In this paper the equivalence between various divisible load-scheduling policies and continuous time Markov chains is demonstrated. This provides a basic unification of both data parallel divisible load scheduling and Markov chain models for the first time in 16 years of research. Such equivalence is demonstrated for divisible scheduling on linear daisy chains and single and two level tree netw...

In this paper we seek to describe the structure of self-dual torsion-free LCA groups. We first present a proof of the structure theorem of self-dual torsion-free metric LCA groups. Then we generalize the structure theorem to a larger class of selfdual torsion-free LCA groups. We also give a characterization of torsion-free divisible LCA groups. Consequently, a complete classification of self-du...

in this paper, the concept of fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) of an ordered group (resp. lattice-ordered group) is introduced and some properties, characterizations and related results are given. also, the fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) generated by a fuzzy subgroup (resp. fuzzy subsemigroup) is characterized. furthermore,...

Convention: all base schemes will be in characteristic p. Writing k or we will assume k = k F p , respectively = F p. We will write X ! S for a p-divisible group over a base S (and sometimes will say \a family of p-divisible groups"), while we tend to write X when we consider a p-divisible group over a base eld (but we are not strict in this convention). Instead of \p-divisible group" one can a...

We give a precise characterization of two important classes of conditionally positive definite (CPD) kernels in terms of integral transforms of infinitely divisible distributions. In particular, we show that for any stationary CPD kernel A(x, y) = f(x − y), f is the log-characteristic function of a uniquely determined infinitely divisible distribution; further, for any additive CPD kernel A(x, ...

There is a one-to-one correspondence between classical one-dimensional infinitely divisible distributions and free infinitely divisible distributions. In this work we study the free infinitely divisible distributions corresponding to the one-dimensional type  distributions. A new characterization of classical type  distributions is given first and the class of type  classical infinitely divi...

Group divisible designs are the most important class of partially balanced incomplete block (PBIB) designs. A list of new group divisible designs with r, k ⩽ 10 is provided.

The divisible load scheduling is a paradigm in the area of distributed computing. The traditional divisible load theory is based on the fact that, the communications and computations are obedient and do not cheat the algorithm. The literature of review shows that the divisible load model fail to achieve its optimal performance, if the processors do not report their true computation rates. The d...