Diarrhoeal diseases in pre-school children in the United Arab Emirates

Little information was available on the epidemiology and etiology of diarrhoeal diseases in pre-school children in U.A.E. Geographically considered as part of the developing world, the U.A.E. could have been expected to have developing world problems - diarrhoea being one of them. This study was conducted to determine why diarrhoea was not at present a leading cause of infantile mortality and morbidity in the study area and to examine the impact of the major health-related interventions on the health-care system. Various sources of information and approaches to analysis were used: 1. Government statistics-information was obtained from the various government departments that collaborated in the interventions made. 2. Background data for the laboratory studies was obtained from routine clinical laboratories at Jazeira Hospital, Central Hospital and the maternity hospital. 3. Qualitative data was derived from observations made during the home visits to the study families for the six month study period, and included reviews with family members. Historical recollections were collected from older people as to the social conditions prior to the oil boom. 4. Quantitative data were obtained from the questionnaire that was administered to a group of study families and from laboratory analysis of specimens collected from these families over the study period. Government sponsored interventions at the primary health-care level seemed to have been successful in preventing diarrhoea. This was probably made possible by the explosion of wealth and affluence that came with the oil-boom and the accompanying change in life-style and attitudes, which made possible the provision of clean water and a sewage system, thus cutting the most important routes of infection

Singularités dans le modèle de Landau-de Gennes pour les cristaux liquides

Nematic liquid crystals are an intermediate phase of matter, sharing properties with liquids and crystalline solids. They are composed of molecules which can flow freely, but tend to align locally along some preferred directions. Nematic phases exhibit defects, which can occur at isolated points or along lines, and are one of their mean features. This thesis mainly aims at discussing some mathematical results about defects and their generation, in the framework of the Landau-de Gennes theory. In the first chapter, we study minimizers of the energy functional in a bounded, smooth domain in dimension two. We show that, as the elastic constant tends to zero, minimizers converge to a locally harmonic map with a finite number of point singularities. Minimizers are biaxial in the core of defects (that is, more than one preferred direction of molecular alignment exists at a given point). Chapter two deals with the asymptotic analysis of minimizers in dimension three. We assume that the energy is comparable to the logarithm of the elastic constant and prove a compactness result. However, the limiting map is now allowed to have line singularities as well as point singularities. We also provide sufficient conditions for the logarithmic energy estimate to be satisfied. In chapter three, we study the existence of radially symmetric minimizers on spherical shells, in dimension three. Finally, in chapter four, we discuss a topological obstruction to the existence of unit vector fields of low regularity, on a compact manifold with boundary. This result can be understood as a first step in the analysis of some variational models for a surface coated with a thin nematic film.Nous nous intéressons aux cristaux liquides nématiques, qui sont une phase de la matière intermédiaire entre les liquides et les solides cristallins. Ces états sont caractérisés par la présence de défauts ponctuels ou de ligne. Le but de cette thèse est d'apporter une contribution à l'étude mathématique des défauts, dans le cadre de la théorie variationnelle de Landau-de Gennes. Dans le premier chapitre, nous étudions les minimiseurs de l'énergie dans des domaines bornés de dimension deux. Lorsque la constante élastique tend vers zéro, les minimiseurs convergent vers une application localement harmonique, avec un nombre fini de singularités ponctuelles. Au voisinage de celles-ci, les minimiseurs sont biaxes (le molécules sont alignées localement dans plusieurs directions). Le deuxième chapitre est consacré à l'analyse asymptotique des minimiseurs en dimension trois, en supposant l'énergie majorée par le logarithme de la constante élastique. Comme dans le cas bidimensionnel, nous obtenons un résultat de compacité des minimiseurs, mais cette fois l'application limite peut présenter à la fois des singularités ponctuelles et de ligne. Nous donnons aussi des conditions suffisantes pour que l'hypothèse sur l'énergie évoquée précédemment soit satisfaite. Le troisième chapitre porte sur l'existence de minimiseurs à symétrie radiale dans une couronne en dimension trois. Enfin, dans le dernier chapitre nous présentons une obstruction topologique à l'existence de champs de vecteurs unitaires de faible régularité, sur des variétés à bord. Ce résultat constitue une étape préliminaire à l'étude de modèles variationnels pour les films nématiques sur une surface