The Development of Science Education Research in Brazil and Contributions from the History and Philosophy of Science

Over the last 50 years a new research area, science education research, has arisen and undergone singular development worldwide. In the specific case of Brazil, research in science education first appeared systematically 40 years ago, as a consequence of an overall renovation in the field of science education. This evolution was also related to the political events taking place in the country. We will use the theoretical work of Rene Kaes on the development of groups and institutions as a basis for our discussion of the most important aspects that have helped the area of science education research develop into an institution and kept it operating as such. The growth of this area of research can be divided into three phases: The first was related to its beginning and early configurations; the second consisted of a process of consolidation of this institution; and the third consists of more recent developments, characterised by a multiplicity of research lines and corresponding challenges to be faced. In particular, we will analyse the special contributions to this study gleaned from the field known as the history and philosophy of science.

Theory and applications of fuzzy Volterra integral equations

Formulations of fuzzy integral equations in terms of the Aumann integral do not reflect the behavior of corresponding crisp models. Consequently, they are ill-adapted to describe physical phenomena, even when vagueness and uncertainty are present. A similar situation for fuzzy ODEs has been obviated by interpretation in terms of families of differential inclusions. The paper extends this formalism to fuzzy integral equations and shows that the resulting solution sets and attainability sets are fuzzy and far better descriptions of uncertain models involving integral equations. The investigation is restricted to Volterra type equations with mildly restrictive conditions, but the methods are capable of extensive generalization to other types and more general assumptions. The results are illustrated by integral equations relating to control models with fuzzy uncertainties.

Modeling of phase equilibrium and vapor adsorption on carbon black based on a combination of a lattice theory and equation of state

A thermodynamic approach is developed in this paper to describe the behavior of a subcritical fluid in the neighborhood of vapor-liquid interface and close to a graphite surface. The fluid is modeled as a system of parallel molecular layers. The Helmholtz free energy of the fluid is expressed as the sum of the intrinsic Helmholtz free energies of separate layers and the potential energy of their mutual interactions calculated by the 10-4 potential. This Helmholtz free energy is described by an equation of state (such as the Bender or Peng-Robinson equation), which allows us a convenient means to obtain the intrinsic Helmholtz free energy of each molecular layer as a function of its two-dimensional density. All molecular layers of the bulk fluid are in mechanical equilibrium corresponding to the minimum of the total potential energy. In the case of adsorption the external potential exerted by the graphite layers is added to the free energy. The state of the interface zone between the liquid and the vapor phases or the state of the adsorbed phase is determined by the minimum of the grand potential. In the case of phase equilibrium the approach leads to the distribution of density and pressure over the transition zone. The interrelation between the collision diameter and the potential well depth was determined by the surface tension. It was shown that the distance between neighboring molecular layers substantially changes in the vapor-liquid transition zone and in the adsorbed phase with loading. The approach is considered in this paper for the case of adsorption of argon and nitrogen on carbon black. In both cases an excellent agreement with the experimental data was achieved without additional assumptions and fitting parameters, except for the fluid-solid potential well depth. The approach has far-reaching consequences and can be readily extended to the model of adsorption in slit pores of carbonaceous materials and to the analysis of multicomponent adsorption systems. (C) 2002 Elsevier Science (USA).

Child-care attendance and common morbidity: evidence of association in the literature and questions of design

Papers on child-care attendance as a risk factor for acute respiratory infections and diarrhea were reviewed. There was great variety among the studies with regard to the design, definition of exposure and definition of outcomes. All the traditional epidemiological study designs have been used. The studies varied in terms of how child-care attendance in general was defined, and for different settings. These definitions differed especially in relation to the minimum time of attendance required. The outcomes were also defined and measured in several different ways. The analyses performed were not always appropriate, leading to sets of results of uneven quality, and composed of different measures of association relating different exposures and outcomes, that made summarizing difficult. Despite that, the results reported were remarkably consistent. Only two of the papers reviewed failed to show some association between child-care attendance and increased acute respiratory infections, or diarrhea. On the other hand, the magnitude of the associations reported varied widely, especially for lower respiratory infections. Taken together, the studies so far published provide evidence that children attending child-care centers, especially those under three years of age, are at a higher risk of upper respiratory infections, lower respiratory infections, and diarrhea. The studies were not consistent, however, in relation to attendance at child-care homes. Children in such settings were sometimes similar to those in child-care centers, sometimes similar to those cared for at home, and sometimes presented an intermediate risk.