Clinical interviews administered to third- to sixth-graders explored children's conceptualizations of rational number and of certain extensive physical quantities. We found within child consistency in reasoning about diverse aspects of rational number. Children's spontaneous acknowledgement of the existence of numbers between 0 and 1 was strongly related to their induction that numbers are infi...

We study the freely infinitely divisible distributions that appear as the laws of free subordinators. This is the free analog of classically infinitely divisible distributions supported on [0,∞), called the free regular measures. We prove that the class of free regular measures is closed under the free multiplicative convolution, t boolean power for 0 ≤ t ≤ 1, t free multiplicative power for t ...

A divisible load (job, task) can be arbitrarily divided into independent small load fractions which are assigned to processors in a parallel or distributed computing system for simultaneous processing. Given an arbitrarily divisible load without precedence constraint and a parallel/distributed computing system with communication delays, the problem of divisible load distribution is to find the ...

Abstract. We show that the fixed-point formula in an equivariant complex-oriented cohomology theory E, applied to the free loop space of a manifold X, defines a (renormalized) Riemann-Roch formula for the quotient of the group law of E by a free cyclic subgroup. If E is K-theory, this explains how the elliptic genus associated to the Tate elliptic curve emerges from Witten’s analysis of the fix...

In this paper the equivalence between various divisible load-scheduling policies and continuous time Markov chains is demonstrated. The problem is to show optimal divisible load schedules for various network topologies have Markov chain analogs. This paper is a continuation of our initial short paper [1] that introduced this unification between divisible load theory and Markov chain models for ...

A random variableX is geometrically infinitely divisible iff for every p ∈ (0, 1) there exists random variable Xp such that X d = ∑T (p) k=1 Xp,k, where Xp,k’s are i.i.d. copies of Xp, and random variable T (p) independent of {Xp,1, Xp,2, . . .} has geometric distribution with the parameter p. In the paper we give some new characterization of geometrically infinitely divisible distribution. The...

In the class of abelian groups a subclass of two-divisible-groups is singled out, and in the latter, a subclass of uniquely-two-divisible-groups. With every such a group a special geometrical structure, more precisely the structure of “congruence of vectors” is correlated. The notion of “affine vector space” (denoted by AffVect) is introduced. This term is defined by means of suitable axiom sys...