On differentiability and analyticity of positive definite functions

We derive a set of differential inequalities for positive definite functions based on previous results derived for positive definite kernels by purely algebraic methods. Our main results show that the global behavior of a smooth positive definite function is, to a large extent, determined solely by the sequence of even-order derivatives at the origin: if a single one of these vanishes then the function is constant; if they are all non-zero and satisfy a natural growth condition, the function is real-analytic and consequently extends holomorphically to a maximal horizontal strip of the complex plane.

Solutions of second-order and fourth-order ODEs on the half-line

We start by studying the existence of positive solutions for the differential equation u '' = a(x)u - g(u), with u ''(0) = u(+infinity) = 0, where a is a positive function, and g is a power or a bounded function. In other words, we are concerned with even positive homoclinics of the differential equation. The main motivation is to check that some well-known results concerning the existence of homoclinics for the autonomous case (where a is constant) are also true for the non-autonomous equation. This also motivates us to study the analogous fourth-order boundary value problem {u((4)) - cu '' + a(x)u = vertical bar u vertical bar(p-1)u u'(0) = u'''(0) = 0, u(+infinity) = u'(+infinity) = 0 for which we also find nontrivial (and, in some instances, positive) solutions.

O lugar do género, dos homens e das mulheres na sociologia portuguesa: uma análise a partir da Associação Portuguesa de Sociologia e seus congressos

O e-working paper que se apresenta insere-se no campo analítico da sociologia da ciência, e tem como objectivos, por um lado, compreender como o género se constitui, ou não, como um elemento estruturante na distribuição dos actores pelo campo disciplinar e, por outro lado, explorar as configurações que a sociologia do género tem assumido na produção científica nacional. Os Congressos Portugueses de Sociologia (1988 a 2008), e a Associação Portuguesa de Sociologia constituíram o material empírico que possibilitou o exercício. This e-working paper integrates the realm of sociology of science, and aimed, on one hand, to understand how gender is a structural element in the distribution of actors within the disciplinary field and, on the other hand, to explore the configurations of sociology of gender in the scientific production. Therefore, the analysis is produced from two privileged empirical objects: the Portuguese Congress of Sociology (1988 to 2008) and the Portuguese Association of Sociology.

Positive Solutions of the Dirichlet Problem for the One-dimensional Minkowski-Curvature Equation

We discuss existence and multiplicity of positive solutions of the Dirichlet problem for the quasilinear ordinary differential equation-(u' / root 1 - u'(2))' = f(t, u). Depending on the behaviour of f = f(t, s) near s = 0, we prove the existence of either one, or two, or three, or infinitely many positive solutions. In general, the positivity of f is not required. All results are obtained by reduction to an equivalent non-singular problem to which variational or topological methods apply in a classical fashion.

Unified min-max and interlacing theorems for linear operators

There exist striking analogies in the behaviour of eigenvalues of Hermitian compact operators, singular values of compact operators and invariant factors of homomorphisms of modules over principal ideal domains, namely diagonalization theorems, interlacing inequalities and Courant-Fischer type formulae. Carlson and Sa [D. Carlson and E.M. Sa, Generalized minimax and interlacing inequalities, Linear Multilinear Algebra 15 (1984) pp. 77-103.] introduced an abstract structure, the s-space, where they proved unified versions of these theorems in the finite-dimensional case. We show that this unification can be done using modular lattices with Goldie dimension, which have a natural structure of s-space in the finite-dimensional case, and extend the unification to the countable-dimensional case.

Cidadania e diversidade em saúde: necessidades e estratégias de promoção de equidade nos cuidados

Este artigo introduz o conceito de cidadania associado à sua concretização no âmbito da saúde em contextos de diversidade. Conjuga resultados de vários projetos de investigação de cariz qualitativo como forma de ilustrar algumas das estratégias concebidas pelo Estado e pela sociedade civil em resposta às mudanças trazidas pelas migrações internacionais. Assim, identificam-se as necessidades da população, as barreiras de acesso aos cuidados de saúde, as principais fontes de desigualdades e iniquidade e algumas das estratégias desenvolvidas na promoção da equidade em saúde, alertando para a importância de levar em consideração as questões culturais e as de índole socioeconómica.

Positive radial solutions of the Dirichlet problem for the Minkowski-Curvature equation in a ball

We study the existence and multiplicity of positive radial solutions of the Dirichlet problem for the Minkowski-curvature equation { -div(del upsilon/root 1-vertical bar del upsilon vertical bar(2)) in B-R, upsilon=0 on partial derivative B-R,B- where B-R is a ball in R-N (N >= 2). According to the behaviour off = f (r, s) near s = 0, we prove the existence of either one, two or three positive solutions. All results are obtained by reduction to an equivalent non-singular one-dimensional problem, to which variational methods can be applied in a standard way.