Benthic foraminiferal distribution on the southeastern Brazilian shelf and upper slope

Foraminiferal data were obtained from 66 samples of box cores on the southeastern Brazilian upper margin (between 23.8A degrees-25.9A degrees S and 42.8A degrees-46.13A degrees W) to evaluate the benthic foraminiferal fauna distribution and its relation to some selected abiotic parameters. We focused on areas with different primary production regimes on the southern Brazilian margin, which is generally considered as an oligotrophic region. The total density (D), richness (R), mean diversity (H) over bar`, average living depth (ALD(X) ) and percentages of specimens of different microhabitats (epifauna, shallow infauna, intermediate infauna and deep infauna) were analyzed. The dominant species identified were Uvigerina spp., Globocassidulina subglobosa, Bulimina marginata, Adercotryma wrighti, Islandiella norcrossi, Rhizammina spp. and Brizalina sp.. We also established a set of mathematical functions for analyzing the vertical foraminiferal distribution patterns, providing a quantitative tool that allows correlating the microfaunal density distributions with abiotic factors. In general, the cores that fit with pure exponential decaying functions were related to the oligotrophic conditions prevalent on the Brazilian margin and to the flow of the Brazilian Current (BC). Different foraminiferal responses were identified in cores located in higher productivity zones, such as the northern and the southern region of the study area, where high percentages of infauna were encountered in these cores, and the functions used to fit these profiles differ appreciably from a pure exponential function, as a response of the significant living fauna in deeper layers of the sediment. One of the main factors supporting the different foraminiferal assemblage responses may be related to the differences in primary productivity of the water column and, consequently, in the estimated carbon flux to the sea floor. Nevertheless, also bottom water velocities, substrate type and water depth need to be considered.

Alternative Tasks for the Teaching and the Learning of functions: analysis of an intervention in the High School

In this paper we focus on the application of two mathematical alternative tasks to the teaching and learning of functions with high school students. The tasks were elaborated according to the following methodological approach: (i) Problem Solving and/or mathematics investigation and (ii) a pedagogical proposal, which defends that mathematical knowledge is developed by means of a balance between logic and intuition. We employed a qualitative research approach (characterized as a case study) aimed at analyzing the didactic pedagogical potential of this type of methodology in high school. We found that tasks such as those presented and discussed in this paper provide a more significant learning for the students, allowing a better conceptual understanding, becoming still more powerful when one considers the social-cultural context of the students.

Exact correlation functions in particle-reaction models with immobile particles

Exact results on particle densities as well as correlators in two models of immobile particles, containing either a single species or else two distinct species, are derived. The models evolve following a descent dynamics through pair annihilation where each particle interacts once at most throughout its entire history. The resulting large number of stationary states leads to a non-vanishing configurational entropy. Our results are established for arbitrary initial conditions and are derived via a generating function method. The single-species model is the dual of the 1D zero-temperature kinetic Ising model with Kimball-Deker-Haake dynamics. In this way, both in finite and semi-infinite chains and also the Bethe lattice can be analysed. The relationship with the random sequential adsorption of dimers and weakly tapped granular materials is discussed.