The notion of a filter F ∈ 2²x has been extended to that of a : prefilter: ƒ ∈ 1²x, generalised filter ƒ ∈ 2²x x and fuzzy filter ᵩ ∈ 1¹x. A uniformity is a filter with some other conditions and the notion of a uniformity D ∈ 2²xxx has been extended to that of a : fuzzy uniformity d ∈ 1²xxx , generalised uniformity ∈ 1²xxx and super uniformity b ∈ 1¹x. We establish categorical embeddings from the category of uniform spaces into the categories of fuzzy uniform spaces, generalised uniform spaces and super uniform spaces and also categorical embeddings into the category of super uniform spaces from the categories of fuzzy uniform spaces and generalised uniform spaces.

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In this paper, we will be concerned primarily with series of functions and a particular type of convergence which will be described. The purpose of this paper is to familiarize the reader with the concept of uniform convergence. In the main it is a compilation of material found in various references and revised to conform to standard notation.

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Orientador: Francisco de Alencar / Banca: Paula da Cruz Landim / Banca: Suzana Barreto Martins / Resumo: O uniforme escolar faz parte do cotidiano dos estudantes brasileiros desde meados do século XX e ainda hoje continua sendo um artefato amplamente utilizado, tanto por escolas públicas como particulares. Deste modo, algumas considerações e análises devem ser feitas em relação ao desenvolvimento do uniforme que, assim como qualquer peça do segmento do vestuário, deve resultar em produto que atenda às expectativas do usuário. Na revisão de literatura, foram levantadas informações sobre a implantação dos uniformes escolares, seu processo produtivo e as propriedades essenciais de um produto do vestuário, e por meio de pesquisa qualitativa, buscou-se descobrir qual o cenário atual neste segmento, sob o ponto de vista não só do usuário como também das escolas e das confecções. O resultado dessa pesquisa foi a elaboração de Diretrizes Projetuais para o Desenvolvimento de Uniformes Escolares, as quais objetivam elucidar requisitos importantes a serem considerados durante a concepção e o desenvolvimento do vestuário escolar, assim como, proporcionar alicerces para os profissionais responsáveis por esta atividade, de modo que a mesma seja realizada de forma adequada e com um resultado satisfatório / Abstract: The school uniform is part of brazilian routine since the mid-nineteenth century, and still remains a widely used device by both public and private schools. Therefore, some considerations and analysis must be done in relation to the development of the uniforms that, like any other segment of the apparel, should result in a product that answers user expectations. In the literature review, information were obtained about the implementation of school uniforms, their production process and the essential properties of the product's apparel, and through a qualitative research, it was attempted to discover which is the real scenario in this segment, from the point of view not only by the user but also schools and confections. The result of this research was the formulation of the Projectual/Guidelines for the development of School Uniforms, which aim to elucidate important requirements to be considered during the design and development of school clothing, as well as provide pillars for the professionals responsible for this activity, so that it is done property and with a satisfactory result / Mestre

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Abstract The dynamic models for different linear or nonlinear beam structures are proposed in this dissertation. The proposed mathematical model for a turbo-disk, which is valid for whatever isotropic or orthotropic turbo-blades with or without shrouds, accounts for the geometric pretwist and taper angles, and considers coupling effect among bending and torsion effect as well. The Kelvin-Voigt internal and external damping effects have been included in the formulation. The effect of fiber orientation on the natural frequencies of a fiber-reinforced orthotropic turbo-blade has also been investigated. The eigenvalue problems of a single pre-twisted taper-blade or a shrouded turbo-blade group are formulated by employing the differential quadrature method (DQM). The DQM is used to convert the partial differential equations of a tapered pre-twisted beam system into a discrete eigenvalue problem. The Chebyshev-Gauss- Lobatto sample point equation is used to select the sample points in these analyses. The effect of the number of sample points on the accuracy of the calculated natural frequencies has also been studied. The integrity and computational efficiency of the DQM in this problem will be demonstrated through a number of case studies. The effects of design parameters, i.e. Kelvin-Voigt internal and linear external damping coefficients, the fiber orientation, and the rotation speed on the dynamic behavior for a pretwisted turbo-blade are investigated. The dynamic response of a nonlinear electrode actuator used in the MEMS has also been formulated and analyzed by employing the proposed DQM algorithm. The transitional responses of the derived nonlinear systems are calculated by using the Wilson¡V method. Results indicated the curve shape of the electrode and the cantilever actuator may affect the pull-in behavior and the residual vibration of the electrostatic actuators significantly. Numerical results demonstrated the validity and the efficiency of the DQM in solving different type beam problems.

Acoustic point-source reflection from an unperturbed seabed with a continuously varying density and sound speed profile in a fluid-like sediment layer overlying an elastic basement is considered in this paper. This fundamental problem has illuminated many interesting phenomena about the effects of sediment stratification on acoustic wave interactions with the seabeds. The analysis employs the analytical solutions for the Helmholtz equation in the sediment layer, in which the density and the sound speed are, respectively, described by three kinds of geological models. The results have demonstrated that the effects of sediment stratifacation are confined in a region in range, where the reflection field is dominated by the reflected ray bundles containing ray components with the grazing angles which are neither too steep nor too shallow. The effects of many other factors, such as frequency, sediment thickness, basement elasticity, on the reflection fields are investigated, in particular, the interface wave component may become important in the region close to the seabed, if the sediment thickness is relatively thin in comparison with the acoustic wave length.