Distinguishing partitions of complete multipartite graphs

A \textit{distinguishing partition} of a group $X$ with automorphism group ${aut}(X)$ is a partition of $X$ that is fixed by no nontrivial element of ${aut}(X)$. In the event that $X$ is a complete multipartite graph with its automorphism group, the existence of a distinguishing partition is equivalent to the existence of an asymmetric hypergraph with prescribed edge sizes. An asymptotic result is proven on the existence of a distinguishing partition when $X$ is a complete multipartite graph with $m_1$ parts of size $n_1$ and $m_2$ parts of size $n_2$ for small $n_1$, $m_2$ and large $m_1$, $n_2$. A key tool in making the estimate is counting the number of trees of particular classes

Bounding Betti numbers of bipartite graph ideals

We prove a conjectured lower bound of Nagel and Reiner on Betti numbers of edge ideals of bipartite graphs

NZ and the EU, 12 months after enlargement Annual Europa Lecture. NCRE Online Paper No. 05/01, 10 May 2005

[From the Introduction]. Today, as we mark the 60th Anniversary of 'Victory in Europe' in the Second World War, and recall New Zealand's involvement in the conflicts that wracked Europe in the last century, we need to recognise the historical significance of EU enlargement. Enlargement has had important consequences for New Zealand's interests in Europe, and our relations both with European countries and the European Union. These have been reflected in the Prime Minister opening New Zealand's Embassy in Warsaw just over two weeks ago. The Embassy will have responsibility not just for our relations with Poland, but also with the three Baltic nations of Estonia, Latvia and Lithuania, which I visited in September last year. Poland was chosen for its size and relative weight. It is the largest of the new member states and the sixth largest overall

Who Uses Rare Books and What For

published or submitted for publicatio

Generalized Twisted Quantum Doubles and the McKay Correspondence

We consider a class of quasi-Hopf algebras which we call \emph{generalized twisted quantum doubles}. They are abelian extensions H = \mb{C}[\bar{G}] \bowtie \mb{C}[G] ($G$ is a finite group and $\bar{G}$ a homomorphic image), possibly twisted by a 3-cocycle, and are a natural generalization of the twisted quantum double construction of Dijkgraaf, Pasquier and Roche. We show that if $G$ is a subgroup of SU_2(\mb{C}) then $H$ exhibits an orbifold McKay Correspondence: certain fusion rules of $H$ define a graph with connected components indexed by conjugacy classes of $\bar{G}$, each connected component being an extended affine Diagram of type ADE whose McKay correspondent is the subgroup of $G$ stabilizing an element in the conjugacy class. This reduces to the original McKay Correspondence when $\bar{G} = 1$.Comment: 5 figure

How Remittances Contribute to Poverty Reduction: a Stabilizing Effect

We argue in this paper that migrants remittances contribute significantly to poverty reduction in developing countries and that their effect is all the more important that they are sent to countries which are more vulnerable. Since migrants remittances represent an important source of income for households living in home countries, these flows may have an effect on poverty in developing countries. Several microeconomic studies have shown that remittances often play an insurance role for migrants' families, but no analysis studied the stabilizing role played by remittances at the macroeconomic level. This specificity could be all the more determinant for developing countries that they are characterised by macroeconomic instability, especially trade instability based on their dependency on basic products. While the negative effect of instability on development is largely recognized, to our knowledge, instability has not been taken into account at the macroeconomic level in the debate on the role played by remittances in development of home countries. Using a panel sample of 65 developing countries over the period 1980-2005, we first find that remittances have a significant and positive effect on poverty reduction in countries of origin. Furthermore, the effect of macroeconomic instability, and more precisely of trade instability and of climatic instability on poverty in home countries, is all the more attenuated that remittances are important. This result about the stabilizing role of remittances in developing countries confirms the microeconomic theory according to which remittances can play an insurance role for migrants' families.

SPS market analysis

A market analysis task included personal interviews by GE personnel and supplemental mail surveys to acquire statistical data and to identify and measure attitudes, reactions and intentions of prospective small solar thermal power systems (SPS) users. Over 500 firms were contacted, including three ownership classes of electric utilities, industrial firms in the top SIC codes for energy consumption, and design engineering firms. A market demand model was developed which utilizes the data base developed by personal interviews and surveys, and projected energy price and consumption data to perform sensitivity analyses and estimate potential markets for SPS