Geology and geochronology of the Betara region in south-southeastern Brazil: Evidence for possible Statherian (1.80-1.75 Ga) and Calymmian (1.50-1.45 Ga) extension events

The results of geological mapping, chemical analysis and radiometric dating of metabasic rocks of Betara Formation, and mapping and dating of those present in the Betara basement nucleus together with mylonitic granodiorite and syenogranite are reported here. U-Pb analysis of bulk zircon fractions from the metabasic rocks of the basement nucleus yielded a Statherian age of 1790 +/- 22 Ma, while the metabasic rocks from the upper part of the Betara Formation yielded a Calymmian age between 1500 and 1450 Ma. This age is a minimum for the deposition of the Betara Formation. The older metabasic rocks are associated with post-tectonic, possibly anorogenic syenogranite, while the younger ones are gabbro or very porphyritic ankaramite whose REE patterns are consistent with crystallization from an N-MORB parent magma. The observations and data point to the probable events associated with extensional processes of the end of Paleoproterozoic and early Mesoproterozoic. Similar registers of Statherian (1.80-1.75 Ga) and Calymmian (1.50-1.45 Ga) extensional events are recorded in other parts of the South American and African continents. The Neoproterozoic witnessed the formation and junction of the tectonic slices which formed the Apiai domain during the assemblage of western Gondwana. (C) 2010 International Association for Gondwana Research. Published by Elsevier B.V. All rights reserved.

Thermal history versus sedimentary history: OSL sensitivity of quartz grains extracted from rocks and sediments

The optically stimulated luminescence (OSL) sensitivity of quartz has a significant influence on luminescence dating procedures. Furthermore, identifying the natural controls of quartz OSL sensitivity is an important step towards new applications of OSL in geology such as provenance tracing. We evaluate the OSL sensitivity (total and the proportion of the informally assigned fast, medium and slow components) of single grains of quartz extracted from 10 different igneous and metamorphic rocks with known formation conditions; and from fluvial and coastal sediments with different sedimentary histories and known source rocks. This sample suite allows assessment of the variability of the OSL sensitivity of single quartz grains with respect to their primary origin and sedimentary history. We observed significant variability in the OSL sensitivity of grains within all studied rock and sediment samples, with the brightest grains of each sample being those dominated by the fast component. Quartz from rocks formed under high temperature (> 500 degrees C) conditions, such as rhyolites and metamorphic rocks from the amphibolite facies, display higher OSL sensitivity. The OSL sensitivity of fluvial sediments which have experienced only a short transport distance is relatively low. These sediments show a small increase in OSL sensitivity downstream, mainly due to a decreasing fraction of ""dim"" grains. The quartz grains from coastal sands present very high sensitivity and variability, which is consistent with their long sedimentary history. The high variability of the OSL sensitivity of quartz from coastal sands is attributed more to the mixture of grains with distinct sedimentary histories than to the provenance from many types of source rocks. The temperature of crystallization and the number of cycles of burial and solar exposure are suggested as the main natural factors controlling the OSL sensitivity of quartz grains. The increase in OSL sensitivity due to cycles of erosion and deposition surpasses the sensitivity inherited from the source rock, with this increase being mainly related to the sensitization of fast OSL components. The discrimination of grains with different sedimentary histories through their OSL sensitivities can allow the development of quantitative provenance methods based on quartz. (C) 2010 Elsevier B.V. All rights reserved.

Decay of geometry for Fibonacci critical covering maps of the circle

We study the growth of Df `` (f(c)) when f is a Fibonacci critical covering map of the circle with negative Schwarzian derivative, degree d >= 2 and critical point c of order l > 1. As an application we prove that f exhibits exponential decay of geometry if and only if l <= 2, and in this case it has an absolutely continuous invariant probability measure, although not satisfying the so-called Collet-Eckmann condition. (C) 2009 Elsevier Masson SAS. All rights reserved.

ABELIANIZED OBSTRUCTION FOR FIXED POINTS OF FIBER-PRESERVING MAPS OF SURFACE BUNDLES

Let f: M -> M be a fiber-preserving map where S -> M -> B is a bundle and S is a closed surface. We study the abelianized obstruction, which is a cohomology class in dimension 2, to deform f to a fixed point free map by a fiber-preserving homotopy. The vanishing of this obstruction is only a necessary condition in order to have such deformation, but in some cases it is sufficient. We describe this obstruction and we prove that the vanishing of this class is equivalent to the existence of solution of a system of equations over a certain group ring with coefficients given by Fox derivatives.

NIELSEN COINCIDENCE THEORY OF FIBRE-PRESERVING MAPS AND DOLD`S FIXED POINT INDEX

Let M -> B, N -> B be fibrations and f(1), f(2): M -> N be a pair of fibre-preserving maps. Using normal bordism techniques we define an invariant which is an obstruction to deforming the pair f(1), f(2) over B to a coincidence free pair of maps. In the special case where the two fibrations axe the same and one of the maps is the identity, a weak version of our omega-invariant turns out to equal Dold`s fixed point index of fibre-preserving maps. The concepts of Reidemeister classes and Nielsen coincidence classes over B are developed. As an illustration we compute e.g. the minimal number of coincidence components for all homotopy classes of maps between S(1)-bundles over S(1) as well as their Nielsen and Reidemeister numbers.

THE FUNDAMENTAL GROUP OF THE SPACE OF MAPS FROM A SURFACE INTO THE PROJECTIVE PLANE

In this work we compute the fundamental group of each connected component of the function space of maps from it closed surface into the projective space

Fibonacci bimodal maps

We introduce the Fibonacci bimodal maps on the interval and show that their two turning points are both in the same minimal invariant Cantor set. Two of these maps with the same orientation have the same kneading sequences and, among bimodal maps without central returns, they exhibit turning points with the strongest recurrence as possible.

Coincidence properties for maps from the torus to the Klein bottle

The authors study the coincidence theory for pairs of maps from the Torus to the Klein bottle. Reidemeister classes and the Nielsen number are computed, and it is shown that any given pair of maps satisfies the Wecken property. The 1-parameter Wecken property is studied and a partial negative answer is derived. That is for all pairs of coincidence free maps a countable family of pairs of maps in the homotopy class is constructed such that no two members may be joined by a coincidence free homotopy.

A full family of multimodal maps on the circle

We exhibit a family of trigonometric polynomials inducing a family of 2m-multimodal maps on the circle which contains all relevant dynamical behavior.

Coincidence Wecken homotopies versus Wecken homotopies relative to a fixed homotopy in one of the maps

We study the 1-parameter Wecken problem versus the restricted Wecken problem, for coincidence free pairs of maps between surfaces. For this we use properties of the function space between two surfaces and of the pure braid group on two strings of a surface. When the target surface is either the 2-sphere or the torus it is known that the two problems are the same. We classify most pairs of homotopy classes of maps according to the answer of the two problems are either the same or different when the target is either projective space or the Klein bottle. Some partial results are given for surfaces of negative Euler characteristic. (C) 2010 Elsevier B.V. All rights reserved.

Henon-like maps with arbitrary stationary combinatorics

We extend the renormalization operator introduced in [A. de Carvalho, M. Martens and M. Lyubich. Renormalization in the Henon family, I: universality but non-rigidity. J. Stat. Phys. 121(5/6) (2005), 611-669] from period-doubling Henon-like maps to Henon-like maps with arbitrary stationary combinatorics. We show that the renonnalization picture also holds in this case if the maps are taken to be strongly dissipative. We study infinitely renormalizable maps F and show that they have an invariant Cantor set O on which F acts like a p-adic adding machine for some p > 1. We then show, as for the period-doubling case in the work of de Carvalho, Martens and Lyubich [Renormalization in the Henon family, I: universality but non-rigidity. J. Stat. Phys. 121(5/6) (2005), 611-669], that the sequence of renormalizations has a universal form, but that the invariant Cantor set O is non-rigid. We also show that O cannot possess a continuous invariant line field.

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.

Prediction of the economic activity from the short and long-term interest rate differential: new evidences in Chile and the United States of America cases

The purpose of this work is to verify the stability of the relationship between real activity and interest rate spread. The test is based on Chen (1988) and Osorio and Galea (2006). The analysis is applied to Chile and the United States, from 1980 to 1999. In general, in both cases the relationship was statistically significant in early 80s, but a break point is found in both countries during that decades, suggesting that the relationship depends on the monetary rule follow by the Central Bank.

Use of self-organizing maps and molecular descriptors to predict the cytotoxic activity of sesquiterpene lactones

Some sesquiterpene lactones (SLs) are the active compounds of a great number of traditionally medicinal plants from the Asteraceae family and possess considerable cytotoxic activity. Several studies in vitro have shown the inhibitory activity against cells derived from human carcinoma of the nasopharynx (KB). Chemical studies showed that the cytotoxic activity is due to the reaction of alpha,beta-unsaturated carbonyl structures of the SLs with thiols, such as cysteine. These studies support the view that SLs inhibit tumour growth by selective alkylation of growth-regulatory biological macromolecules, such as key enzymes, which control cell division, thereby inhibiting a variety of cellular functions, which directs the cells into apoptosis. In this study we investigated a set of 55 different sesquiterpene lactones, represented by 5 skeletons (22 germacranolides, 6 elemanolides, 2 eudesmanolides, 16 guaianolides and nor-derivatives and 9 pseudoguaianolides), in respect to their cytotoxic properties. The experimental results and 3D molecular descriptors were submitted to Kohonen self-organizing map (SOM) to classify (training set) and predict (test set) the cytotoxic activity. From the obtained results, it was concluded that only the geometrical descriptors showed satisfactory values. The Kohonen map obtained after training set using 25 geometrical descriptors shows a very significant match, mainly among the inactive compounds (similar to 84%). Analyzing both groups, the percentage seen is high (83%). The test set shows the highest match, where 89% of the substances had their cytotoxic activity correctly predicted. From these results, important properties for the inhibition potency are discussed for the whole dataset and for subsets of the different structural skeletons. (C) 2008 Elsevier Masson SAS. All rights reserved.