Strong surjectivity of maps from 2-complexes into the 2-sphere

Given a model 2-complex K(P) of a group presentation P, we associate to it an integer matrix Delta(P) and we prove that a cellular map f : K(P) -> S(2) is root free (is not strongly surjective) if and only if the diophantine linear system Delta(P) Y = (deg) over right arrow (f) has an integer solution, here (deg) over right arrow (f) is the so-called vector-degree of f

Tokamak magnetic field lines described by simple maps

The magnetic field line structure in a tokamak can be obtained by direct numerical integration of the field line equations. However, this is a lengthy procedure and the analysis of the solution may be very time-consuming. Otherwise we can use simple two-dimensional, area-preserving maps, obtained either by approximations of the magnetic field line equations, or from dynamical considerations. These maps can be quickly iterated, furnishing solutions that mirror the ones obtained from direct numerical integration, and which are useful when long-term studies of field line behavior are necessary (e.g. in diffusion calculations). In this work we focus on a set of simple tokamak maps for which these advantages are specially pronounced.

Geochemistry of iron and manganese in soils and sediments of a mangrove system, Island of Pai Matos (Cananeia - SP, Brazil)

Five zones along a transect of 180 m were selected for study on the Island of Pai Matos (Sao Paulo, Brazil). Four of the zones are colonised by vascular plants (Spartina SP, Laguncularia LG, Avicennia AV and Rhizophora RH) and were denominated soils, and the other zone, which lacks vegetation, was denominated sediment (SD). The geochemical conditions differed significantly in soils and sediment and also at different depths. The soils were oxic (Eh > 350 mV) or suboxic (Eh: 350-100 mV) at the surface and anoxic (Eh < 100 mV) at depth, whereas in the sediment anoxic conditions prevailed at all depths, but with a lower concentration of sulphides in the pore water and pyrite in the solid fraction. Under these geochemical conditions Fe is retained in the soils, while the Mn tends to be mobilized and lost. The most abundant form of iron oxyhydroxide was lepidocrocite (mean concentration for all sites and depths, 45 +/- 19 mu mol g(-1)), followed by goethite (30 19 mu mol g(-1))and ferrihydrite (19 +/- 11 mu mol g(-1)),with significant differences among the mean concentrations. There was a significant decrease with depth in all the types of Fe oxyhydroxides measured, particularly the poorly crystalline forms. The pyrite fraction was an important component of the free Fe pool (non-silicate Fe) in all soils as well as in the sediment, especially below 20 cm depth (mean concentration for all sites and depths, 60 +/- 54 mu mol CI). Furthermore, the mean concentration of Fe-pyrite for all sites and depths was higher than that obtained for any of the three Fe oxyhydroxides measured. The Fe-AVS was a minor fraction, indicating that the high concentrations of dissolved Fe in the soils in the upper area of the transect result from the oxidation of Fe sulphides during low tide. Mossbauer spectroscopy also revealed that most of the Fe (III) was associated with silicates, in this case nontronite. The presence of crystals of pyrite associated with phyllosilicates in samples from the upper layer of the soils may indicate that pyritization of this form of Fe(III) is more rapid than usually reported for ocean bed sediments. The sequential extraction of Mn did not reveal any clearly dominant fraction, with the Mn-carbonate fraction being the most prevalent, followed by exchangeable Mn and oxides of Mn, whereas pyrite-Mn and Mn associated with crystalline Fe-oxides were present at significantly lower concentrations. The high concentration of dissolved Mn found in the soils in the lower part of the transect is consistent with the fact that the solubility is determined by the carbonate fraction. Unlike for Fe, in the soils in the higher zone, which are subject to intense drainage during low tide, there was loss of Mn, as reflected by the concentration of total Mn. (C) 2008 Elsevier B.V. All rights reserved.

A geochemical and lead isotopic record from a small pond in a remote equatorial island, Fernando de Noronha, Brazil

A 72 cm long core was collected from Lagoa da Viracao (LV), a small poind in the Fernando de Noronha island, northern Brazil. Sediments from the lower section of the core (20-72 cm depth) contain essentially mineral matter, while in the upper section (0-20 cm depth) mineral matter is mixed with organic matter. Lithogenic conservative elements - Si, Al, Fe, Ti, Co, Cr, Cu, Ba, Ga, Hf, Nb, Ni, Y, V, Zn, Zr and REE - exhibit remarkably constant values throughout the core, with concentrations similar to those of the bedrock. The vertical distribution of soluble elements - Ca, Mg, Na, K, P, Mn and Sr - is also homogeneous, but these elements are systematically depleted in relation to the bedrock. LOI, TOC, Br, Se, Hg and Pb, although showing nearly constant values in the lower section of the core, are significantly enriched in the upper section. The concentration profiles of Br and Se suggest that they may be accounted for by natural processes, related to the slight affinity of these elements for organic matter. On the other hand, the elevated levels of Hg and Pb in recent sediments may be explained by their long-range atmospheric transport and deposition. Furthermore, the isotopic composition of Pb clearly indicates that anthropogenic sources contributed to the Pb burden in the uppermost pond sediments.

Equivariant Nielsen root theory for G-maps

Let X be a compact Hausdorff space, Y be a connected topological manifold, f : X -> Y be a map between closed manifolds and a is an element of Y. The vanishing of the Nielsen root number N(f; a) implies that f is homotopic to a root free map h, i.e., h similar to f and h(-1) (a) = empty set. In this paper, we prove an equivariant analog of this result for G-maps between G-spaces where G is a finite group. (C) 2010 Elsevier B.V. All rights reserved.