Renato H. L. Pedrosa

Invariant surfaces of the Heisenberg groups

SummaryWe fix a left-invariant metric g in the eisenberg group,H3, and give a complete classification of the constant mean curvature surfaces (including minimal) which are invariant with respect to 1-dimensional closed subgroups of the connected component of the isometry group of (H3, g). In addition to finding new examples, we organize in a common framework results that have appeared in various forms in the literature, by the systematic use of Riemannian transformation groups. Using the existence of a family of spherical surfaces for all values of nonzero mean curvature, we show that there are no complete graphs of constant mean curvature. We extend some of these results to the higher dimensional Heisenberg groupsH2n+1.

Access to higher education in Brazil

This article presents an overview of the recent expansion of higher education [HE] in Brazil, with a focus on access and equity issues. [The authors] analyze affirmative action policies and legislation, and the impact of those policies on the equity of access. Research shows that affirmative action policies have had a positive impact on reducing inequalities in HE in Brazil, but secondary education is still the main bottleneck for further progress, both in terms of expanding higher education and of making access more equitable. [The authors] then analyze how expansion has been occurring differently by sector (public versus private), and show some structural changes that are emerging in the private sector, in particular regarding the split between non-profit/for-profit private higher education and the recent growth in distance learning.

ProFIS: A New Paradigm for Higher Education in Brazil

Public universities represent nowadays a relatively small part of the Brazilian higher education system, both in terms of number of institutions and in terms of enrolment. Approximately 3/4 of all undergraduate students in Brazil attend private institutions. Public institutions are, on average, much more selective than those in the private system. This profile has two basic causes: the higher prestige of public universities and the fact that they do not charge any tuition fees. However, many of the students who are accepted at public universities come from wealthy families, and relatively fewer are from poor families or from minority groups, such as afro-descendents. The higher selectivity has a clear effect of inhibiting them from applying to a public Higher Education Institution (HEI), as we will see in the case of the University of Campinas (Unicamp), one of the most selective universities in Brazil.

Some Recent Results Regarding Symmetry and Symmetry-breaking Properties of Optimal Composite Membranes

The study of vibrating membranes is a classical subject in mathematical physics, and is at the origin of many important developments in the theory of partial differential equations. Among the most studied aspects of the subject is the relationship between the geometry of the membrane and properties of the frequencies of its natural modes of vibration, given by the eigenvalues of 2 order elliptic operators, in particular of the Laplacian. Classic references on the subject are the books by Lord Rayleigh ([19]), by Courant and Hilbert ([10]) and by Pólya and Szegö ([18]). A general source for problems on eigenvalues and membranes is [1]. The purpose of this note is to present a survey of recent results on symmetry properties (and lack of them) of domains in R which have minimal first Dirichlet eigenvalue, when the domain represents a vibrating membrane composed by materials of two distinct densities (a composite membrane). We discuss both the bounded and the 1-periodic cases. There are partial symmetry and symmetrybreaking results. The main technique for the symmetry results is that of rearrangements of functions. For the symmetry-breaking results, one uses eigenvalue estimates which follow from elliptic theory and classical orthogonal polynomial theory (Jacobi polynomials). We present various results and include proofs for the 1-periodic case. The main sources for the results presented below are [4], [7] and [17]. We end with a list of open problems.

A universidade e a inclusão social

), Burton Clark coloca quais seriam os temas sur-gidos no estudo da educacao superior americana, a partir de 1945. Osdois principais, segundo a analise: desigualdade na educacao superior (in-cluindo classe social, raca, etnicidade e genero) e impacto da experien-cia e transformacoes que a vida universitaria teria sobre os estudantesque por ela transitam.Esse temas continuam centrais nos estudos sobre

A representation theorem for languages with generalized quantifiers through back-and-forth methods

We obtain in this paper a representation of the formulae of extensions ofLωω by generalized quantifiers through functors between categories of first-order structures and partial isomorphisms. The main tool in the proofs is the back-and-forth technique. As a corollary we obtain the Caicedos version of Fraïssés theorem characterizing elementary equivalence for such languages. We also discuss informally some geometrical interpretations of our results.