Deformations of Annuli on Riemann surfaces with Smallest Mean Distortion

Let $A$ and $A'$ be two circular annuli and let $\rho$ be a radial metric defined in the annulus $A'$. Consider the class $\mathcal H_\rho$ of $\rho-$harmonic mappings between $A$ and $A'$. It is proved recently by Iwaniec, Kovalev and Onninen that, if $\rho=1$ (i.e. if $\rho$ is Euclidean metric) then $\mathcal H_\rho$ is not empty if and only if there holds the Nitsche condition (and thus is proved the J. C. C. Nitsche conjecture). In this paper we formulate an condition (which we call $\rho-$Nitsche conjecture) with corresponds to $\mathcal H_\rho$ and define $\rho-$Nitsche harmonic maps. We determine the extremal mappings with smallest mean distortion for mappings of annuli w.r. to the metric $\rho$. As a corollary, we find that $\rho-$Nitsche harmonic maps are Dirichlet minimizers among all homeomorphisms $h:A\to A'$. However, outside the $\rho$-Nitsche condition of the modulus of the annuli, within the class of homeomorphisms, no such energy minimizers exist. % However, %outside the $\rho-$Nitsche range of the modulus of the annuli, %within the class of homeomorphisms, no such energy minimizers exist. This extends some recent results of Astala, Iwaniec and Martin (ARMA, 2010) where it is considered the case $\rho=1$ and $\rho=1/|z|$.Comment: Some misprints are corrected in this version (see Lemma~5.1

Income Distribution and Labour Movement in China after WTO Membership: A CGE Analysis

applied CGE modelling, China, WTO, labour movement, inequality

Effects of WTO membership on income distribution and labour movement in China – A CGE analysis

Using a CGE model (PRCGEM) updated to 2002, the paper explores how WTO membership could affect earnings in 40 industries across 31 regions (and 8 regional blocks) of China during the period 2002–2007. Taking into account labour movement between regions within China, the direct contribution of WTO membership to overall economic growth and development is predicted to be small, with a rise in real GDP of only 6.48% short term and 5.6% long term. However, structural economic change and the WTO shock should increase regional output, especially in the established coastal economies. Regional labour movement is found to increase 69.2% at the completion of economic structural reforms. A slight decrease in the Gini coefficient for income inequality is also anticipated.applied CGE modelling; China; WTO; labour movement; inequality

Log-sine evaluations of Mahler measures, II

We continue the analysis of higher and multiple Mahler measures using log-sine integrals as started in "Log-sine evaluations of Mahler measures" and "Special values of generalized log-sine integrals" by two of the authors. This motivates a detailed study of various multiple polylogarithms and worked examples are given. Our techniques enable the reduction of several multiple Mahler measures, and supply an easy proof of two conjectures by Boyd.Comment: 35 page

TTA school-based research consortium initiative, the evaluation, final report

This is the final report of the evaluation of th School-Based Research Consortium Initiative which ran in England from 1998 to 2001. The initiative was sponsored via a public/private partnership between the Teacher Training Agency (TTA), a UK Government agency, and the Centre for British Teachers (CfBT), a private not-for-profit company. The aim of the initiative was to create local infrastructures of support and action for teachers to engage ‘in and with’ research. Those infrastructures were made up of consortia, consisting in each case of a small number of schools together with a university department of education and at least one local education authority (LEA). Over the three years that it ran, the initiative spawned a considerable range and volume of research activities, including peer observation of teaching, peer review of videos of teaching, interview-based study, surveys measuring such things as rewards and sanctions in the classroom. In addition to well-developed teacher-university collaborations and some joint work with local education authorities, there were many examples of teacher-teacher collaboration (some of it between different schools), and also times when teachers and pupils worked together to devise, carry out or interpret research activity. In practice, the initiative created an environment in which it was possible to develop new research relationships across a range of partners, rather than merely transfer the locus of research to schools. Three aspects of teacher experience of the initiative are important to highlight. The first was the overwhelming testimony of teachers that the value of the initiative for them was the rediscovery of their professional confidence in a climate of low trust accountability, characterised by constant monitoring, target setting and bureaucratic demands. The second was the growth of familiarity with research practices that teachers gained through working collaboratively with their peers, with pupils, and with colleagues from the university. The third was how the process of research itself was necessarily situated in teachers’ own practices

Lattice study of trapped fermions at unitarity

We present a lattice study of up to N=20 unitary fermions confined to a harmonic trap. Our preliminary results show better than 1% agreement with high precision solutions to the many-body Schrodinger equation for up to N=6. We are able to make predictions for larger N which were inaccessible by the Hamiltonian approach due to computational limitations. Harmonic traps are used experimentally to study cold atoms tuned to a Feshbach resonance. We show that they also provide certain benefits to numerical studies of many-body correlators on the lattice. In particular, we anticipate that the methods described here could be used for studying nuclear physics.Comment: 7 pages, 5 figures, presented at the XXVIII International Symposium on Lattice Field Theory (Lattice 2010), Villasimius, Italy, June 14-19 201