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Now showing items 21-30 of 66

#### Pick Interpolation and the Distance Formula

(University of Waterloo, 2012-05-09)

The classical interpolation theorem for the open complex unit disk, due to Nevanlinna and Pick in the early 20th century, gives an elegant criterion for the solvability of the problem as an eigenvalue problem. In the 1960s, ...

#### Zigzags of Finite, Bounded Posets and Monotone Near-Unanimity Functions and Jónsson Operations

(University of Waterloo, 2009-09-25)

We define the notion of monotone operations admitted by partially ordered sets,
specifically monotone near-unanimity functions and Jónsson operations. We then
prove a result of McKenzie's in [8] which states that if a ...

#### Contributions to the model theory of partial differential fields

(University of Waterloo, 2013-08-28)

In this thesis three topics on the model theory of partial differential fields are considered: the generalized Galois theory for partial differential fields, geometric axioms for the theory of partial differentially closed ...

#### Algebraic characterization of multivariable dynamics

(University of Waterloo, 2009-03-26)

Let X be a locally compact Hausdorﬀ space along with n proper continuous maps σ = (σ1 , · · · , σn ). Then the pair (X, σ) is called a dynamical system. To each system one can associate a universal operator algebra called ...

#### Degree Spectra of Unary relations on ω and ζ

(University of Waterloo, 2009-08-13)

Let X be a unary relation on the domain of (ω,<). The degree spectrum of X on (ω,<) is the set of Turing degrees of the image of X in all computable presentations of (ω,<). Many results are known about the types of degree ...

#### Use-Bounded Strong Reducibilities

(University of Waterloo, 2009-08-20)

We study the degree structures of the strong reducibilities $(\leq_{ibT})$ and $(\leq_{cl})$, as well as $(\leq_{rK})$ and $(\leq_{wtt})$. We show that any noncomputable c.e. set is part of a uniformly c.e. copy of ...

#### Asymptotic Estimates for Rational Spaces on Hypersurfaces in Function Fields

(University of Waterloo, 2010-06-29)

The ring of polynomials over a finite field has many arithmetic properties similar to those of the ring of rational integers. In this thesis, we apply the Hardy-Littlewood circle method to investigate the density of rational ...

#### On the Erdös-Turán conjecture and related results

(University of Waterloo, 2011-08-29)

The Erdös-Turán Conjecture, posed in 1941 in, states that if a subset B of natural numbers is such that every positive integer n can be written as the sum of a bounded number of terms from B, then the number of such ...

#### A survey of Roth's Theorem on progressions of length three

(University of Waterloo, 2011-12-19)

For any finite set B and a subset A⊆B, we define the density of A in B to be the value α=|A|/|B|. Roth's famous theorem, proven in 1953, states that there is a constant C>0, such that if A⊆{1,...,N} for a positive integer ...

#### Lower order terms of moments of L-functions

(University of Waterloo, 2011-06-17)

<p>Given a positive integer k, Conrey, Farmer, Keating, Rubinstein and Snaith conjectured a formula for the asymptotics of the k-th moments of the central values of quadratic Dirichlet L-functions. The conjectured formula ...