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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
21

Combinatorial Considerations on Two Models from Statistical Mechanics

Thapper, Johan January 2007 (has links)
Interactions between combinatorics and statistical mechanics have provided many fruitful insights in both fields. A compelling example is Kuperberg’s solution to the alternating sign matrix conjecture, and its following generalisations. In this thesis we investigate two models from statistical mechanics which have received attention in recent years. The first is the fully packed loop model. A conjecture from 2001 by Razumov and Stroganov opened the field for a large ongoing investigation of the O(1) loop model and its connections to a refinement of the fully packed loop model. We apply a combinatorial bijection originally found by de Gier to an older conjecture made by Propp. The second model is the hard particle model. Recent discoveries by Fendley et al. and results by Jonsson suggests that the hard square model with cylindrical boundary conditions possess some beautiful combinatorial properties. We apply both topological and purely combinatorial methods to related independence complexes to try and gain a better understanding of this model.
22

Combinatorial Considerations on Two Models from Statistical Mechanics

Thapper, Johan January 2007 (has links)
<p>Interactions between combinatorics and statistical mechanics have provided many fruitful insights in both fields. A compelling example is Kuperberg’s solution to the alternating sign matrix conjecture, and its following generalisations. In this thesis we investigate two models from statistical mechanics which have received attention in recent years.</p><p>The first is the fully packed loop model. A conjecture from 2001 by Razumov and Stroganov opened the field for a large ongoing investigation of the O(1) loop model and its connections to a refinement of the fully packed loop model. We apply a combinatorial bijection originally found by de Gier to an older conjecture made by Propp.</p><p>The second model is the hard particle model. Recent discoveries by Fendley et al. and results by Jonsson suggests that the hard square model with cylindrical boundary conditions possess some beautiful combinatorial properties. We apply both topological and purely combinatorial methods to related independence complexes to try and gain a better understanding of this model.</p>
23

Existência e multiplicidade de solução para uma classe de equações elípticas via teoria de Morse. / Existence and multiplicity of solution for a class of elliptic equations via Morse theory.

PEREIRA, Denilson da Silva. 25 July 2018 (has links)
Submitted by Johnny Rodrigues (johnnyrodrigues@ufcg.edu.br) on 2018-07-25T17:05:28Z No. of bitstreams: 1 DENILSON DA SILVA PEREIRA - DISSERTAÇÃO PPGMAT 2010..pdf: 630527 bytes, checksum: 8a6ec5b5fb5e2a462945183d2180a573 (MD5) / Made available in DSpace on 2018-07-25T17:05:28Z (GMT). No. of bitstreams: 1 DENILSON DA SILVA PEREIRA - DISSERTAÇÃO PPGMAT 2010..pdf: 630527 bytes, checksum: 8a6ec5b5fb5e2a462945183d2180a573 (MD5) Previous issue date: 2010-12 / Neste trabalho estudamos a existência e multiplicidade de soluções para uma certa classe de problemas elípticos. Utilizaremos métodos variacionais juntamente com a teoria de Morse em dimensão infinita. / In this work, we study the existence and multiplicity of solution for a large class of Elliptic problems. The main tools used are variational methods together with the infinite dimensional Morse Theory.
24

Matrizes de conexão via o complexo de Morse-Witten / Connection matrices via the Morse-Witten

Lima, Dahisy Valadão de Souza, 1986- 08 May 2010 (has links)
Orientador: Ketty Abaroa de Rezende / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-16T15:34:50Z (GMT). No. of bitstreams: 1 Lima_DahisyValadaodeSouza_M.pdf: 1595993 bytes, checksum: 49a95ad790c477c7d049695a123d9acd (MD5) Previous issue date: 2010 / Resumo: Dada uma variedade suave e fechada M, o complexo de Morse-Witten associado a uma função de Morse f : M ? R e a uma métrica Riemanniana g em M consiste de grupos de cadeia gerados pelos pontos críticos de f e um operador bordo que conta linhas de fluxos isoladas do fluxo gradiente negativo. A homologia do complexo de Morse-Witten é isomorfa à homologia singular de M. Dado um conjunto invariante isolado S, uma matriz de conexão para uma decomposição de Morse de S é uma matriz de homomorfismos entre os índices homológicos de Conley dos conjuntos de Morse. A matriz de conexão é capaz de prover informações dinâmicas sobre um fluxo. De fato, esta matriz pode detectar a existência de órbitas conectantes entre os conjuntos de Morse de S. O complexo de Morse-Witten está relacionado à teoria de matrizes de conexão. Mais precisamente, o operador bordo do complexo de Morse-Witten é um caso especial de matriz de conexão / Abstract: Given a smooth closed manifold M, the Morse-Witten complex associated to a Morse function f : M ? R and a Riemannian metric g on M consists of chain groups generated by the critical points of f and a boundary operator counting isolated flow lines of the negative gradient flow. The homology of the Morse-Witten complex is isomorphic to the singular homology of M. Give a isolated invariant set S, a connection matrix for a Morse decomposition of S is a matrix of homomorphism between the Conley homology indices of Morse sets. The connection matrix is capable of providing dynamical information of a flow. In fact, this matrix can detect the existence of connecting orbits among Morse sets of S: The Morse-Witten complex is related to connection matrices theory. More precisely, the boundary operator of the Morse-Witten complex is a special case of connection matrix / Mestrado / Matematica / Mestre em Matemática
25

Multiplicidade de soluções para sistemas gradientes semilineares ressonantes / Multiplicity of solutions for semilinear resonance gradient systems

Silva, Edcarlos Domingos da 05 November 2009 (has links)
Orientadores: Djairo Guedes de Figueiredo, Francisco Odair Vieira de Paiva / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-13T06:21:00Z (GMT). No. of bitstreams: 1 Silva_EdcarlosDomingosda_D.pdf: 993704 bytes, checksum: d68d4e58a916f7d2428f76207a8cb4da (MD5) Previous issue date: 2009 / Resumo: Nesta tese lidamos com três classes de sistemas gradientes ressonantes. A primeira classe é um sistema com ressonância do tipo Landesman-Lazer. A segunda classe é um sistema fortemente ressonante enquanto a terceira classe é um sistema com ressonância no infinito e na origem. Analisamos as questões de existência e multiplicidade de soluções em cada uma das classes mencionadas. Para obtermos os nossos principais resultados aplicamos alguns métodos variacionais, tais como, teoremas Min-Max e minimização. Além disso, usamos a Teoria de Morse para distinguirmos soluções dados por métodos variacionais distintos. / Abstract: In this thesis we deal with three classes of gradient elliptic systems with resonance. The first class is a resonant system of Landesman-Lazer type. The second class is a system of strong resonance type while the third class is a system with resonance at infinity and at origin. We are concerned about the questions of existence and multiplicity of solutions in each of the classes mentioned. To obtain our main results we apply variational methods, such as, Min-max theorems and minimization. Moreover, we use Morse Theory to distinguish the solutions given by different variational methods. / Doutorado / Doutor em Matemática
26

A dinamica por tras da sequencia espectral / The dynamic behind the spectral sequence

Silveira, Mariana Rodrigues da 30 April 2008 (has links)
Orientador: Ketty Abaroa de Rezende / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-10T21:02:39Z (GMT). No. of bitstreams: 1 Silveira_MarianaRodriguesda_D.pdf: 1531895 bytes, checksum: 3c73a8eb791483b1f0216d6f2627969b (MD5) Previous issue date: 2008 / Resumo: Neste trabalho, apresentamos um algoritmo para um complexo de cadeias C e sua diferencial dada por uma matriz de conexão _ que determina uma seqüência espectral associada (Er, dr). Mais especificamente, um sistema gerador de Er em termos da base original de C é obtido bem como a identificação de todas as diferenciais dr p : Er p ! Er p-r. Explorando a implicação dinâmica da diferencial não nula, mostramos a existência de um caminho unindo a singularidade que gera E0 p e a singularidade que gera E0 p-r no caso em que a conexão direta pelo fluxo não existe. Este caminho é composto pela justaposição de órbitas do fluxo e do fluxo reverso e prova ser importante em algumas aplicações / Abstract: In this work, we present an algorithm for a chain complex C and its di_erential given by a connection matrix _ which determines an associated spectral sequence (Er, dr). More specifically, a system spanning Er in terms of the original basis of C is obtained as well as the identi_cation of all di_erentials dr p : Er p ! Er p-r. In exploring the dynamical implication of a nonzero di_erential, we prove the existence of a path joining the singularities generating E0 p and E0 p-r in the case that a direct connection by a _ow line does not exist. This path is made up of juxtaposed orbits of the _ow and of the reverse _ow and which proves to be importantin some applications / Doutorado / Geometria e Topologia/Sistemas Dinamicos / Doutor em Matemática
27

Discrete Morse complex of images = algorithms, modeling and applications = Complexo discreto de Morse para imagens: algoritmos, modelagem e aplicações / Complexo discreto de Morse para imagens : algoritmos, modelagem e aplicações

Silva, Ricardo Dutra da, 1982- 11 May 2013 (has links)
Orientador: Hélio Pedrini / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Computação / Made available in DSpace on 2018-08-24T00:14:20Z (GMT). No. of bitstreams: 1 Silva_RicardoDutrada_D.pdf: 13549105 bytes, checksum: 3d49e5116a70a72601ba4cc3b3c85762 (MD5) Previous issue date: 2013 / Resumo: A Teoria de Morse é importante para o estudo da topologia em funções escalares como elevação de terrenos e dados provenientes de simulações físicas, a qual relaciona a topologia de uma função com seus pontos críticos. A teoria contínua foi adaptada para dados discretos através de construções como os complexos de Morse-Smale e o complexo discreto de Morse. Complexos de Morse têm sido aplicados em processamento de imagens, no entanto, ainda existem desafios envolvendo algoritmos e considerações práticas para a computação e modelagem dos complexos para imagens. Complexos de Morse podem ser usados como um meio de definir a conexão entre pontos de interesse em imagens. Normalmente, pontos de interesse são considerados como elementos independentes descritos por informação local. Tal abordagem apresenta limitações uma vez que informação local pode não ser suficiente para descrever certas regiões da imagem. Pontos de mínimo e máximo são comumente utilizados como pontos de interesse em imagens, os quais podem ser obtidos a partir dos complexos de Morse, bem como sua conectividade no espaço de imagem. Esta tese apresenta uma abordagem dirigida por algoritmos e estruturas de dados para computar o complexo de Morse discreto em imagens bidimensionais. A construção é ótima e permite fácil manipulação do complexo. Resultados teóricos e experimentais são apresentados para mostrar que o método é eficaz. Experimentos realizados incluem a computação de homologia persistente e hierarquias de complexos sobre dados de elevação de terrenos. Outra contribuição é a proposição de um operador topológico, chamado Contexto Local de Morse, computado sobre complexos de Morse, para extrair vizinhanças de pontos de interesse para explorar a informação estrutural de imagens. O contexto local de Morse é usado no desenvolvimento de um algoritmo que auxilia a redução do número de casamentos incorretos entre pontos de interesse e na obtenção de uma medida de confiança para tais correspondências. A abordagem proposta é testada em pares de imagens sintéticas e de imagens subaquáticas, para as quais métodos existentes podem obter muitas correspondências incorretas / Abstract: The Morse theory is important for studying the topology of scalar functions such as elevation of terrains and data from physical simulations, which relates the topology of a function to critical points. The smooth theory has been adapted to discrete data through constructions such as the Morse-Smale complexes and the discrete Morse complex. Morse complexes have been applied to image processing, however, there are still challenges involving algorithms and practical considerations for computation and modeling of the complexes. Morse complexes can be used as means of defining the connectedness of interest points in images. Usually, interest points are considered as independent elements described by local information. Such an approach has its limitations since local information may not suffice for describing certain image regions. Minimum and maximum points are widely used as interest points in images, which can be obtained from Morse complexes, as well as their connectivity in the image space. This thesis presents an algorithmic and data structure driven approach to computing the discrete Morse complex of 2-dimensional images. The construction is optimal and allows easy manipulation of the complex. Theoretical and applied results are presented to show the effectiveness of the method. Applied experiments include the computation of persistent homology and hierarchies of complexes over elevation terrain data. Another contribution is the proposition of a topological operator, called Local Morse Context (LMC), computed over Morse complexes, for extracting neighborhoods of interest points to explore the structural information in images. The LMC is used in the development of a matching algorithm, which helps reducing the number of incorrect matches between images and obtaining a confidence measure of whether a correspondence is correct or incorrect. The approach is tested in synthetic and challenging underwater stereo pairs of images, for which available methods may obtain many incorrect correspondences / Doutorado / Ciência da Computação / Doutor em Ciência da Computação
28

Existencia e multiplicidade de soluções para a Equação de Schrodinger não-linear em Rn / Existence and multiplicity of solutions for the non-linear Schrodinger Equation in Rn

Malavazi, Mazílio Coronel, 1983- 16 February 2007 (has links)
Orientador: Francisco Odair Vieira de Paiva, Aloisio Freiria Neves / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-08T02:49:07Z (GMT). No. of bitstreams: 1 Malavazi_MazilioCoronel_M.pdf: 786706 bytes, checksum: 9e4d9aae3bd0fdd46d7adf64ce8958ef (MD5) Previous issue date: 2007 / Resumo: Nesta dissertação obtemos resultados de multiplicidade de soluções fracas não triviais para o problema -Du + V (x)u = f (x; u); x 2 RN; onde V é contínua, f é C1, com f (x; 0) = 0 e f é assintoticamente linear. Utilizamos métodos variacionais e a teoria de grupos críticos, para obtermos e distinguirmos as soluções. Apresentamos também resultados de existência de solução não trivial para o problema -Du + V (x)u = f (u); x 2 RN; onde V e f são funções contínuas. Utilizamos as técnicas de concentração de compacidade e de aproximação do domínio por subconjuntos limitados, para obtermos a solução / Abstract: In this dissertation we get resulted of multiplicity of not trivial weak solutions for the problem -Du + V (x)u = f (x; u); x 2 RN; where V is continuous, f is C1, with f (x; 0) = 0 and f is asymptotically linear. We use variationals methods and the theory of critical groups, to get and to distinguish the solutions. We also present results of existence of not trivial solution for the problem -Du + V (x)u = f (u); x 2 RN; where V and f are continuous functions. We use the techniques of concentration of compactness and approximation of the domain for bounded subsets, to get the solution / Mestrado / Mestre em Matemática
29

On The Goresky-Hingston Product

Maiti, Arun 25 January 2017 (has links)
In [GH09] M. Goresky and N. Hingston described and investigated various properties of a product on the cohomology of the free loop space of a closed, oriented manifold M relative to the constant loops. In this thesis we will give Morse and Floer theoretic descriptions of the product. There is a theorem due to J. Jones in [JJ87] which describes an isomorphism between cohomology of the free loop space and Hochschild homology of the singular cochain algebra of M with rational coefficients. We will use the theorem of J. Jones to find an algebraic model for the Goresky-Hingston product. We then use the algebraic model to explore further properties and applications of the Goresky Hingston product. In particular we use it to compute the ring structure for the n-spheres.
30

ANALYTIC AND TOPOLOGICAL COMBINATORICS OF PARTITION POSETS AND PERMUTATIONS

Jung, JiYoon 01 January 2012 (has links)
In this dissertation we first study partition posets and their topology. For each composition c we show that the order complex of the poset of pointed set partitions is a wedge of spheres of the same dimension with the multiplicity given by the number of permutations with descent composition c. Furthermore, the action of the symmetric group on the top homology is isomorphic to the Specht module of a border strip associated to the composition. We also study the filter of pointed set partitions generated by knapsack integer partitions. In the second half of this dissertation we study descent avoidance in permutations. We extend the notion of consecutive pattern avoidance to considering sums over all permutations where each term is a product of weights depending on each consecutive pattern of a fixed length. We study the problem of finding the asymptotics of these sums. Our technique is to extend the spectral method of Ehrenborg, Kitaev and Perry. When the weight depends on the descent pattern, we show how to find the equation determining the spectrum. We give two length 4 applications, and a weighted pattern of length 3 where the associated operator only has one non-zero eigenvalue. Using generating functions we show that the error term in the asymptotic expression is the smallest possible.

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