Transitory interest-rate pegs under imperfect credibility

Housing construction, measured by housing starts, leads GDP in a number of countries. Measured as residential investment, the lead is observed only in the US and Canada; elsewhere, residential investment is coincident. Variants of existing theory, however, predict housing construction lagging GDP. In all countries in the sample, nominal interest rates are low ahead of GDP peaks. Introducing fully-amortizing mortgages and an estimated process for nominal interest rates into a standard model aligns the theory with the observations on starts; one-period loans are insufficient to generate the lead. Longer time to build then makes residential investment cyclically coinciden

Power laws, scale invariance, and generalized Frobenius series: Applications to Newtonian and TOV stars near criticality

We present a self-contained formalism for analyzing scale invariant differential equations. We first cast the scale invariant model into its equidimensional and autonomous forms, find its fixed points, and then obtain power-law background solutions. After linearizing about these fixed points, we find a second linearized solution, which provides a distinct collection of power laws characterizing the deviations from the fixed point. We prove that generically there will be a region surrounding the fixed point in which the complete general solution can be represented as a generalized Frobenius-like power series with exponents that are integer multiples of the exponents arising in the linearized problem. This Frobenius-like series can be viewed as a variant of Liapunov's expansion theorem. As specific examples we apply these ideas to Newtonian and relativistic isothermal stars and demonstrate (both numerically and analytically) that the solution exhibits oscillatory power-law behaviour as the star approaches the point of collapse. These series solutions extend classical results. (Lane, Emden, and Chandrasekhar in the Newtonian case; Harrison, Thorne, Wakano, and Wheeler in the relativistic case.) We also indicate how to extend these ideas to situations where fixed points may not exist -- either due to ``monotone'' flow or due to the presence of limit cycles. Monotone flow generically leads to logarithmic deviations from scaling, while limit cycles generally lead to discrete self-similar solutions.Comment: 35 pages; IJMPA style fil

Inclusive, adaptive design for students with severe learning disabilities

Young adults with severe disabilities and learning difficulties (SLD) have very limited access to appropriate learning resources. Their unique individual needs and requirements prevent them from accessing traditional methods of online learning, and resources tend not to be age appropriate. The majority of SLD learners has difficulty accessing a computer with standard peripherals such as a mouse and relies on assistive technologies (e.g. switches) to do so. Each learner tends to have specific needs that must be addressed in order to provide an accessible and adaptive platform for learning. The aim of this research project was, with the assistance and support of the learners and their tutors, to design and develop an adaptable and inclusive online learning environment specifically catering for the needs of young adults with SLD. Each stage of development was prototyped and assessed in the college environment to ensure the needs of the learners were thoroughly addressed. 1