Humans-with-media and continuing education for mathematics teachers in online environments

This paper begins by situating online mathematics education in Brazil within the context of research on digital technology over the past 25?years. I argue that Brazilian research on technology in mathematics education can be divided into four phases, and then present an example that ??blends?? aspects of the second and third phases. Phase two can be characterized by research with software designed to address traditional mathematics topics, such as functions, while the third phase is characterized by online courses. The data presented show creative solutions for a problem designed for collectives of humans-with-function-software. The paper is analyzed from a perspective that emphasizes the role of different technologies as teachers and professors collaborate to produce knowledge about the use of mathematical software in regular face-to-face classrooms. A model of online education is presented. Finally, the paper discusses how technology may change collaboration and teaching approaches in continuing education, as it allows for greater integration of online learning with teachers?? classroom activities in schools. In this case, the online platform plays an active role in the learning collective composed of humans-with-media.     

Online mathematics teacher education: overview of an emergent field of research

Online mathematics teacher education is characterized as an emergent area of research in mathematics education. We identify some key topics that require further research: communities and networks of teachers in online environments; sustainability of these communities and kinds of organizational structures; knowledge-building practices in technology-mediated work group interactions; and online interactions among teachers. The emergence of new research issues also gives rise to new theoretical approaches or the adaptation of existing theoretical perspectives that are presented in this special issue. We summarize some of these theoretical perspectives and attempt to show how online environments have changed them, as well as some theoretical problems that remain to be solved.     

Testing the Goodwin growth-cycle macroeconomic dynamics in Brazil

This paper discusses the empirical validity of Goodwin’s (1967) macroeconomic model of growth with cycles by assuming that the individual income distribution of the Brazilian society is described by the Gompertz–Pareto distribution (GPD). This is formed by the combination of the Gompertz curve, representing the overwhelming majority of the population (∼99%), with the Pareto power law, representing the tiny richest part (∼1%). In line with Goodwin’s original model, we identify the Gompertzian part with the workers and the Paretian component with the class of capitalists. Since the GPD parameters are obtained for each year and the Goodwin macroeconomics is a time evolving model, we use previously determined, and further extended here, Brazilian GPD parameters, as well as unemployment data, to study the time evolution of these quantities in Brazil from 1981 to 2009 by means of the Goodwin dynamics. This is done in the original Goodwin model and an extension advanced by Desai et al. (2006). As far as Brazilian data is concerned, our results show partial qualitative and quantitative agreement with both models in the studied time period, although the original one provides better data fit. Nevertheless, both models fall short of a good empirical agreement as they predict single center cycles which were not found in the data. We discuss the specific points where the Goodwin dynamics must be improved in order to provide a more realistic representation of the dynamics of economic systems.     

Interplay between spin frustration and thermal entanglement in the exactly solved Ising–Heisenberg tetrahedral chain

The spin-1/2 Ising–Heisenberg tetrahedral chain is exactly solved using its local gauge symmetry (the total spin of the Heisenberg bonds is locally conserved) and the transfer-matrix approach. Exact results derived for spin–spin correlation functions are employed to obtain the frustration temperature. In addition, we have exactly calculated a concurrence quantifying thermal entanglement. It is shown that the frustration and threshold temperature coincide at sufficiently low temperatures, while they exhibit a very different behavior in the high-temperature region when tending towards completely different asymptotic limits. The threshold temperature additionally shows a notable reentrant behavior when it extends over a narrow temperature region above the classical ground state without any quantum correlations.     

Layer Lengths, Torsion Theories and the Finitistic Dimension

Let $\mathcal{C}$ be a length-category. Generalizing the Loewy length, we propose the layer length associated with a torsion theory, which is a new measure for objects of $\mathcal{C}$ . As an application, we use the layer lengths and the Igusa–Todorov function to get a theorem (see Theorem 6.4) having as corollaries the main results of Huard et al. (Bull Lond Math Soc 41:367–376, 2009) and Wang (Commun Algebra 22(7):419–449, 1994).     

Physical measures and absolute continuity for one-dimensional center direction

For a class of partially hyperbolic C^k$C^k$, k>1$k>1$ diffeomorphisms with circle center leaves we prove the existence and finiteness of physical (or Sinai–Ruelle–Bowen) measures, whose basins cover a full Lebesgue measure subset of the ambient manifold. Our conditions hold for an open and dense subset of all C^k$C^k$ partially hyperbolic skew-products on compact circle bundles.     

Direct carrier–envelope phase stabilization of a soliton-effect compressed sub-two-cycle pulse source through nonlinear mixing of solitonic and dispersive waves

We present a carrier–envelope phase (CEP) stabilized sub-two-cycle 5.2 fs pulse source based on soliton-effect self-compression of femtosecond laser pulses in millimetre-long highly nonlinear photonic crystal fibres. We employ a simple and efficient scheme to generate a strong (40–60 dB, configuration dependent) CEP beat signal directly from the pulse source via f-to-2f interferometry where the second harmonic of the main soliton pulse is mixed with the isolated dispersive blue/green radiation peak that is also generated in the compression process, obviating the need for additional spectral broadening mechanisms.     

Thermal behavior of 1,2-dipalmitoyl-sn-3-phosphoglycerocholine bi- and multi-layers, deposited with physical vapor deposition under ellipsometric growth control

1,2-dipalmitoyl-sn-3-phosphoglycerocholine membranes were deposited onto a silicon substrate (Si/SiO(2)) using physical vapor deposition with in situ ellipsometric thickness control. Along several heating cycles it was possible to identify well-defined boundaries for gel, ripple, liquid crystalline, and fluid-disordered phases. Particularly, the second order transition between gel and ripple phase was clearly identified in the range of ~28-34 °C using Raman spectroscopy. Atomic force microscopy and imaging ellipsometry (IE) were used to observe and characterize the ripple phase undulations of period λ = 20.8 nm and average height h = 19.95 nm along the temperature interval of ~34 to 40 °C. Clusters/agglomerations heights of more than twice the membrane thickness were observed with IE, induced by heating cycles.     

Hybrid materials: Magnetite-Polyethylenimine-Montmorillonite, as magnetic adsorbents for Cr(VI) water treatment

Hybrid materials formed by the combination of a sodium rich Montmorillonite (MMT), with magnetite nanoparticles (40nm, Fe(3)O(4) NPs) coated with Polyethylenimine polymer (PEI 800g/mol or PEI 25000g/mol) were prepared. The intercalation of the magnetite nanoparticles coated with PEI among MMT platelets was achieved by cationic exchange. The resulting materials presented a high degree of exfoliation of the MMT sheets and a good dispersion of Fe(3)O(4) NPs on both the surface and among the layers of MMT. The presence of amine groups in the PEI structure not only aids the exfoliation of the MMT layers, but also gives to the hybrid material the necessary functionality to interact with heavy metals. These hybrid materials were used as magnetic sorbent for the removal of hexavalent chromium from water. The effect that pH, Cr(VI) concentration, and adsorbent material composition have on the Cr(VI) removal efficiency was studied. A complete characterization of the materials was performed. The hybrid materials showed a slight dependence of the removal efficiency with the pH in a wide range (1-9). A maximum amount of adsorption capacity of 8.8mg/g was determined by the Langmuir isotherm. Results show that these hybrid materials can be considered as potential magnetic adsorbent for the Cr(VI) removal from water in a wide range of pH.     

Effect of Substrate Concentration on Dark Fermentation Hydrogen Production Using an Anaerobic Fluidized Bed Reactor

The effect of substrate (glucose) concentration on the stability and yield of a continuous fermentative process that produces hydrogen was studied. Four anaerobic fluidized bed reactors (AFBRs) were operated with a hydraulic retention time (HRT) from 1 to 8 h and an influent glucose concentration from 2 to 25 g L⁻¹. The reactors were inoculated with thermally pre-treated anaerobic sludge and operated at a temperature of 30 °C with an influent pH around 5.5 and an effluent pH of about 3.5. The AFBRs with a HRT of 2 h and a feed strength of 2, 4, and 10 g L⁻¹ showed satisfactory H₂ production performance, but the reactor fed with 25 g L⁻¹ of glucose did not. The highest hydrogen yield value was obtained in the reactor with a glucose concentration of 2 g L⁻¹ when it was operated at a HRT of 2 h. The maximum hydrogen production rate value was achieved in the reactor with a HRT of 1 h and a feed strength of 10 g L⁻¹. The AFBRs operated with glucose concentrations of 2 and 4 g L⁻¹ produced greater amounts of acetic and butyric acids, while AFBRs with higher glucose concentrations produced a greater amount of solvents.