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...

Then H need not be divisible, i.e., we need not have pH D H . We only know H is contained in pG. Moreover, for x in H , there need not exist an infinite sequence y1;y2;y3:::: such that py2 D y1, py3 D y2; ::. We only know that there exist arbitrarily long finite such sequences. There does exist a unique maximal divisible subgroup D of M , and D is a subgroup of H . Moreover, M DD ̊N where N is a...

Given a system model where machines have distinct speeds and power ratings but are otherwise compatible, we consider various problems of scheduling under resource constraints on the system which place the restriction that not all machines can be run at once. These can be power, energy, or makespan constraints on the system. Given such constraints, there are problems with divisible as well as no...

The divisible load model is motivated by divisible load theory, where both communication and computation can be arbitrarily divisible into as many independent partitions as required and facilitates a good approximation for many real-world application systems such as those arising in large physics experiments. Scheduling an application with divisible load in data grid is significantly important ...

261 Davis, J.A., New constructions of divisible designs, Discrete Mathematics 120 (1993) 261-268. A construction is given for a (p2"(p+l),p,p2"+ 1(p+l),p2"+ ,p"(p+l)) (pa prime) divisible difference set in the group H x z~.+, where His any abelian group of order p+ 1. This can be used to generate a symmetric semi-regular divisible design; this is a new set of parameters for .l. 1 ;<'0, and thos...

1. In the first theorem of [3], Wiegandt incorrectly states that a semimodule is complete if and only if it is divisible. (See §2 for definitions.) In this paper we show (in §3) that his theorem should read: a semimodule is complete if and only if it is a divisible group. Divisible semimodules which are not necessarily groups are discussed in §4, in connection with Wiegandt's second theorem. It...