Theorems on existence and global dynamics for the Einstein equations

This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations. It draws attention to open questions in the field. The local-in-time Cauchy problem, which is relatively well understood, is surveyed. Global results for solutions with various types of symmetry are discussed. A selection of results from Newtonian theory and special relativity that offer useful comparisons is presented. Treatments of global results in the case of small data and results on constructing spacetimes with prescribed singularity structure or late-time asymptotics are given. A conjectural picture of the asymptotic behaviour of general cosmological solutions of the Einstein equations is built up. Some miscellaneous topics connected with the main theme are collected in a separate section.Comment: Submitted to Living Reviews in Relativity, major update of Living Rev. Rel. 5 (2002)

On critical behaviour in systems of Hamiltonian partial differential equations

We study the critical behaviour of solutions to weakly dispersive Hamiltonian systems considered as perturbations of elliptic and hyperbolic systems of hydrodynamic type with two components. We argue that near the critical point of gradient catastrophe of the dispersionless system, the solutions to a suitable initial value problem for the perturbed equations are approximately described by particular solutions to the Painlev\ue9-I (PI) equation or its fourth-order analogue P2I. As concrete examples, we discuss nonlinear Schr\uf6dinger equations in the semiclassical limit. A numerical study of these cases provides strong evidence in support of the conjecture

Miíases associadas com alguns fatores sócio-econômicos em cinco áreas urbanas do Estado do Rio de Janeiro Myiasis associated with some socioeconomic factors in five urban areas of the State of Rio de Janeiro

Trata-se de um estudo epidemiológico descritivo com o objetivo de avaliar a ocorrência de miíases humanas em áreas urbanas de quatro municípios do Estado do Rio de Janeiro. Foram analisados 71 pacientes que procuraram espontaneamente o atendimento em Postos de Saúde, no período de outubro de 1999 a outubro de 2003. Maior prevalência da doença foi encontrada em adultos e idosos acima de 51 anos (42,3%) e em menores de 10 anos (33,8%). Do total dos casos estudados, 62% incluíam-se no nível sócio-econômico baixo; 60,6% eram do sexo masculino e 33,8% dos indivíduos infestados, sem profissão. Nos casos analisados as espécies bioagentes foram Cochliomyia hominivorax (Coquerel, 1858); Dermatobia hominis (Linnaeus Jr, 1781) e Cochliomyia macellaria (Fabricius, 1775). Os resultados apontam para a associação da doença com as condições de vida e de higiene dos pacientes, sinalizando para a necessidade de atenção mais específica à saúde dos grupos mais vulneráveis.<br>This was a descriptive epidemiological study with the aim of evaluating the occurrence of human myiasis in urban areas of four municipalities in the State of Rio de Janeiro. Seventy-one patients who spontaneously sought attendance at primary healthcare units between October 1999 and October 2003 were examined. The disease was more prevalent among adults, including in individuals more than 51 years old (42.3%), and among children less than 10 years old (33.8%). From all the cases studied, 62% were of low socioeconomic level; 60.6% were male; and 33.8% of the infested individuals were unemployed. In the cases analyzed, the bioagent species were Cochliomyia hominivorax (Coquerel, 1858), Dermatobia hominis (Linnaeus Jr, 1781) and Cochliomyia macellaria (Fabricius, 1775). The results point towards an association between the disease and the patients’ living and hygiene conditions. This indicates the need for more specific healthcare among more vulnerable groups