Teste de propriedades em grafos consiste no estudo de algoritmos aleatórios sublineares que determinam se um grafo $G$ de entrada com $n$ vértices satisfaz uma dada propriedade ou se é necessário adicionar ou remover mais do que $\\epsilon{n \\choose 2}$ arestas para fazer $G$ satisfazê-la, para algum parâmetro $\\epsilon$ de erro fixo. Uma propriedade de grafos $P$ é dita testável se, para todo $\\epsilon > 0$, existe um tal algoritmo para $P$ cujo tempo de execução é independente de $n$. Um dos resultados de maior importância nesta área, provado por Alon e Shapira, afirma que toda propriedade hereditária de grafos é testável. Neste trabalho, apresentamos resultados análogos para torneios --- grafos completos nos quais são dadas orientações para cada aresta. / Graph property testing is the study of randomized sublinear algorithms which decide if an input graph $G$ with $n$ vertices satisfies a given property or if it is necessary to add or remove more than $\\epsilon{n \\choose 2}$ edges to make $G$ satisfy it, for some fixed error parameter $\\epsilon$ . A graph property $P$ is called testable if, for every $\\epsilon > 0$, there is such an algorithm for $P$ whose run time is independent of $n$. One of the most important results in this area is due to Alon and Shapira, who showed that every hereditary graph property is testable. In this work, we show analogous results for tournaments --- complete graphs in which every edge is given an orientation.

Submitted by Daniella Santos (daniella.santos@ufma.br) on 2017-06-22T12:57:55Z No. of bitstreams: 1 Diego Araújo.pdf: 749439 bytes, checksum: e6b630a6b28df216e5e6fc70dbeead61 (MD5) / Made available in DSpace on 2017-06-22T12:57:55Z (GMT). No. of bitstreams: 1 Diego Araújo.pdf: 749439 bytes, checksum: e6b630a6b28df216e5e6fc70dbeead61 (MD5) Previous issue date: 2017-05-02 / The main goal of this work is to discuss some topics about hyperbolic dynamical systems. We collect results and definitions that are dispersed, or even in works of generalized context. Thus, we propose a tour that begins with the definition of orbit, passes through classical results like Hartman-Grobman Theorem and shadowing lemma, and ends with the Omega stability theorem. / O objetivo deste trabalho é dissertar sobre alguns tópicos dos sistemas dinâmicos hiberbólicos. Nós coletamos resultados e definicões que em sua maioria encontram-se dispersos, ou ainda, em obras de contexto generalizado. Assim, nos propomos a fazer uma caminhada que começa com a definicão de órbita, passa por resultados clássicos como o Teorema de Hartman-Grobman e o Lema de Sombreamento, e termina com o teorema da Omega estabilidade.

O objetivo deste trabalho e computar, em alguns casos espec cos, os geradores do radical de um ideal no anel de polinômios K[x1, ..., xn]. Para isso, utilizamos a teoria das bases de Groebner. Primeiramente, usamos o Lema de Seidenberg para computar os geradores do radical de um ideal zero-dimensional onde K e um corpo perfeito e depois utilizamos os resultados de R. Matsumoto para um corpo K de caracter stica positiva e perfeito. / The goal of this work is to compute in some speci c cases the generators of the radical ideal in a polynomial ring K[x1, ..., xn]. For this, we use the theory of Groebner bases. First, we use Lemma Seidenberg to compute the generators of the radical of an zero-dimensional ideal, where K is a perfect eld and then we used the results of R. Matsumoto for a eld K of positive characteristic and perfect.

Submitted by Marcos Samuel (msamjunior@gmail.com) on 2017-06-26T11:00:39Z No. of bitstreams: 1 DissertacaoJulio.pdf: 1733332 bytes, checksum: 4720e2f2b5a50f27f079ef7fde8586af (MD5) / Approved for entry into archive by Vanessa Reis (vanessa.jamile@ufba.br) on 2017-06-29T12:59:40Z (GMT) No. of bitstreams: 1 DissertacaoJulio.pdf: 1733332 bytes, checksum: 4720e2f2b5a50f27f079ef7fde8586af (MD5) / Made available in DSpace on 2017-06-29T12:59:40Z (GMT). No. of bitstreams: 1 DissertacaoJulio.pdf: 1733332 bytes, checksum: 4720e2f2b5a50f27f079ef7fde8586af (MD5) / A principal proposta deste trabalho é usar o Lema de Sperner como uma ferramenta matemática para realizar divisões de objetos formado por partes que apresentam particularidades em que todos os envolvidos se sintam satisfeitos. Apesar deste lema ser usado também na topologia para provar o teorema do ponto fixo, evitaremos usar os conceitos topológicos e limitaremos o número de participantes nas divisões a três para não ultrapassarmos o nível compreensível ao Ensino Médio. Apresentaremos alguns jogos relacionados com o lema de Sperner mostrando através de tal lema que nesses jogos não existe a possibilidade de empate. Por fim, mostraremos o Teorema do ponto fixo de Brouwer, em dimensão dois, usando o Lema de Sperner para um triângulo.

O objetivo deste trabalho e computar, em alguns casos espec cos, os geradores do radical de um ideal no anel de polinômios K[x1, ..., xn]. Para isso, utilizamos a teoria das bases de Groebner. Primeiramente, usamos o Lema de Seidenberg para computar os geradores do radical de um ideal zero-dimensional onde K e um corpo perfeito e depois utilizamos os resultados de R. Matsumoto para um corpo K de caracter stica positiva e perfeito. / The goal of this work is to compute in some speci c cases the generators of the radical ideal in a polynomial ring K[x1, ..., xn]. For this, we use the theory of Groebner bases. First, we use Lemma Seidenberg to compute the generators of the radical of an zero-dimensional ideal, where K is a perfect eld and then we used the results of R. Matsumoto for a eld K of positive characteristic and perfect.

En el presente artículo de divulgación se expone un gran aporte que Gerard Debreu hizo en el tema de representación de relaciones en (4). En realidad, su aporte yace dentro de la demostración del Lema 1 de (4), donde reconstruye la imagen de una funión con valores en R para conseguir continuidad, este hecho es lo que posteriormente se hace referencia como el Lema Gap de Debreu. Aquí exponemos las construcciones de Debreu para conseguir una función continua que represente a una relación completamente ordenada definida en un espacio topológico.

Master of Agribusiness / Department of Agricultural Economics / Bill B. Golden / While Kansas, and specifically western Kansas, are known by many to be the backbone of agriculture in our nation, much of that productivity has been built on the heels of the invention and efficiency of irrigation technology. Unfortunately, recharge and replenishment of the High Plains - Ogallala Aquifer has not kept pace with the demands of agricultural production, and current indications state that without the implementation of conservation or management practices that the aquifer in Kansas could be depleted by 2060 (Steward, et al. 2013). The producers of Kansas are committed to long-term solutions to preserve their way of life, espouse their commitment to natural resources and the environment, and ensure the viability of their operations for years to come. This study analyzed the economic impact of a proposed Local Enhanced Management Area (LEMA) for Groundwater Management District ¬(GMD) #4. While there currently is a LEMA in a portion of GMD #4 known as the Sheridan 6 LEMA, the board of GMD #4 has initiated the process to institute a district-wide LEMA that would affect a large portion of the 10-county area of the groundwater management district (Cheyenne, Rawlins, Decatur, Sherman, Thomas, Sheridan, Graham, Wallace, Logan, and Gove Counties). To complete the analysis for the proposed policy change, multiple scenarios were derived using the IMPLAN software. The first model serves as the baseline scenario and provides status quo information on the current irrigated cropping economics of GMD #4. The second scenario assumes that a district-wide LEMA would require a 25% reduction in groundwater use, compared to current irrigation practices. To achieve this reduction in groundwater use, irrigated acreage was reduced by 25% and transitioned to dryland production. For the third and final scenario, an optimal irrigated crop-mix ratio is determined based on the current shift in production as reported by the producers in the Sheridan 6 LEMA. While this scenario does not reduce irrigated acres, it shows the economic gains that can be captured by using less water-intensive crops as part of the crop-mix ratio. The reduction in irrigation is also imbedded in that the acreage in which production is shifted away from is more water intensive towards acreage that is less water-intensive. Due to a reduction in groundwater use for irrigation, the study determined that there is a negative economic impact in relation to employment and total output in the GMD #4 area. There are 173 less individuals employed from the 25% reduction in groundwater use. Additionally, direct output is reduced by $44.6 million and total output is reduced by $60.0 million. This equates to a $194.49 reduction per acre on a per-acre basis. The study further showed that the economic impact could be lessened by the use of a crop-mix shift as evidenced in the current Sheridan 6 LEMA. The assessment of a crop-mix shift decreased the loss of direct output by $12.0 million to $265.0 million and total output by $16.5 million to $357.1 million. On a per-acre basis, this is a reduction of $140.97, or mitigation of $53.52 in loss per acre due to the use of an optimal crop-mix shift. While agricultural production is highly dependent on many factors, it can be universally agreed that the landscape of agriculture would be different if water was not an available resource. It is the hope that this research will provide a starting point for the producers of GMD #4 to have a conversation about the economic costs associated with the implementation of a LEMA, as well as discuss other options and opportunities to make educated, well-informed decisions that are impactful both now and for generations to come.

O objetivo deste trabalho e computar, em alguns casos espec cos, os geradores do radical de um ideal no anel de polinômios K[x1, ..., xn]. Para isso, utilizamos a teoria das bases de Groebner. Primeiramente, usamos o Lema de Seidenberg para computar os geradores do radical de um ideal zero-dimensional onde K e um corpo perfeito e depois utilizamos os resultados de R. Matsumoto para um corpo K de caracter stica positiva e perfeito. / The goal of this work is to compute in some speci c cases the generators of the radical ideal in a polynomial ring K[x1, ..., xn]. For this, we use the theory of Groebner bases. First, we use Lemma Seidenberg to compute the generators of the radical of an zero-dimensional ideal, where K is a perfect eld and then we used the results of R. Matsumoto for a eld K of positive characteristic and perfect.

Teste de propriedades em grafos consiste no estudo de algoritmos aleatórios sublineares que determinam se um grafo $G$ de entrada com $n$ vértices satisfaz uma dada propriedade ou se é necessário adicionar ou remover mais do que $\\epsilon{n \\choose 2}$ arestas para fazer $G$ satisfazê-la, para algum parâmetro $\\epsilon$ de erro fixo. Uma propriedade de grafos $P$ é dita testável se, para todo $\\epsilon > 0$, existe um tal algoritmo para $P$ cujo tempo de execução é independente de $n$. Um dos resultados de maior importância nesta área, provado por Alon e Shapira, afirma que toda propriedade hereditária de grafos é testável. Neste trabalho, apresentamos resultados análogos para torneios --- grafos completos nos quais são dadas orientações para cada aresta. / Graph property testing is the study of randomized sublinear algorithms which decide if an input graph $G$ with $n$ vertices satisfies a given property or if it is necessary to add or remove more than $\\epsilon{n \\choose 2}$ edges to make $G$ satisfy it, for some fixed error parameter $\\epsilon$ . A graph property $P$ is called testable if, for every $\\epsilon > 0$, there is such an algorithm for $P$ whose run time is independent of $n$. One of the most important results in this area is due to Alon and Shapira, who showed that every hereditary graph property is testable. In this work, we show analogous results for tournaments --- complete graphs in which every edge is given an orientation.

Este trabalho aborda principalmente dois tópicos em Análise Funcional. No primeiro tópico, estudamos zeros de polinômios em espaços de Banach reais. Apresentamos resultados devidos a J. Ferrer, estabelecendo que todo polinômio fracamente contínuo sobre os subconjuntos limitados de um espaço de Banach, de dual não separável na topologia fraca estrela, admite um subespaço linear fechado de dual não separável na topologia fraca estrela, no qual o polinômio se anula. No segundo tópico, exibimos a versão multilinear do Lema de Phelps devido a R. Aron, A. Cardwell., D. García e I. Zalzuendo. / We study two topics in Functional Analysis. In the first topic, we study zeros of polynomials on real Banach spaces. We present results due to J. Ferrer, stating that every polynomial weakly continuous on bounded subsets of a Banach space, whose dual is not separable in the weak-star topology, admits a closed linear subspace whose dual is not separable in the weak- star topology either, where the polynomial vanishes. In the second topic, we show a multilinear version for the Phelps\' Lemma by R. Aron, A. Cardwell., D. García and I. Zalzuendo.