Brazilian <Emphasis Type="Italic">Dioscoreaceas</Emphasis> starches

Determination of the characteristics of native starches is crucial in order to select their best application in various industrial fields. Thus, two different types of non-traditional native starches from the Dioscoreaceas species (Dioscorea sp. and Dioscorea piperifolia Humb. var. Wild) were studied regarding their thermal, structural and rheological properties. The results were contrasted with traditional commercial starch sources (potato, cassava and corn). From the thermogravimetric results (TG/DTG), D. piperifolia starch obtained the highest thermal stability of the samples, except for potato starch. Furthermore, using differential scanning calorimetry and viscoamylograph profiles (RVA), it was found that the Dioscoreaceas starches presented a higher onset (T _o) temperature and susceptibility to retrogradation. They also showed lower values in relation to relative crystallinity, which was calculated from their X-ray patterns and tendency to white (L*) colour. The shapes of the Discoreaceas starch granules were determined using electron microscopy; it was found that as the potato starch the Dioscoreaceas starches showed a wide range of particle size.     

Characterization of Gasoline by 1H Nuclear Magnetic Resonance and Chemometrics

Automotive fuel adulteration is an old and significant problem. One common type of fuel adulteration is the addition of diesel to gasoline. Unsupervised models were developed through hierarchical cluster and principal component analysis models. Supervised models through partial least square discriminant analysis using ¹H nuclear magnetic resonance spectra as the input were used to classify samples as adulterated or unadulterated. Quantitative models were developed using partial least squares to determine the gasoline and diesel concentrations in the samples. This set contained samples composed of pure gasoline and anhydrous ethanol reproducing commercial gasoline and other samples treated with diesel. Hierarchical cluster and principal component analysis did not distinguish between adulterated and unadulterated samples except for the most adulterated materials. However, partial least square discriminant analysis classified 100% of the samples correctly. The partial least square algorithm provided excellent regression models for the gasoline and diesel content. The determination coefficient was 0.9920 for both models, whereas the root mean square error of cross-validation and root mean square error of prediction for the diesel model were 2.32 and 1.42%, respectively, and 2.40 and 1.38% for the gasoline model.     

Existence,uniqueness and stability of equilibrium states for non-uniformly expanding maps

We prove existence of finitely many ergodic equilibrium states for a large class of non-uniformly expanding local homeomorphisms on compact metric spaces and Hölder continuous potentials with not very large oscillation. No Markov structure is assumed. If the transformation is topologically mixing there is a unique equilibrium state, it is exact and satisfies a non-uniform Gibbs property. Under mild additional assumptions we also prove that the equilibrium states vary continuously with the dynamics and the potentials (statistical stability) and are also stable under stochastic perturbations of the transformation.     

Collectives of humans-with-media in mathematics education: notebooks, blackboards, calculators, computers and … notebooks throughout 100 years of ICMI

The main aim of this study was to present evidence of the ways in which different media have conditioned and dramatically reorganized education, in general, and mathematics education, in particular. After an introduction of the theme, we discuss the epistemological perspective that provides the foundation for our analysis: the notion of humans-with-media. Then, we briefly illustrate how the medium is related to the scientific production of mathematical knowledge. We take a detour into the world of art to examine how devices and instruments have historically been associated with the production of mathematical knowledge. Then, we review studies on the history of education to show how traditional media were introduced into schools and have influenced education. In particular, we examine how devices such as blackboards and notebooks, which were novelties a 100 years ago, came to be accepted in schools and the mathematical activities that were promoted with their use. Finally, we discuss how information technology has changed education and how the Internet may have an impact on mathematics education comparable to that of the notebook over a century ago.