Learning to Understand: Mathematical Preparation of Prospective Teachers

This paper describes the development of a two-course sequence in mathematics content for prospective elementary teachers. Community college and university personnel collaborated to develop a course sequence that would prepare prospective elementary teachers to teach mathematics with an understanding of concepts to support their abstract mathematical knowledge. The strategy was to begin with a broad vision and then focus on the smaller pieces which would achieve that vision. The course changes are validated by documents published by various educational and mathematical groups advocating an increased emphasis on teaching for understanding rather than rote learning. Significant change is difficult without support from colleagues and sufficient time, both necessary to the change process. The noteworthy components of Austin Community College’s revised course are a safe environment in which students become independent learners and written communication as an integral part of the course resulting in students who have increased their conceptual understanding. As a result of taking the course, students accept responsibility for their own learning, have increased self-confidence, and show enthusiasm for mathematics. While requiring a major commitment from faculty, the results are well worth the effort

Demand properties in household Nash equilibrium

We study noncooperative household models with two agents and several voluntarily contributed public goods, deriving the counterpart to the Slutsky matrix and demonstrating the nature of the deviation of its properties from those of a true Slutsky matrix in the unitary model. We demonstrate the importance of distinguishing between cases in which there are and are not jointly contributed public goods and provide results characterising both cases. Demand properties are contrasted with those for collective models and conclusions drawn regarding the possibility of empirically testing the collective model against noncooperative alternatives

Noncooperative household demand

We study noncooperative household models with two agents and several voluntarily contributed public goods, deriving the counterpart to the Slutsky matrix and demonstrating the nature of the deviation of its properties from those of a true Slutsky matrix in the unitary model. We provide results characterising both cases in which there are and are not jointly contributed public goods. Demand properties are contrasted with those for collective models and conclusions drawn regarding the possibility of empirically testing the collective model against noncooperative alternatives and the noncooperative model against a general alternative. (C) 2010 Elsevier Inc. All rights reserved

Anti-deSitter gravitational collapse

We describe a formalism for studying spherically symmetric collapse of the massless scalar field in any spacetime dimension, and for any value of the cosmological constant $\Lambda$. The formalism is used for numerical simulations of gravitational collapse in four spacetime dimensions with negative $\Lambda$. We observe critical behaviour at the onset of black hole formation, and find that the critical exponent is independent of $\Lambda$.Comment: 4 pages, 2 figures, revtex4, version to appear in CQ

Comparative mortality levels among selected species of captive animals

We present life tables by single year of age and sex for groups of animals and for 42 individual mostly mammalian species. Data are derived from the International Species Information System. The survivorship of most of these species has never been mapped systematically. We demonstrate that, in most of the groups, female survivorship significantly exceeds that of males above age five. Wild-born animals do not have mortality that differs significantly from captive-born animals. While most species have mortality that rises with age above the juvenile stage, there are several groups for which the age pattern of mortality is nearly level.ISIS, longevity, mortality, survivorship

Rigorous theory of nuclear fusion rates in a plasma

Real-time thermal field theory is used to reveal the structure of plasma corrections to nuclear reactions. Previous results are recovered in a fashion that clarifies their nature, and new extensions are made. Brown and Yaffe have introduced the methods of effective quantum field theory into plasma physics. They are used here to treat the interesting limiting case of dilute but very highly charged particles reacting in a dilute, one-component plasma. The highly charged particles are very strongly coupled to this background plasma. The effective field theory proves that this mean field solution plus the one-loop term dominate; higher loop corrections are negligible even though the problem involves strong coupling. Such analytic results for very strong coupling are rarely available, and they can serve as benchmarks for testing computer models.Comment: 4 pages and 2 figures, presented at SCCS 2005, June 20-25, Moscow, Russi

Dimension-Dependence of the Critical Exponent in Spherically Symmetric Gravitational Collapse

We study the critical behaviour of spherically symmetric scalar field collapse to black holes in spacetime dimensions other than four. We obtain reliable values for the scaling exponent in the supercritical region for dimensions in the range $3.5\leq D\leq 14$. The critical exponent increases monotonically to an asymptotic value at large $D$ of $\gamma\sim0.466$. The data is well fit by a simple exponential of the form: $\gamma \sim 0.466(1-e^{-0.408 D})$.Comment: 5 pages, including 7 figures New version contains more data points, one extra graph and more accurate error bars. No changes to result

An investigation of herpes simplex virus promoter activity compatible with latency establishment reveals VP16-independent activation of immediate-early promoters in sensory neurones

Herpes simplex virus (HSV) type-1 establishes lifelong latency in sensory neurones and it is widely assumed that latency is the consequence of a failure to initiate virus immediate-early (IE) gene expression. However, using a Ore reporter mouse system in conjunction with Ore-expressing HSV-1 recombinants we have previously shown that activation of the IE ICPO promoter can precede latency establishment in at least 30 % of latently infected cells. During productive infection of non-neuronal cells, IE promoter activation is largely dependent on the transactivator VP16 a late structural component of the virion. Of significance, VP16 has recently been shown to exhibit altered regulation in neurones; where its de novo synthesis is necessary for IE gene expression during both lytic infection and reactivation from latency. In the current study, we utilized the Ore reporter mouse model system to characterize the full extent of viral promoter activity compatible with cell survival and latency establishment. In contrast to the high frequency activation of representative IE promoters prior to latency establishment, cell marking using a virus recombinant expressing Ore under VP16 promoter control was very inefficient. Furthermore, infection of neuronal cultures with VP16 mutants reveals a strong VP16 requirement for IE promoter activity in non-neuronal cells, but not sensory neurones. We conclude that only IE promoter activation can efficiently precede latency establishment and that this activation is likely to occur through a VP16-independent mechanism

Real estate stock selection and attribute preferences

The majority of studies that explore property portfolio construction and management strategies utilise highly aggregated ex-post data, but stock selection is known to be a significant determinant of portfolio performance. Thus, here we look at stock selection, focusing on the choices faced by investors, necessitating the collection and analysis of primary data, carried out utilising conjoint analysis. This represents a new step in property research, with the data collection undertaken using a simulation exercise. This enables fund managers to make hypothetical purchase decisions, viewing properties comprising a realistic bundle of attributes and making complex contemporaneous trade-offs between attributes, subject to their stated market and economic forecasts and sector specialism. In total 51 fund managers were surveyed, producing 918 purchase decisions for analysis, with additional data collected regarding fund and personal characteristics. The results reveal that ‘fixed’ property characteristics (location and obsolescence) are dominant in the decision-making process, over and above ‘manageable’ tenant and lease characteristics which can be explicitly included within models of probabilities of income variation. This reveals investors are making ex-ante risk judgements and are considering post acquisition risk management strategies. The study also reveals that behavioural factors affect acquisition decisions

On the correlation functions of the domain wall six vertex model

We propose an (essentially combinatorial) approach to the correlation functions of the domain wall six vertex model. We reproduce the boundary 1-point function determinant expression of Bogoliubov, Pronko and Zvonarev, then use that as a building block to obtain analogous expressions for boundary 2-point functions. The latter can be used, at least in principle, to express more general boundary (and bulk) correlation functions as sums over (products of) determinants.Comment: LaTeX2e, requires eepic, 25 pages, including 29 figure