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Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 184 for “"Lemma"”.
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Distance Sets and Gap Lemma
Many problems in geometric measure theory are centered around finding conditions and structures on a set to guarantee that its distance set must be large. Two notions of structure that are of importance in this work are Hausdorff dimension and thickness. Recent progress has been made on …
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An Overview of the Constructive Local Lemma
<p>The Local Lemma has been a powerful tool in probabilistic combinatorics. Recent advances by Moser and Tardos have provided an algorithmic variant of the Local Lemma. We provide an overview of the analysis of their algorithm, and provide an implementation of the algorithm to a hypergraph coloring …
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A topological generalization of Schwarz' lemma
The classical lemma of Schwarz states that if f(a) = zg(z) where g(z) is holomorphic inside the unit circle, and if |f(z)| < 1 when |s| < 1, then |f(z)| < |z| when |z| < 2. The proof for this is based on the fast that if f(s) is holomorphic in a region, its absolute value has no relative maxima in …
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Selected Applications of the Nash-Williams Lemma
… formal statement and proof of the Nash-Williams Lemma. Reconstructibility conditions concerned with comparing the size and order of general graphs will then be established with an in depth look at conditions dealing with the minimum, average and maximum degrees of bidegreed, tridegreed, and …
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Deterministic algorithms for the Lovász Local Lemma
The Lovász Local Lemma [6] (LLL) is a powerful result in probability theory that states that the probability that none of a set of bad events happens is nonzero if the probability of each event is small compared to the number of events that depend on it. It is often used in combination with the …
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Extensions to a Lemma of Bernik with Applications in the area of Metric Diophantine Approximation
This thesis is concerned with two extensions to a result of V. I Bernik [23] from 1983 which provides a quantitative description of the fact that two relatively prime polynomials in Z[x] cannot both have very small absolute values (in terms of their degrees and heights) in an interval unless that …
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Symmetric formulation of the Kalman-Yakubovich-Popov lemma and its application to distributed control of positive systems
Restriction data tranferred 2014-07-01T11:36:06-05:00 Original Data Group with Access Administrator Release Date: 2015-02-03 13:47:48 UTC Reason: Author requested closed access (OA after 2yrs) in Vireo ETD system
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Regularity and removal lemmas and their applications
… one of its prevalent applications, the removal lemma. First, we prove a new lower bound on the number of parts required in a version of Szemerédi's regularity lemma, determining the order of the tower height in that version up to a constant factor. This addresses a question of Gowers. Next, we …
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Explicit formulas for weighted orbital integrals for the inhomogeneous and semi-Lie arithmetic fundamental lemmas conjectured for the full spherical Hecke algebra
As an analog to the Jacquet-Rallis fundamental lemma that appears in the relative trace formula approach to the Gan-Gross-Prasad conjectures, the arithmetic fundamental lemma was proposed by Wei Zhang and used in an approach to the arithmetic Gan-Gross-Prasad conjectures. The Jacquet-Rallis …
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Delta-System Methods in Contemporary Graph Theory
… is one in graph representations. We develop a lemma on traces of hypergraphs, extending results of Balogh and Bollobas. We then use this lemma, along with probabilistic methods, to show that for every positive integer k, almost every graph has no k-minimum-difference-representation. This …
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On the Constructive Content of Proofs
… is infinitary combinatorics. Higman's Lemma, having an elegant non-constructive proof due to Nash-Williams, constitutes an interesting case for the problem of discovering the constructive content behind a classical proof. We give two distinct solutions to this problem. First, we present …
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Linear Forms in Logarithms and Fibonacci Numbers
… D(64)-Diophantine triples. A generalization of Lemma 1 of [1] was also found, a lemma on Diophantine triples and Pellian equations which is key in establishing the main result in [2]. This paper includes this result and its proof, which involves a correction of the proof of Lemma 1 of [1]. This …
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A Critical Edition of the Hexaplaric Fragments of Job 22-42
… provides the critical text. The Hebrew and Greek lemmas are listed first, followed by the hexaplaric attribution and lemma. All variants to the attribution and lemma are listed in the appartuses underneath along with editorial notes. Chapter 4 contains the readings that are of dubious significance …
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Utilization of Partitions in Graph Structures
… and conjectures which require the Regularity lemma require unique methods to improve the bounds on known results. In this work the upper bounds for Gallai-Ramsey using $k$ colors is lowered to at most $k(n-1) +3n$ for even cycles and $(2^{k+3}-3)n \log n$ for odd cycles. Also, with the ideas …
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Twisted Gan-Gross-Prasad conjecture for unramified quadratic extensions
… particular, we reduce the required fundamental lemma to the Jacquet-Rallis fundamental lemma.
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Razonamiento mecanizado en álgebra homológica
… of Homological Algebra, known as "Perturbation Lemma". This lemma is intensively used in the software system "Kenzo", devoted to symbolic computation in Homological Algebra. To this end, we use the proof assistant "Isabelle". Our main motivations are to increase the knowledge in the algorithmic …
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Quadratic Reciprocity: Proofs and Applications
… We begin with a proof that depends on Gauss's lemma and Eisenstein's lemma. We then describe another proof due to Eisentein using the $n$th roots of unity. Then we provide a modern proof published in 1991 by Rousseau. In the second part of the thesis, we present two applications of quadratic …
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Exhaustivity, continuity, and strong additivity in topological Riesz spaces.
… the Diestel-Faires Theorem and the Meyer-Nieberg Lemma in this setting. Also, embedding properties of Banach lattices are linked to the notion of strong additivity. The Meyer-Nieberg Lemma is extended to the setting of topological Riesz spaces and uniform absolute continuity and uniformly …
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On the Cohomology of the Complement of a Toral Arrangement
… to state and prove extension of Brieskorn's Lemma theorem.
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