Random Heegaard splittings

A random Heegaard splitting is a 3-manifold obtained by using a random walk of length n on the mapping class group as the gluing map between two handlebodies. We show that the joint distribution of random walks of length n and their inverses is asymptotically independent, and converges to the product of the harmonic and reflected harmonic measures defined by the random walk. We use this to show that the translation length on the curve complex of a random walk grows linearly in the length of the walk, and similarly, that distance in the curve complex between the disc sets of a random Heegaard splitting grows linearly in n. In particular, this implies that a random Heegaard splitting is hyperbolic with asymptotic probability one.Comment: 31 pages, 5 figures, revised versio

Stochastic user equilibrium assignment with elastic demand

It is well-known that, in deterministic user equilibrium assignment, it is straightforward to allow for elastic demand. The research described in this paper sets out to show that the same is true for stochastic user equilibrium assignment with elastic demand (SUEED). It presents a new objective function for SUEED, and a simple solution algorithm that can be implemented by only a minor modification to existing assignment software. A numerical example illustrates the working of the algorith

Lighting up learning: mathematics becoming less of a \u27killer subject\u27 in KwaZulu-Natal, South Africa

This paper reports the findings of an evaluative study of an initiative, in its sixth year of implementation, enhancing the learning and teaching of mathematics in 20 disadvantaged secondary schools in KwaZulu-Natal (KZN), South Africa, twenty years after democracy. Findings highlight the importance of initial and ongoing professional development for under-qualified teachers. Support and strategies that have enhanced the achievement in mathematics of learners in these still under-resourced schools, are described

Generalization of the Banach contraction principle

We introduce the concept of shifting distance functions, and we establish a new fixed point theorem which generalizes the Banach contraction principle. An example is provided to illustrate our result.Comment: 6 page

False Promises: Migrant Workers in the Global Garment Industry (Discussion Paper)

This document is part of a digital collection provided by the Martin P. Catherwood Library, ILR School, Cornell University, pertaining to the effects of globalization on the workplace worldwide.  Special emphasis is placed on labor rights, working conditions, labor market changes, and union organizing.CCC_False_Promises.pdf: 1932 downloads, before Oct. 1, 2020