The shape of hyperbolic Dehn surgery space

In this paper we develop a new theory of infinitesimal harmonic deformations for compact hyperbolic 3-manifolds with ``tubular boundary''. In particular, this applies to complements of tubes of radius at least R_0 = \arctanh(1/\sqrt{3}) \approx 0.65848 around the singular set of hyperbolic cone manifolds, removing the previous restrictions on cone angles. We then apply this to obtain a new quantitative version of Thurston's hyperbolic Dehn surgery theorem, showing that all generalized Dehn surgery coefficients outside a disc of ``uniform'' size yield hyperbolic structures. Here the size of a surgery coefficient is measured using the Euclidean metric on a horospherical cross section to a cusp in the complete hyperbolic metric, rescaled to have area 1. We also obtain good estimates on the change in geometry (e.g. volumes and core geodesic lengths) during hyperbolic Dehn filling. This new harmonic deformation theory has also been used by Bromberg and his coworkers in their proofs of the Bers Density Conjecture for Kleinian groups.Comment: 46 pages, 3 figure

It’s driving her mad: gender differences in the effects of commuting on psychological well-being

In this paper, we seek to explore the effects of commuting time on the psychological well-being of men and women in the UK. We use annual data from the British Household Panel Survey in a fixed effects panel framework that includes variables known to determine well-being, as well as factors which may provide compensation for commuting such as income, job satisfaction and housing quality. Our results show that, even after all these variables are considered, commuting still has an important detrimental effect on the well-being of women, but not men, and this result is robust to numerous different specifications. We explore possible explanations for this gender difference and can find no evidence that it is due to women´s shorter working hours or weaker occupational position. Rather women´s greater sensitivity to commuting time seems to be a result of their larger responsibility for day-to-day household tasks, including childcare

Can the nuclear symmetry potential at supra-saturation densities be negative?

In the framework of an Isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model, for the central $^{197}$Au+$^{197}$Au reaction at an incident beam energy of 400 MeV/nucleon, effect of nuclear symmetry potential at supra-saturation densities on the pre-equilibrium clusters emission is studied. It is found that for the positive symmetry potential at supra-saturation densities the neutron to proton ratio of lighter clusters with mass number $A\leq3$ ($(n/p)_{A\leq3}$) is larger than that of the weighter clusters with mass number $A>3$ ($(n/p)_{A>3}$), whereas for the negative symmetry potential at supra-saturation densities the $(n/p)_{A\leq3}$ is \emph{smaller} than that of the $(n/p)_{A>3}$. This may be considered as a probe of the negative symmetry potential at supra-saturation densities.Comment: 5 pages, 3 figures, 1 table, to be publishe

WIL: Achieving intended and unintended learning outcomes of university study

Students in Hong Kong commonly have some form of part-time work, so the question is ‘do they need to gain more workplace experience?’ However, the purpose of work-integrated learning (WIL) is not to generate income, as is the case with a part-time job. Indeed, WIL can be of benefit in four main areas: academic, personal, skill development and career (Dressler and Keeling, 2004). University students, being novices, have the potential through WIL to identify the learning gap between requirements in university study and the workplace, personal interests and potential careers, and espoused theories and theories in use in the real world. Despite the differing nature and varied WIL opportunities organized by universities in Hong Kong, students can plan the intended learning outcomes related to the programme they are studying when first assigned to WIL activities. Focus group interviews were conducted with five student groups from the Hong Kong Polytechnic University on their WIL experiences in 2006, and it was noted that some students did not know the scale and types of tasks involved, although they did know where to report for duty. Furthermore, they had supervisors with different levels of commitment to supervision. As they reflected on their experiences, the students reported both excitement and disappointment in their WIL activities. Some perceived that they had gained good experience during the placement period and wished they could have done more, but some were disappointed because they were given only limited duties. However, they believed that good lessons had been learned when enabled to reflect on the whole experience. A lot of effort was made between the university and its industrial partners to prepare WIL placements (Abeysekera, 2006). It was found that the key to maximizing learning opportunities was to engage these students in setting realistic learning goals and preparing them for learning when interacting with stakeholders in the workplace, and the WIL opportunities provided did promote reflection on the gap between academic learning and learning in a work-related context..postprintThe WACE International Conference on Work Integrated Learning 'University-Industry Collaboration for Real Life Education' (生活教育下的「大學－企業協作」), Hong Kong, 3-5 February 2010

Learners' strategies with multiple representations

This empirical study investigated how varied instantiations of mathematical representations influenced learners' strategies. The analysis took into account gazes, utterances, actions and writings of 18 learners performing 3 tasks using static, dynamic, and interactive instantiations. Results show a variation in frequencies of strategies that the participants of the study employed for using multiple representations. This indicates that varying instantiations of multiple representations influences learners' strategies