Simplicity of <Emphasis Type="Italic">C</Emphasis>*-algebras associated to row-finite locally convex higher-rank graphs

In a previous work, the authors showed that the C*-algebra C*(Λ) of a row-finite higher-rank graph Λ with no sources is simple if and only if Λ is both cofinal and aperiodic. In this paper, we generalise this result to row-finite higher-rank graphs which are locally convex (but may contain sources). Our main tool is Farthing’s “removing sources” construction which embeds a row-finite locally convex higher-rank graph in a row-finite higher-rank graph with no sources in such a way that the associated C*-algebras are Morita equivalent.     

UCT-Kirchberg algebras have nuclear dimension one

We prove that every Kirchberg algebra in the UCT class has nuclear dimension 1. We first show that Kirchberg 2-graph algebras with trivial _K0$K_0$ and finite _K1$K_1$ have nuclear dimension 1 by adapting a technique developed by Winter and Zacharias for Cuntz algebras. We then prove that every Kirchberg algebra in the UCT class is a direct limit of 2-graph algebras to obtain our main theorem.     

Dynamics of the Douglas-Rachford Method for Ellipses and <Emphasis Type="Italic">p</Emphasis>-Spheres

We expand upon previous work that examined the behavior of the iterated Douglas-Rachford method for a line and a circle by considering two generalizations:that of a line and an ellipse and that of a line together with a p-sphere. With computer assistance we discover a beautiful geometry that illustrates phenomena which may affect the behavior of the iterates by slowing or inhibiting convergence for feasible cases. We prove local convergence near feasible points, and—seeking a better understanding of the behavior—we employ parallelization in order to study behavior graphically. Motivated by the computer-assisted discoveries, we prove a result about behavior of the method in infeasible cases.     

Ubi Caritas? — Modelling beliefs about charities

In this paper we report on a project in which we explored with a number of officers from different charities their beliefs about charitable giving, and built explicit models of these beliefs so that they might be examined in a more systematic way than they can be when just talking about them. We discuss some of the issues and problems around creating and using explicit models of individuals' beliefs to share wisdom, and report some of the things that happened when we sought to do this. We suggest that our approach provides practical help with the problems of sharing views.OR has traditionally been geared to those organizations who are able and willing to pay for it; in this paper we report on an OR project in organizations to whom it has not usually been available.