Student and expert perceptions of the role of mathematics within physics

Students’ perceptions of the role of mathematics within physics were examined. I propose that the identification of physics as a science based ultimately on experiment is a threshold concept: transformation from a naïve view that physics is based upon mathematics to an expert view that physics is based on experiment is difficult for students. Seven students taking first-year university physics were interviewed in two focus groups; nine practising physicists from academia and industry (considered as experts) were interviewed as six individuals plus one focus group of three participants. Of particular interest was the ‘expert’ view emphasizing the conceptual nature of physics. This was a threshold in understanding that had not been crossed by students. Rather, students viewed mathematics and physics as being more strongly connected than did practising physicists; specifically that “maths explains physics”. Experts consider this view as holding back a student’s understanding of the subject and preventing them from becoming effective physicists. It is troublesome to students because they are less able to identify the relevant concepts before trying to tackle a problem with mathematics, making their approach less likely to be effective, however, both groups (physicists and students) identified physics as belonging to ‘the real world’ and that mathematics shows how physical entities can be combined or related, indicating student responses are not completely naïve. Opinions on how best to teach mathematical concepts in physics varied considerably across participants

Measuring the Effects of "Adults Only" Age Restrictions on Condominium Prices

Current U.S. housing policy prohibits discrimination in the sale or rental of housing or in the provision of brokerage services on the basis of race, color, religion, sex, national origin, disability, or familial status. Since 1988, an exception to this policy has permitted owners and operators of buildings and facilities that were intended to be operated as housing for older persons to discriminate against younger residents, including families with children and pregnant women, without violating the nation's fair housing laws. This exception was clarified by the Housing for older persons. The purpose of this study is to consider whether such restrictions have a measurable effect on housing prices. Based on data from condominium transactions in southeast Florida, the results presented here suggest that age restrictions have a positive price effect, holding other determinants of condominium prices constant.

Quantization with operators appropriate to shapes of trajectories and classical perturbation theory

Quantization is discussed for molecular systems having a zeroth order pair of doubly degenerate normal modes. Algebraic quantization is employed using quantum operators appropriate to the shape of the classical trajectories or wave functions, together with Birkhoff-Gustavson perturbation theory and the W eyl correspondence for operators. The results are compared with a previous algebraic quantization made with operators not appropriate to the trajectory shape. Analogous results are given for a uniform semiclassical quantization based on Mathieu functions of fractional order. The relative sensitivities of these two methods (AQ and US) to the use of operators and coordinates related to and not related to the trajectory shape is discussed. The arguments are illustrated using principally a Hamiltonian for which many previous results are available

Measuring Vertical Property Tax Inequity in Multi-Family Property Markets

Previous researchers have proposed numerous methods for detecting and measuring vertical inequity in property tax systems, where vertical equity refers to the assessment of all properties in a taxing jurisdiction at the same proportion of their market values. With evidence of inequitable assessments, property owners may be able to reduce property tax expenses by challenging their properties’ assessed values. This study demonstrates the application and interpretation of alternative methods for measuring vertical inequity in multi-family property markets using sample data. The results indicate that vertical inequities do exist in this sample, with lower valued properties being assessed at a higher proportion of market value than are higher value properties. This study suggests that owners of properties in lower value ranges in this market should carefully monitor the assessment process to minimize their property tax expense.

Prepotentials for (2,2) Supergravity

We present a complete solution of the constraints for two-dimensional, N=2 supergravity in N=2 superspace. We obtain explicit expressions for the covariant derivatives in terms of the vector superfield $H^m$ and, for the two versions of minimal (2,2) supergravity, a chiral or twisted chiral scalar superfield $\phi$.Comment: 16 pages, BRX-TH-36

Subthreshold dynamics of a single neuron from a Hamiltonian perspective

We use Hamilton's equations of classical mechanics to investigate the behavior of a cortical neuron on the approach to an action potential. We use a two-component dynamic model of a single neuron, due to Wilson, with added noise inputs. We derive a Lagrangian for the system, from which we construct Hamilton's equations. The conjugate momenta are found to be linear combinations of the noise input to the system. We use this approach to consider theoretically and computationally the most likely manner in which such a modeled neuron approaches a firing event. We find that the firing of a neuron is a result of a drop in inhibition, due to a temporary increase in negative bias of the mean noise input to the inhibitory control equation. Moreover, we demonstrate through theory and simulation that, on average, the bias in the noise increases in an exponential manner on the approach to an action potential. In the Hamiltonian description, an action potential can therefore be considered a result of the exponential growth of the conjugate momenta variables pulling the system away from its equilibrium state, into a nonlinear regime