develops path and scaling properties of Poisson products of arbitrary pulses with non-compact support such as multiplicative and exponential shot-noise processes...

Providing QoS and performance guarantees to arbitrarily divisible loads has become a significant problem for many cluster-based research computing facilities. With the emergence of Grid applications that require simultaneous access to multi-site resources, supporting advance reservations in a cluster has become increasingly important. While progress is being made in scheduling arbitrarily divis...

Multiplicative processes and multifractals proved useful in various applications ranging from hydrodynamic turbulence to computer network traffic. It was recently shown and explained how and why multifractal analysis could be fruitfully placed in the general framework of infinitely divisible cascades. The aim of this contribution is to design processes, called Infinitely Divisible Cascading (ID...

A divisible load distribution algorithm on k-dimensional meshes and tori is proposed and analyzed. It is found that by using our algorithm, the speed-up of parallel processing of a divisible load on k-dimensional meshes and tori is bounded from above by a quantity independent of network size, due to communication overhead and limited network connectivity. In particular, it is shown that for k-d...