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The main purpose of this exposition is to explore the relations between the notions of covariant derivative, connection, and spray. We begin by introducing the basic definitions and then use a method of Gromoll, Klingenberg and Meyer to show that covariant derivatives and connections on vector bundles are in a natural one-to-one correspondence. We conclude by showing that on the tangent bundle of a manifold, sprays and "symmetric" connections are in a natural one-to-one correspondence. Although we use a different method, this re-establishes a result of Ambrose, Palais, and Singer. / Science, Faculty of / Mathematics, Department of / Graduate

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Reducing the amount of metal used within a timber structure has many advantages, particularly when dealing with connections. Fire resistance and durability are commonly cited benefits. In addition the use of alternative connector materials minimises thermal bridging and can also provide a lighter weight structural solution. Existing contemporary forms of non-metallic timber connections are commonly provided through the use of adhesives. However, these connections are reliant on a need for careful offsite, prefabricated construction. Traditional green oak carpentry connections provide a mechanically fastened non-metallic solution. However, carpentry connections are not widely compatible with contemporary architectural design or with the use of modern engineered timber products such as glulam. Building upon research completed at the University of Bath, the aim of this thesis was to develop a mechanical, non-metallic connection system suitable for contemporary applications. Specific objectives were to investigate the structural performance of a defined connection system and to develop analysis methods to facilitate design. A review of the literature demonstrated a lack of uptake and use of mechanical non-metallic connections. Guidance for the design of mechanical fasteners reflects the lack of innovation and research into the use of non-metallic materials. Following an initial experimental investigation of non-metallic materials, an experimental testing programme was completed to investigate the use of glass fibre reinforced plastic (GFRP) dowels in conjunction with densified veneer wood (DVW) plates. The findings of the experimental study demonstrate that the use of these materials can provide a robust connection system for contemporary applications. The results of the experimental work provide guidance on dowel spacing requirements, connection response to load and connection failure modes. The failure modes of the proposed connection system were shown to be unique to the materials used and specific strength analysis methods have been developed to predict connection yield and ultimate strength. A method for predicting initial connection stiffness was also developed through the use of a beam on elastic foundation model.

In my work I have solved the main problem- to find all conform symmetrical Г1, Г1,2 and Г2- connections of the first degree. Also there were showed that the conform symmetrical affinical nonholonomical connections don’t exist. There were found the necessary and sufficient factors, so that the IP(1,n)– symmetrical connections would be conformed symmetrical. Ready conform symmetrical connections are all the local connections of conform symmetrical differential equations. These connections can be employed in theories of mathematical physics, where can be used these differential equations.

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Resumo: O bambu é considerado um dos mais antigos materiais para habitações, porém, o desenvolvimento de tecnologia própria, como material de construção de qualidade, vem acontecendo somente nas últimas três décadas, quando surgiu uma discussão mundial sobre sustentabilidade. A variável ambiental passou, então, a ser considerada em qualquer projeto de desenvolvimento, uma vez que influencia tanto na disponibilidade futura de matérias-primas e energia, quanto na qualidade de vida das populações. Uma das maiores dificuldades no pleno emprego do bambu na construção civil são as conexões estruturais entre seus elementos, que não permitem o uso da tecnologia de ligações aplicada a outros materiais, como o aço e a madeira maciça, para efetuar com eficiência a transferência de esforços, inviabilizando toda potencialidade estrutural oferecida pelo bambu. Este trabalho faz uma ampla revisão dos principais aspectos de arquitetura com bambu, bem como das técnicas de construção e conexões utilizadas. A partir de uma estratégia geral de inovação, baseada no processo de desenvolvimento de produtos, foi proposto o design de uma nova conexão estrutural, com execução de protótipo e projeto arquitetônico para ilustração de sua aplicação. Esta nova ligação visou contribuir com a viabilização da utilização do bambu na construção civil, pelo incremento tecnológico do material / Abstract: Bamboo is considered one of the oldest materials for housing, but the development of technoloy as quality construction material is happening only in the last three decades when a wordwide discussion about sustainability, where the environmental variable is to be considered in any development project, since it affects the future availability of raw materials and energy, as in the quality of life of people with improved environmental conditions. One of the biggest difficulties in full employment in the construction of bamboo are structural connections between its elements, which do not allow the use of executable technology of other materials such as steel and timber, for their efficiently transfer efforts, using all structural offered by bamboo creditworthiness. This work is a comprehensive review of the main aspects of the bamboo culture, as well as construction techniques and connections used. From an overall strategy of innovation, based on the product development process to design a new connection is proposed. This rebonding aims to serve as a contribution to the process of enabling the use of bamboo in construction, by technological increment of the material / Orientador: Marco Antonio dos Reis Pereira / Coorientador: Paula da Cruz Landim / Banca: Antonio Ludovico Beraldo / Mestre

Kowalski's connection graph method provides a representation for logic programs which allows for the incorporation of better procedural control techniques than standard logic programming languages. A proposed search strategy for visual recognition which combines top-down and bottom-up techniques has been incorporated in a connection graph implementation. The connection graph representation also allows for the natural incorporation of constraint satisfaction techniques in logic programming. Kowalski's approach to incorporating constraint satisfaction techniques in connection graphs is examined in detail. It is shown that his approach is not efficient enough to be used as a general preprocessing algorithm but that a modified version may be of use. Increased control of search and the incorporation of consistency techniques increase the procedural adequacy of logic programs for representing knowledge without compromising the descriptive capacity of the form. / Science, Faculty of / Computer Science, Department of / Graduate

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