Global ETD Search
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 12 of 12 for “"Diophantine Approximation"”.
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Some Topics in Diophantine Approximation
L'abstract è presente nell'allegato / the abstract is in the attachment
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Diophantine Approximation as Cosmic Censor for AdS Black Holes
The present thesis reveals a novel connection of Diophantine approximation arising from small divisors to general relativity, more precisely, the Strong Cosmic Censorship conjecture. The main results provide theorems which resolve a linear scalar analog of the Strong Cosmic Censorship conjecture in …
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Dynamics on homogeneous spaces and applications to simultaneous diophantine approximation
We give some new results about diophantine simultaneous inequalities involving one quadratic form and one linear generalising the Oppenheim conjecture. In the first part we compute an exact lower asymptotic estimate of the number of integral values taken by such pairs, by using uniform distribution …
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A Contribution to Metric Diophantine Approximation : the Lebesgue and Hausdorff Theories
This thesis is concerned with the theory of Diophantine approximation from the point of view of measure theory. After the prolegomena which conclude with a number of conjectures set to understand better the distribution of rational points on algebraic planar curves, Chapter 1 provides an extension …
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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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Some Metric Theorems on Polynomials
The theory of metric Diophantine approximation can be studied from many di�erent perspectives. The problems studied in this thesis all concern questions on integer polynomials. Simultaneous rational approximation to integer polynomials is studied in the p-adic metric. Next, the nature of the …
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Arithmetic and dynamical systems
… systems and number theory. We look at two diophantine approximation problems in local �fields of positive characteristic, one a generalisation of the Khintchine{Groshev theorem, another a central limit theorem. We also prove a P�olya{Carlson dichotomy result for a large class of adelicly …
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Some Results on the Degeneracy of Entire Curves and Integral Points in the Complements of Divisors
… the important results in Nevanlinna Theory and Diophantine Approximation Theory. Next, a result by the author and Min Ru \cite{LR} is presented. In chapter 3, we extend the Second Main Theorem to the case of holomorphic curves into algebraic varieties intersecting numerically equivalent ample …
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Frequency-domain analysis of memoryless nonlinearities having large-signal, almost periodic excitations
… of the series. Starting with a theorem from Diophantine Approximation, it is proven that the normalized (Hertzian) phases corresponding to a set of M basis frequencies have their fractional parts uniformly distributed in an M-dimensional unit cube. This property of uniform phase distribution …
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Applications of dynamical systems to Farey sequences and continued fractions
… and Zaharescu, and independently Boca, to a Diophantine approximation problem of Erdős, Szüsz, and Turán. The latter two topics of this thesis establish properties of the Farey map F by analyzing the transfer operators of F and the Gauss map G, well known maps of the unit interval relating to …
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Beatty ratios, algorithms related to Sturmian sequences and uniform distribution theory
… sequence. The proofs of these theorems use Diophantine approximation, continued fractions and various number theoretic and combinatorial arguments. The third portion of this thesis deals with a topic related to a theorem that begun as a conjecture of Steinhaus. This well known Three Gap …
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Lattice Extensions and Zeros of Multilinear Polynomials
<p>We treat several problems related to the existence of lattice extensions preserving certain geometric properties and small-height zeros of various multilinear polynomials. An extension of a Euclidean lattice $L_1$ is a lattice $L_2$ of higher rank containing $L_1$ so that the intersection of …