A demonstração feita por Erdos da existência de grafos com cintura e número cromático grandes é uma das primeiras aplicações do método probabilístico. Essa demonstração fornece um limite para o número de vértices de um grafo desse tipo, que é exponencial na cintura quando o número cromático é fixado. O foco deste texto, no entanto, são as construções determinísticas de grafos com cintura e número cromático grandes e os números de vértices dos grafos obtidos. As construções elementares conhecidas fornecem apenas grafos com um número Ackermanniano de vértices. O texto começa com uma breve repetição das demonstrações probabilísticas da existência de grafos e hipergrafos com cintura e número cromático grandes. Depois, a busca por construções determinísticas é motivada apresentando-se algumas construções para o caso particular de grafos livres de triângulo e com número cromático grande. São construídos os grafos de Tutte, Zykov, Mycielski e Kneser, os grafos de shift e os de planos projetivos finitos. Os números de vértices dessas construções são computados e comparados. De fato, a construção a partir de planos projetivos finitos tem um número polinomial de vértices. A parte principal do texto são as construções de grafos e hipergrafos com cintura e número cromático grandes. A primeira construção apresentada foi feita por Kriz. Ela foi a primeira construção para grafos com cintura e número cromático grandes que não envolvia hipergrafos. A segunda construção apresentada foi feita por Nesetril e Rödl. Essa construção antecede a de Kriz. Ela utiliza a amalgamação entre grafos e hipergrafos para obter um hipergrafo uniforme com cintura e número cromático grandes. A terceira e última construção apresentada foi encontrada por Alon, Kostochka, Reiniger, West e Zhu. Essa construção consegue obter hipergrafos uniformes com cintura e número cromático grandes diretamente a partir de um grafo, que é uma certa árvore aumentada. Em particular, essa construção obtém grafos com cintura e número cromático grandes sem envolver hipergrafos. Os números de vértices dos hipergrafos obtidos por essas construções são computados e comparados. / The proof by Erdos of the existence of graphs with high girth and high chromatic number is one of the first applications of the probabilistic method. This proof gives a bound on the number of vertices of such graphs, which is exponential on the girth if the chromatic number is fixed. The focus of this text is however on the deterministic construction of graphs with high girth and high chromatic number and on the number of vertices of the obtained graphs. The elementary known constructions can only give us graphs with an Ackermannian number of vertices. We begin by briefly repeating the probabilistic proofs of the existence of graphs and hypergraphs with high girth and high chromatic number. Then we motivate the search for deterministic constructions of such graphs by showing some constructions for the special case of triangle-free graphs with high chromatic number. We construct Tutte, Zykov, Mycielski and Kneser graphs, the shift graphs and graphs built from finite projective planes. We count and compare the number of vertices of the graphs obtained by each of these constructions. In fact, the construction based on finite projective planes gives us graphs with a polynomial number of vertices. The main part of the text consists of constructions of graphs and hypergraphs with high girth and high chromatic number. The first construction we present is due to Kriz. This was the first construction to give graphs with high girth and high chromatic number without using hypergraphs. The second construction we present is due to Nesetril and Rödl. This construction precedes the one by Kriz. It uses amalgamations between graphs and hypergraphs to obtain uniform hypergraphs with high girth and high chromatic number. The third and last construction we show was found by Alon, Kostochka, Reiniger, West and Zhu. This construction manages to build uniform hypergraphs with high girth and high chromatic number directly from a single graph, which is an augmented-tree. In particular, it constructs graphs with high girth and high chromatic number without using hypergraphs. We count and compare the number of vertices of the hypergraphs obtained by these constructions.

An E-graph is constructed by replacing each edge in a core graph G with a copy of a graph H. An important property of E-graphs is that their invariant values can be determined from parameters of the original graphs G and H. We determine chromatic number, clique number, vertex and edge cover numbers, vertex and edge independence numbers, circumference, and girth of E-graphs. A characterization of hamiltonian E-graphs is also given.

This research sought to establish residual stress distribution characteristics in typical pipe and vessel welds by carrying out a comprehensive parametric study using an advanced sequentially coupled thermo-mechanical finite element procedure. The parametric study covered vessel and pipe components with a ranging radius to thickness ratio from r/t=2 to 100, for thickness ranging from t=1/4” to 10”. Component materials varied from low carbon steel to high alloy steels, such as stainless steel and titanium alloy. Furthermore, a structural mechanics based framework is proposed to generalize through-thickness residual stress distributions for a broad spectrum of joint geometry and welding conditions. The results of this study have been shown to provide both a significantly improved understanding of important parameters governing residual stresses in pipe and vessel welds, as well as a unified scheme for achieving consistent residual stress prescriptions for supporting fitness-for-service assessments of engineering structures. Specific contributions of this investigation may be summarized as follows: (a) A welding heating input characterization procedure has been developed and validated to relate prescribed temperature thermal modeling procedure to conventional linear input definition. With this development, a large number of parametric analyses can be carried in a cost-effective manner without relying on the heat flux based weld pool model that can be exhaustive and time-consuming. (b) A set of governing parameters controlling important residual stress distribution characteristics regardless of joint types, materials, and welding procedures have been identified. These are characteristic heat input intensity and radius over thickness ratio. (c) A shell theory based residual stress estimation scheme has been developed to interrelate all parametric analysis results for circumferential girth welds, which can also be used to estimate residual stress distributions in both through-thickness and at any distance away from the weld, for cases that are not covered in the parametric study. (d) In a similar manner, a curve bar theory based residual stress estimation scheme has also been developed for longitudinal seam welds. These developments can significantly advance the residual stress profile prescription methods stipulated in the current national and international FFS Codes and Standards such as 2007 API 579 RP/ASME FFS-1 and BS 7910: 2011.

Low-density parity-check (LDPC) codes have been shown to have good error correcting performance approaching Shannon’s limit. Good error correcting performance enables efficient and reliable communication. However, a LDPC code decoding algorithm needs to be executed efficiently to meet cost, time, power and bandwidth requirements of target applications. The constructed codes should also meet error rate performance requirements of those applications. Since their rediscovery, there has been much research work on LDPC code construction and implementation. LDPC codes can be designed over a wide space with parameters such as girth, rate and length. There is no unique method of constructing LDPC codes. Existing construction methods are limited in some way in producing good error correcting performing and easily implementable codes for a given rate and length. There is a need to develop methods of constructing codes over a wide range of rates and lengths with good performance and ease of hardware implementability. LDPC code hardware design and implementation depend on the structure of target LDPC code and is also as varied as LDPC matrix designs and constructions. There are several factors to be considered including decoding algorithm computations,processing nodes interconnection network, number of processing nodes, amount of memory, number of quantization bits and decoding delay. All of these issues can be handled in several different ways. This thesis is about construction of LDPC codes and their hardware implementation. LDPC code construction and implementation issues mentioned above are too many to be addressed in one thesis. The main contribution of this thesis is the development of LDPC code construction methods for some classes of structured LDPC codes and techniques for reducing decoding time. We introduce two main methods for constructing structured codes. In the first method, column-weight two LDPC codes are derived from distance graphs. A wide range of girths, rates and lengths are obtained compared to existing methods. The performance and implementation complexity of obtained codes depends on the structure of their corresponding distance graphs. In the second method, a search algorithm based on bit-filing and progressive-edge growth algorithms is introduced for constructing quasi-cyclic LDPC codes. The algorithm can be used to form a distance or Tanner graph of a code. This method could also obtain codes over a wide range of parameters. Cycles of length four are avoided by observing the row-column constraint. Row-column connections observing this condition are searched sequentially or randomly. Although the girth conditions are not sufficient beyond six, larger girths codes were easily obtained especially at low rates. The advantage of this algorithm compared to other methods is its flexibility. It could be used to construct codes for a given rate and length with girths of at least six for any sub-matrix configuration or rearrangement. The code size is also easily varied by increasing or decreasing sub-matrix size. Codes obtained using a sequential search criteria show poor performance at low girths (6 and 8) while random searches result in good performing codes. Quasi-cyclic codes could be implemented in a variety of decoder architectures. One of the many options is the choice of processing nodes interconnect. We show how quasi-cyclic codes processing could be scheduled through a multistage network. Although these net-works have more delay than other modes of communication, they offer more flexibility at a reasonable cost. Banyan and Benes networks are suggested as the most suitable networks. Decoding delay is also one of several issues considered in decoder design and implementation. In this thesis, we overlap check and variable node computations to reduce decoding time. Three techniques are discussed, two of which are introduced in this thesis. The techniques are code matrix permutation, matrix space restriction and sub-matrix row-column scheduling. Matrix permutation rearranges the parity-check matrix such that rows and columns that do not have connections in common are separated. This techniques can be applied to any matrix. Its effectiveness largely depends on the structure of the code. We show that its success also depends on the size of row and column weights. Matrix space restriction is another technique that can be applied to any code and has fixed reduction in time or amount of overlap. Its success depends on the amount of restriction and may be traded with performance loss. The third technique already suggested in literature relies on the internal cyclic structure of sub-matrices to achieve overlapping. The technique is limited to LDPC code matrices in which the number of sub-matrices is equal to row and column weights. We show that it can be applied to other codes with a lager number of sub-matrices than code weights. However, in this case maximum overlap is not guaranteed. We calculate the lower bound on the amount of overlapping. Overlapping could be applied to any sub-matrix configuration of quasi-cyclic codes by arbitrarily choosing the starting rows for processing. Overlapping decoding time depends on inter-iteration waiting times. We show that there are upper bounds on waiting times which depend on the code weights. Waiting times could be further reduced by restricting shifts in identity sub-matrices or using smaller sub-matrices. This overlapping technique can reduce the decoding time by up to 50% compared to conventional message and computation scheduling. Techniques of matrix permutation and space restriction results in decoder architectures that are flexible in LDPC code design in terms of code weights and size. This is due to the fact that with these techniques, rows and columns are processed in sequential order to achieve overlapping. However, in the existing technique, all sub-matrices have to be processed in parallel to achieve overlapping. Parallel processing of all code sub-matrices requires the architecture to have the number of processing units at least equal to the number sub-matrices. Processing units and memory space should therefore be distributed among the sub-matrices according to the sub-matrices arrangement. This leads to high complexity or inflexibility in the decoder architecture. We propose a simple, programmable and high throughput decoder architecture based on matrix permutation and space restriction techniques. / Thesis(Ph.D.) -- University of Adelaide, School of Electrical and Electronic Engineering, 2007

Low-density parity-check (LDPC) codes have been shown to have good error correcting performance approaching Shannon’s limit. Good error correcting performance enables efficient and reliable communication. However, a LDPC code decoding algorithm needs to be executed efficiently to meet cost, time, power and bandwidth requirements of target applications. The constructed codes should also meet error rate performance requirements of those applications. Since their rediscovery, there has been much research work on LDPC code construction and implementation. LDPC codes can be designed over a wide space with parameters such as girth, rate and length. There is no unique method of constructing LDPC codes. Existing construction methods are limited in some way in producing good error correcting performing and easily implementable codes for a given rate and length. There is a need to develop methods of constructing codes over a wide range of rates and lengths with good performance and ease of hardware implementability. LDPC code hardware design and implementation depend on the structure of target LDPC code and is also as varied as LDPC matrix designs and constructions. There are several factors to be considered including decoding algorithm computations,processing nodes interconnection network, number of processing nodes, amount of memory, number of quantization bits and decoding delay. All of these issues can be handled in several different ways. This thesis is about construction of LDPC codes and their hardware implementation. LDPC code construction and implementation issues mentioned above are too many to be addressed in one thesis. The main contribution of this thesis is the development of LDPC code construction methods for some classes of structured LDPC codes and techniques for reducing decoding time. We introduce two main methods for constructing structured codes. In the first method, column-weight two LDPC codes are derived from distance graphs. A wide range of girths, rates and lengths are obtained compared to existing methods. The performance and implementation complexity of obtained codes depends on the structure of their corresponding distance graphs. In the second method, a search algorithm based on bit-filing and progressive-edge growth algorithms is introduced for constructing quasi-cyclic LDPC codes. The algorithm can be used to form a distance or Tanner graph of a code. This method could also obtain codes over a wide range of parameters. Cycles of length four are avoided by observing the row-column constraint. Row-column connections observing this condition are searched sequentially or randomly. Although the girth conditions are not sufficient beyond six, larger girths codes were easily obtained especially at low rates. The advantage of this algorithm compared to other methods is its flexibility. It could be used to construct codes for a given rate and length with girths of at least six for any sub-matrix configuration or rearrangement. The code size is also easily varied by increasing or decreasing sub-matrix size. Codes obtained using a sequential search criteria show poor performance at low girths (6 and 8) while random searches result in good performing codes. Quasi-cyclic codes could be implemented in a variety of decoder architectures. One of the many options is the choice of processing nodes interconnect. We show how quasi-cyclic codes processing could be scheduled through a multistage network. Although these net-works have more delay than other modes of communication, they offer more flexibility at a reasonable cost. Banyan and Benes networks are suggested as the most suitable networks. Decoding delay is also one of several issues considered in decoder design and implementation. In this thesis, we overlap check and variable node computations to reduce decoding time. Three techniques are discussed, two of which are introduced in this thesis. The techniques are code matrix permutation, matrix space restriction and sub-matrix row-column scheduling. Matrix permutation rearranges the parity-check matrix such that rows and columns that do not have connections in common are separated. This techniques can be applied to any matrix. Its effectiveness largely depends on the structure of the code. We show that its success also depends on the size of row and column weights. Matrix space restriction is another technique that can be applied to any code and has fixed reduction in time or amount of overlap. Its success depends on the amount of restriction and may be traded with performance loss. The third technique already suggested in literature relies on the internal cyclic structure of sub-matrices to achieve overlapping. The technique is limited to LDPC code matrices in which the number of sub-matrices is equal to row and column weights. We show that it can be applied to other codes with a lager number of sub-matrices than code weights. However, in this case maximum overlap is not guaranteed. We calculate the lower bound on the amount of overlapping. Overlapping could be applied to any sub-matrix configuration of quasi-cyclic codes by arbitrarily choosing the starting rows for processing. Overlapping decoding time depends on inter-iteration waiting times. We show that there are upper bounds on waiting times which depend on the code weights. Waiting times could be further reduced by restricting shifts in identity sub-matrices or using smaller sub-matrices. This overlapping technique can reduce the decoding time by up to 50% compared to conventional message and computation scheduling. Techniques of matrix permutation and space restriction results in decoder architectures that are flexible in LDPC code design in terms of code weights and size. This is due to the fact that with these techniques, rows and columns are processed in sequential order to achieve overlapping. However, in the existing technique, all sub-matrices have to be processed in parallel to achieve overlapping. Parallel processing of all code sub-matrices requires the architecture to have the number of processing units at least equal to the number sub-matrices. Processing units and memory space should therefore be distributed among the sub-matrices according to the sub-matrices arrangement. This leads to high complexity or inflexibility in the decoder architecture. We propose a simple, programmable and high throughput decoder architecture based on matrix permutation and space restriction techniques. / Thesis(Ph.D.) -- University of Adelaide, School of Electrical and Electronic Engineering, 2007

LIMA, Carlos Vinicius Gomes Costa. Sobre b-coloração de grafos com cintura pelo menos 6. 2013. 60 f. Dissertação (Mestrado em ciência da computação)- Universidade Federal do Ceará, Fortaleza-CE, 2013. / Submitted by Elineudson Ribeiro (elineudsonr@gmail.com) on 2016-07-11T12:13:18Z No. of bitstreams: 1 2013_dis_cvgclima.pdf: 3781619 bytes, checksum: 164aea3629d83f1d6d8ba3efcf3ec056 (MD5) / Approved for entry into archive by Rocilda Sales (rocilda@ufc.br) on 2016-07-14T15:33:44Z (GMT) No. of bitstreams: 1 2013_dis_cvgclima.pdf: 3781619 bytes, checksum: 164aea3629d83f1d6d8ba3efcf3ec056 (MD5) / Made available in DSpace on 2016-07-14T15:33:44Z (GMT). No. of bitstreams: 1 2013_dis_cvgclima.pdf: 3781619 bytes, checksum: 164aea3629d83f1d6d8ba3efcf3ec056 (MD5) Previous issue date: 2013 / The coloring problem is among the most studied in the Graph Theory due to its great theoretical and practical importance. Since the problem of coloring the vertices of a graph G either with the smallest amount of colors is NP-hard, various coloring heuristics are examined to obtain a proper colouring with a reasonably small number of colors. Given a graph G, the b heuristic of colouring comes down to decrease the amount of colors in a proper colouring c, so that, if all vertices of a color class fail to see any color in your neighborhood, then we can change the color to any color these vertices nonexistent in your neighborhood. Thus, we obtain a coloring c ′ with a color unless c. Irving and Molove defined the b-coloring of a graph G as a coloring where every color class has a vertex that is adjacent the other color classes. These vertices are called b-vertices. Irving and Molove also defined the b-chromatic number as the largest integer k, such that G admits a b-coloring by k colors. They showed that determine the value of the b-chromatic number of any graph is NP-hard, but polynomial for trees. Irving and Molove also defined the m-degree of a graph, which is the largest integer m(G) such that there are m(G) vertices with degree at least m(G) − 1. Irving and Molove showed that the m-degree is an upper limit to the b-chromatic number and showed that it is m(T) or m(T)−1 to every tree T, where its value is m(T) if, and only if, T has a good set. In this dissertation, we analyze the relationship between the girth, which is the size of the smallest cycle, and the b-chromatic number of a graph G. More specifically, we try to find the smallest integer g ∗ such that if the girth of G is at least g ∗ , then the b-chromatic number equals m(G) or m(G)−1. Show that the value of g ∗ is at most 6 could be an important step in demonstrating the famous conjecture of Erd˝os-Faber-Lov´asz, but the best known upper limit to g ∗ is 9. We characterize the graphs whose girth is at least 6 and not have a good set and show how b-color them optimally. Furthermore, we show how b-color, also optimally, graphs whose girth is at least 7 and not have good set. / O problema de coloração está entre os mais estudados dentro da Teoria dos Grafos devido a sua grande importância teorica e prática. Dado que o problema de colorir os vértices de um grafo G qualquer com a menor quantidade de cores é NP-difícil, várias heurísticas de coloração são estudadas a fim de obter uma coloração própria com um número de cores razoavelmente pequeno. Dado um grafo G, a heurística b de coloração se resume a diminuir a quantidade de cores utilizadas em uma coloração própria c, de modo que, se todos os vértices de uma classe de cor deixam de ver alguma cor em sua vizinhança, então podemos modificar a cor desses vértices para qualquer cor inexistente em sua vizinhança. Dessa forma, obtemos uma coloração c′ com uma cor a menos que c. Irving e Molove definiram a b-coloração de um grafo G como uma coloração onde toda classe de cor possui um vértice que é adjacente as demais classes de cor. Esses vértices são chamados b-vértices. Irving e Molove também definiram o número b-cromático como o maior inteiro k tal que G admite uma b-coloração por k cores. Eles mostraram que determinar o número b-cromático de um grafo qualquer é um problema NP-difícil, mas polinomial para árvores. Irving e Molove também definiram o m-grau de um grafo, que é o maior inteiro m(G) tal que existem m(G) vértices com grau pelo menos m(G)−1. Irving e Molove mostraram que o m-grau é um limite superior para número b-cromático e mostraram que o mesmo é igual a m(T) ou a m(T)−1, para toda árvore T, onde o número b-cromático é igual a m(T) se, e somente se, T possui um conjunto bom. Nesta dissertação, verificamos a relação entre a cintura, que é o tamanho do menor ciclo, e o número b-cromático de um grafo G. Mais especificamente, tentamos encontrar o menor inteiro g∗ tal que, se a cintura de G é pelo menos g∗, então o número b-cromático é igual a m(G) ou m(G)−1. Mostrar que o valor de g∗ é no máximo 6 poderia ser um passo importante para demonstrar a famosa Conjectura de Erdós-Faber-Lovasz, mas o melhor limite superior conhecido para g∗ é 9. Caracterizamos os grafos cuja cintura é pelo menos 6 e não possuem um conjunto bom e mostramos como b-colori-los de forma ótima. Além disso, mostramos como bicolorir, também de forma ótima, os grafos cuja cintura é pelo menos 7 e não possuem conjunto bom.

Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / The coloring problem is among the most studied in the Graph Theory due to its great theoretical and practical importance. Since the problem of coloring the vertices of a graph G either with the smallest amount of colors is NP-hard, various coloring heuristics are examined to obtain a proper colouring with a reasonably small number of colors. Given a graph G, the b heuristic of colouring comes down to decrease the amount of colors in a proper colouring c, so that, if all vertices of a color class fail to see any color in your neighborhood, then we can change the color to any color these vertices nonexistent in your neighborhood. Thus, we obtain a coloring c ′ with a color unless c. Irving and Molove defined the b-coloring of a graph G as a coloring where every color class has a vertex that is adjacent the other color classes. These vertices are called b-vertices. Irving and Molove also defined the b-chromatic number as the largest integer k, such that G admits a b-coloring by k colors. They showed that determine the value of the b-chromatic number of any graph is NP-hard, but polynomial for trees. Irving and Molove also defined the m-degree of a graph, which is the largest integer m(G) such that there are m(G) vertices with degree at least m(G) − 1. Irving and Molove showed that the m-degree is an upper limit to the b-chromatic number and showed that it is m(T) or m(T)−1 to every tree T, where its value is m(T) if, and only if, T has a good set. In this dissertation, we analyze the relationship between the girth, which is the size of the smallest cycle, and the b-chromatic number of a graph G. More specifically, we try to find the smallest integer g ∗ such that if the girth of G is at least g ∗ , then the b-chromatic number equals m(G) or m(G)−1. Show that the value of g ∗ is at most 6 could be an important step in demonstrating the famous conjecture of Erd˝os-Faber-LovÂasz, but the best known upper limit to g ∗ is 9. We characterize the graphs whose girth is at least 6 and not have a good set and show how b-color them optimally. Furthermore, we show how b-color, also optimally, graphs whose girth is at least 7 and not have good set. / O problema de coloraÃÃo està entre os mais estudados dentro da Teoria dos Grafos devido a sua grande importÃncia teorica e prÃtica. Dado que o problema de colorir os vÃrtices de um grafo G qualquer com a menor quantidade de cores à NP-difÃcil, vÃrias heurÃsticas de coloraÃÃo sÃo estudadas a fim de obter uma coloraÃÃo prÃpria com um nÃmero de cores razoavelmente pequeno. Dado um grafo G, a heurÃstica b de coloraÃÃo se resume a diminuir a quantidade de cores utilizadas em uma coloraÃÃo prÃpria c, de modo que, se todos os vÃrtices de uma classe de cor deixam de ver alguma cor em sua vizinhanÃa, entÃo podemos modificar a cor desses vÃrtices para qualquer cor inexistente em sua vizinhanÃa. Dessa forma, obtemos uma coloraÃÃo c′ com uma cor a menos que c. Irving e Molove definiram a b-coloraÃÃo de um grafo G como uma coloraÃÃo onde toda classe de cor possui um vÃrtice que à adjacente as demais classes de cor. Esses vÃrtices sÃo chamados b-vÃrtices. Irving e Molove tambÃm definiram o nÃmero b-cromÃtico como o maior inteiro k tal que G admite uma b-coloraÃÃo por k cores. Eles mostraram que determinar o nÃmero b-cromÃtico de um grafo qualquer à um problema NP-difÃcil, mas polinomial para Ãrvores. Irving e Molove tambÃm definiram o m-grau de um grafo, que à o maior inteiro m(G) tal que existem m(G) vÃrtices com grau pelo menos m(G)−1. Irving e Molove mostraram que o m-grau à um limite superior para nÃmero b-cromÃtico e mostraram que o mesmo à igual a m(T) ou a m(T)−1, para toda Ãrvore T, onde o nÃmero b-cromÃtico à igual a m(T) se, e somente se, T possui um conjunto bom. Nesta dissertaÃÃo, verificamos a relaÃÃo entre a cintura, que à o tamanho do menor ciclo, e o nÃmero b-cromÃtico de um grafo G. Mais especificamente, tentamos encontrar o menor inteiro g∗ tal que, se a cintura de G à pelo menos g∗, entÃo o nÃmero b-cromÃtico à igual a m(G) ou m(G)−1. Mostrar que o valor de g∗ à no mÃximo 6 poderia ser um passo importante para demonstrar a famosa Conjectura de ErdÃs-Faber-Lovasz, mas o melhor limite superior conhecido para g∗ à 9. Caracterizamos os grafos cuja cintura à pelo menos 6 e nÃo possuem um conjunto bom e mostramos como b-colori-los de forma Ãtima. AlÃm disso, mostramos como bicolorir, tambÃm de forma Ãtima, os grafos cuja cintura à pelo menos 7 e nÃo possuem conjunto bom.

In this work we study two random procedures in cubic graphs with large girth. The first procedure finds a probability distribution on edge-cuts such that each edge is in a randomly chosen cut with probability at least 0.88672. As corollaries, we derive lower bounds for the size of maximum cut in cubic graphs with large girth and in random cubic graphs, and also an upper bound for the fractional cut covering number in cubic graphs with large girth. The second procedure finds a probability distribution on independent sets such that each vertex is in an independent set with probability at least 0.4352. This implies lower bounds for the size of maximum independent set in cubic graphs with large girth and in random cubic graphs, as well as an upper bound for the fractional chromatic number in cubic graphs with large girth.

As recentes descobertas de petróleo e gás na camada do Pré-sal representam um enorme potencial exploratório no Brasil, entretanto, os desafios tecnológicos para a exploração desses recursos minerais são imensos e, consequentemente, têm motivado o desenvolvimento de estudos voltados a métodos e materiais eficientes para suas produções. Os tubos condutores de petróleo e gás são denominados de elevadores catenários ou do inglês \"risers\", e são elementos que necessariamente são soldados e possuem fundamental importância nessa cadeia produtiva, pois transportam petróleo e gás natural do fundo do mar à plataforma, estando sujeitos a carregamentos dinâmicos (fadiga) durante sua operação. Adicionalmente, um dos problemas centrais à produção de óleo e gás das reservas do Pré-Sal está diretamente associado a meios altamente corrosivos, tais como H2S e CO2. Uma forma mais barata de proteção dos tubos é a aplicação de uma camada de um material metálico resistente à corrosão na parte interna desses tubos (clad). Assim, a união entre esses tubos para formação dos \"risers\" deve ser realizada pelo emprego de soldas circunferenciais de ligas igualmente resistentes à corrosão. Nesse contexto, como os elementos soldados são considerados possuir defeitos do tipo trinca, para a garantia de sua integridade estrutural quando submetidos a carregamentos cíclicos, é necessário o conhecimento das taxas de propagação de trinca por fadiga da solda circunferencial. Assim, neste trabalho, foram realizados ensaios de propagação de trinca por fadiga na região da solda circunferencial de Inconel® 625 realizada em tubo de aço API 5L X65 cladeado, utilizando corpos de prova do tipo SEN(B) (Single Edge Notch Bending) com relações entre espessura e largura (B/W) iguais a 0,5, 1 e 2. O propósito central deste trabalho foi de obter a curva da taxa de propagação de trinca por fadiga (da/dN) versus a variação do fator de intensidade de tensão (ΔK) para o metal de solda por meio de ensaios normatizados, utilizando diferentes técnicas de acompanhamento e medição da trinca. A monitoração de crescimento da trinca foi feita por três técnicas: variação da flexibilidade elástica (VFE), queda de potencial elétrico (QPE) e análise de imagem (Ai). Os resultados mostraram que as diferentes relações B/W utilizadas no estudo não alteraram significantemente as taxas de propagação de trinca por fadiga, respeitado que a propagação aconteceu em condições de escoamento em pequena escala na frente da trinca. Os resultados de propagação de trinca por fadiga permitiram a obtenção das regiões I e II da curva da/dN versus ΔK para o metal de solda. O valor de ΔKlim obtido para o mesmo foi em torno de 11,8 MPa.m1/2 e os valores encontrados das constantes experimentais C e m da equação de Paris-Erdogan foram respectivamente iguais a 1,55 x10-10 [(mm/ciclo)/(MPa.m1/2)m] e 4,15. A propagação de trinca no metal de solda deu-se por deformação plástica, com a formação de estrias de fadiga. / Recent oil and gas discoveries in the Pre-Salt layer represent a huge exploration potential in Brazil, however, the technological challenges for the exploitation of these mineral resources are immense and therefore have motivated the development of studies looking for efficient methods and materials for their productions. The oil and gas pipellines, called risers, are elements that are necessarily welded and have fundamental importance in the production chain, since they transport oil and natural gas from the sea bed to the platforms and are subject to dynamic loads (fatigue) during operation. Additionally, one of the central problems in the production of oil and gas in the Pre-Salt reserves is directly associated with a highly corrosive media, such as H2S and CO2. A cheaper way to protect the pipelines from these medias is applying a protective layer of a corrosion resistant metal on the inner diameter of these pipes, creating a cladded pipe. Thus, a joining process of these pipes to form the risers must be carried out by the use of girth welds with a corrosion resistance material similar to the clad metal. As the welded structures are seen as potential location of \"crack like\" defects, to ensure the structural integrity of such component when subjected to repetitive loading conditions, it is necessary to know the fatigue crack growth rates for the girth weld. Therefore, in this work it was carried out fatigue crack propagation tests in the weld region of an API 5L X65 cladded pipe with Inconel® 625, girth welded using Inconel® 625 electrodes. From the welded region, Single Edge Notch Bending specimens, SEN(B), were removed with different thickness and width ratios (B/W= 0.5, 1, and 2). From the fatigue tests, the crack propagation rates (da/dN) as function of the variation of the stress intensity factor (ΔK), were determined for the weld metal, using different crack size measurement techniques: the elastic compliance (EC), electric potential drop (EPD) and image analysis (IA). The results showed that the different B/W ratios used in study did not modified significantly the fatigue crack growth rates, considering that crack propagation took place under small scale yielding conditions. The results of fatigue crack growth tests allowed to obtain the regions I and II of da/dN x ΔK curves for the weld metal. The ΔKth value obtained for the weld metal was around 11,8 MPa.m1/2 and the found values of the experimental constants C and m of Paris-Erdogan\'s equation were respectively equal to 1,55 x10-10 [(mm/cycle)/( MPa.m1/2)m] and 4.15. The micromechanism of fatigue crack growth took place by plastic deformation, with the formation of fatigue striations.

Hypertension and salt-sensitivity are independent risk factors for cardiovascular disease. Although both conditions are idiopathic, they develop due to a complex interplay between susceptibility genes and environmental factors. Given that the kidney plays an important role in regulating blood pressure, in particular, by maintaining sodium and water balance via pressure-natriuresis, it is not surprising that disturbances in the proper functioning of this intrarenal mechanism have been linked to these conditions. Although direct coupling of changes in renal arterial pressure (RAP) to renal interstitial hydrostatic pressure (RIHP) and consequent sodium excretion is well established, few studies have characterized the moment-to-moment aspects of this process. Thus, the main focus of the research presented herein was to characterize the moment-to-moment RAP-RIHP relationship, and assess the functioning of this intrarenal mechanism in various animal models of genetic and environmentally-induced hypertension and/or salt-sensitivity. In adult normotensive rats, the response time of RIHP to acute changes in RAP was rapid (<2 seconds), and the moment-to-moment RAP-RIHP relationship was linear over a wide range of pressures. Additionally, the functioning of this relationship was not affected by inhibition of the renin-angiotensin system and autonomic nervous system. Further, the acute RAP-RIHP relationship was impaired in hypertension and/or salt-sensitivity. Specifically, animals with a hypertensive phenotype (i.e. young spontaneously hypertensive rats [SHR] and pro-atrial natriuretic peptide gene-disrupted mice [ANP -/-]) displayed a rightward shift in the moment-to-moment pressure-natriuresis curve towards higher RAP. This rightward shift was associated with increased structurally-based vascular resistance properties in the hindlimb of young SHR versus their normotensive controls. Salt-sensitive phenotypes were associated with a blunting of this acute mechanism. Specifically, this blunting was evident in both the ANP -/-, a transgenic model of salt-sensitive hypertension, and in adult perinatal iron deficient (PID) rats, a developmentally programmed model of salt-sensitivity. It appears that a blunting in the RAP-RIHP relationship is influenced by an imbalance of key blood pressure modulating factors (e.g. ANP). Further, visceral obesity was associated with salt-sensitivity in PID rats; however the mechanism(s) are yet to be elucidated. Novel methodologies (MRI, abdominal girth) were developed for non-invasive assessment of visceral obesity to aid future research. / Thesis (Ph.D, Pharmacology & Toxicology) -- Queen's University, 2010-05-12 10:11:21.197