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Now showing items 1-10 of 10

#### The Differential Geometry of Instantons

(University of Waterloo, 2009-08-07)

The instanton solutions to the Yang-Mills equations have a vast range of practical applications in field theories including gravitation and electro-magnetism. Solutions to Maxwell's equations, for example, are abelian gauge ...

#### Operator Theoretic Methods in Nevanlinna-Pick Interpolation

(University of Waterloo, 2009-03-31)

This Master's thesis will develops a modern approach to complex interpolation problems studied by Carath\'{e}odory, Nevanlinna, Pick, and Schur in the early $20^{th}$ century. The fundamental problem to solve is as follows: ...

#### 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 ...

#### 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 ...

#### The O'Nan-Scott Theorem for Finite Primitive Permutation Groups, and Finite Representability

(University of Waterloo, 2009-08-06)

The O'Nan-Scott Theorem classifies finite primitive permutation groups into one of five isomorphism classes. This theorem is very useful for answering questions about finite permutation groups since four out of the five ...

#### Moment Polynomials for the Riemann Zeta Function

(University of Waterloo, 2009-01-21)

In this thesis we calculated the coefficients of moment polynomials of the Riemann zeta function for k= 4, 5, 6...13 using cubic acceleration, which is an improved method from quadratic acceleration. We then numerically ...

#### Equality of Number-Theoretic Functions over Consecutive Integers

(University of Waterloo, 2009-04-30)

This thesis will survey a group of problems related to certain number-theoretic functions. In particular, for said functions, these problems take the form of when and how often they are equal over consecutive integers, n ...

#### On the Structure of Nonnegative Semigroups of Matrices

(University of Waterloo, 2009-08-18)

The results presented here are concerned with questions of decomposability of multiplicative semigroups of matrices with nonnegative entries. Chapter 1 covers some preliminary results which become useful in the remainder ...