A coloured window on pre-service teachers’ conceptions of rational numbers

In undergraduate mathematics courses, pre-service elementary school teachers are often faced with the task of re-learning some of the concepts they themselves struggled with in their own schooling. This often involves different cognitive processes and psychological issues than initial learning: pre-service teachers have had many more opportunities to construct understandings and representations than initial learners, some of which may be more complex and engrained; pre-service teachers are likely to have created deeply-held–and often negative–beliefs and attitudes toward certain mathematical ideas and processes. In our recent research, we found that pre-service teachers who used a particular computer-based microworld, one emphasising visual representations of and experimental interactions with elementary number theory concepts, overcame many cognitive and psychological difficulties reported in the literature. In this study, we investigate the possibilities of using a similarly-designed microworld that involves a set of rational number concepts. We describe the affordances of this microworld, both in terms of pre-service teacher learning and research on pre-service teacher learning, namely, the helpful “window” it gave us on the mathematical meaning-making of pre-service teachers. We also show how their interactions with this microworld provided many with a new and aesthetically-rich set of visualisations and experiences.     

In situ TEM studies of metal-carbon reactions.

The reactions which occur between amorphous carbon and a number of first transition metals (Ti, Cr, Fe, Co, Ni, and Cu) have been studied by transmission electron microscopy (TEM). The materials are in thin-film form with the metal layer sandwiched between thicker carbon layers. In four cases, the predominant reaction is the graphitization of the amorphous carbon, at temperatures well below 800 degrees C. This is brought about by the elements themselves in the case of Co and Ni, and by metastable carbides in the case of Fe (Fe3C) and Cr (Cr3C2-x). The Ti-C and Cu-C systems do not exhibit graphitization. For the former, only TiC is produced up to 1000 degrees C, while the carbon does not react at all with copper. In situ TEM studies show the mechanism to be of the dissolution-precipitation type, which is equivalent to the metal-mediated crystallization process for amorphous silicon and germanium. The heat of graphitization is found to be 18-19 kcal/mol-C by differential scanning calorimetry.     

Energy dependence of the reaction mechanism of 11B induced single nucleon transfers on 26Mg

Angular distributions for elastic scattering and for single nucléon stripping reactions induced by a 31 MeV ¹¹B beam on ²⁶Mg have been measured. The DWBA calculations provide a good account of the shape and magnitude of the proton transfer data and of the neutron transition to the $\text{j-}\text{favoured}\text{d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ level in ²⁷Mg, but fail to reproduce the features of the $\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and $\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$ transitions to ²⁷Mg. The j-dependent effects and l-matching conditions are investigated as a function of beam energy and their role in determining the reaction mechanism is examined.     

Particle-hole multiplets in 40Ca observed in the 41Ca(τ, α) reaction

Energy levels in ⁴⁰Ca up to 10.2 MeV have been studied in the neutron pickup reaction ⁴¹Ca(τ, α)⁴⁰Ca with 20 MeV bombarding energy. Thirty excited states have been identified and angular distributions have been measured in the interval from 5° to 40° by means of a split-pole magnetic spectrometer. The angular distributions together with DW calculations have been used to extract l_n values and spectroscopic factors. The l_n = 2 strength distribution for the $\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}\text{d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}$ particle-hole levels is compared to the l_p = 3 strength distribution from pr stripping data.     

Comparing O(N) and SU(N) × SU(N) spin systems in 1 + 1 dimensions to SU(N) gauge theories in 3 + 1 dimensions

We have computed the scale breaking Λ parameters of the euclidean and hamiltonian formulations of the lattice regulated O(N) and SU(N) × SU(N) spin systems in 1 + 1 dimensions in terms of the Λ_PV parameters of the Pauli-Villars regulated continuum models. Using lattice perturbation theory, the renormalized mass gap has been determined in terms of Λ_PV for each model. These results are compared to analogous calculations in SU(N) gauge theories.     

W*-rigidity for the von Neumann algebras of products of hyperbolic groups

We show that if \({\Gamma = \Gamma_1\times\dotsb\times \Gamma_n}\) is a product of \({{\rm n} \geq 2}\) non-elementary ICC hyperbolic groups then any discrete group \({\Lambda}\) which is \({W^*}\)-equivalent to \({\Gamma}\) decomposes as a direct product of n ICC groups and does not decompose as a direct product of k ICC groups when \({{\rm n} \not= {\rm k}}\). This gives a group-level strengthening of Ozawa and Popa’s unique prime decomposition theorem by removing all assumptions on the group \({\Lambda}\). This result in combination with Margulis’ normal subgroup theorem allows us to give examples of lattices in the same Lie group which do not generate stably equivalent II₁ factors.     

Thirty-five years of synthetic studies directed towards the histrionicotoxin family of alkaloids

This article brings together for the first time reviews of all the synthetic attempts towards the spirocyclic histrionicotoxin alkaloids published since the discovery of the group in 1971. This covers 5 total syntheses of the fully unsaturated parent alkaloid HTX-283A, 7 total syntheses of perhydrohistrionicotoxin, 15 total syntheses of other members of this alkaloid family, 25 formal syntheses, and 19 partial syntheses involving the successful formation of the core azaspirocyclic structure but lacking advancement towards the target structure.     

Synthesis, structure and electrical properties of Cu3.21Ti1.16Nb2.63O12 and the CuOx-TiO2-Nb2O5 pseudoternary phase diagram

Subsolidus phase relations in the CuO_x-TiO₂-Nb₂O₅ system were determined at 935 °C. The phase diagram contains one new phase, Cu_3.21Ti_1.16Nb_2.63O₁₂ (CTNO) and one rutile-structured solid solution series, Ti_1−3xCu_xNb_2xO₂: 0<x<0.2335 (35). The crystal structure of CTNO is similar to that of CaCu₃Ti₄O₁₂ (CCTO) with square planar Cu²⁺ but with A site vacancies and a disordered mixture of Cu⁺, Ti⁴⁺ and Nb⁵⁺ on the octahedral sites. It is a modest semiconductor with relative permittivity ∼63 and displays non-Arrhenius conductivity behavior that is essentially temperature-independent at the lowest temperatures.     

Computation of viability kernels: a case study of by-catch fisheries

Traditional means of studying environmental economics and management problems consist of optimal control and dynamic game models that are solved for optimal or equilibrium strategies. Notwithstanding the possibility of multiple equilibria, the models’ users—managers or planners—will usually be provided with a single optimal or equilibrium strategy no matter how reliable, or unreliable, the underlying models and their parameters are. In this paper we follow an alternative approach to policy making that is based on viability theory. It establishes “satisficing” (in the sense of Simon), or viable, policies that keep the dynamic system in a constraint set and are, generically, multiple and amenable to each manager’s own prioritisation. Moreover, they can depend on fewer parameters than the optimal or equilibrium strategies and hence be more robust. For the determination of these (viable) policies, computation of “viability kernels” is crucial. We introduce a MATLAB application, under the name of VIKAASA, which allows us to compute approximations to viability kernels. We discuss two algorithms implemented in VIKAASA. One approximates the viability kernel by the locus of state space positions for which solutions to an auxiliary cost-minimising optimal control problem can be found. The lack of any solution implies the infinite value function and indicates an evolution which leaves the constraint set in finite time, therefore defining the point from which the evolution originates as belonging to the kernel’s complement. The other algorithm accepts a point as viable if the system’s dynamics can be stabilised from this point. We comment on the pros and cons of each algorithm. We apply viability theory and the VIKAASA software to a problem of by-catch fisheries exploited by one or two fleets and provide rules concerning the proportion of fish biomass and the fishing effort that a sustainable fishery’s exploitation should follow.