Browsing Pure Mathematics by Title
Now showing items 135-154 of 165
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Semicrossed Products, Dilations, and Jacobson Radicals
(University of Waterloo, 2017-08-18)We compute the C*-envelope of the isometric semicrossed product of a C*-algebra arising from number theory by the multiplicative semigroup of a number ring R, and prove that it is isomorphic to T[R], the left regular ... -
Semistable rank 2 co-Higgs bundles over Hirzebruch surfaces
(University of Waterloo, 2015-08-07)It has been observed by S. Rayan that the complex projective surfaces that potentially admit non-trivial examples of semistable co-Higgs bundles must be found at the lower end of the Enriques-Kodaira classification. ... -
Series-Parallel Posets and Polymorphisms
(University of Waterloo, 2018-09-04)We examine various aspects of the poset retraction problem for series-parallel posets. In particular we show that the poset retraction problem for series-parallel posets that are already solvable in polynomial time are ... -
Settling Time Reducibility Orderings
(University of Waterloo, 2010-04-28)It is known that orderings can be formed with settling time domination and strong settling time domination as relations on c.e. sets. However, it has been shown that no such ordering can be formed when considering computation ... -
Sidon and Kronecker-like sets in compact abelian groups
(University of Waterloo, 2019-06-07)Let $G$ be a compact abelian group and $\Ga$ be its discrete dual group. In this thesis we study various types of interpolation sets. A subset $E \subset \Ga$ is Sidon if every bounded function on $E$ can be interpolated ... -
Some additive results in F_q[t]
(University of Waterloo, 2015-08-27)We collected several results in integers of additive number theory and translated to results in F_q[t]. The results we collected are related to slim exceptional sets and the asymptotic formula in Waring's problem, a ... -
Some aspects of Cantor sets
(University of Waterloo, 2014-03-28)For every positive, decreasing, summable sequence $a=(a_i)$, we can construct a Cantor set $C_a$ associated with $a$. These Cantor sets are not necessarily self-similar. Their dimensional properties and measures have been ... -
Some Functional Equations Connected with the Utility of Gains and Losses
(University of Waterloo, 2002)The behavioral properties shown by people when they make selections between different choices will be studied. Based on empirical and logical data a mathematical axiomatic model is built. D. Luce is a major ... -
Some Problems in Multiplicative and Additive Number Theory
(University of Waterloo, 2020-07-27)In this thesis, we obtain several results in number theory. Let $k\geqslant 1$ be a natural number and $\omega_k(n)$ denote the number of distinct prime factors of a natural number $n$ with multiplicity $k$. We estimate ... -
Some results on binary forms and counting rational points on algebraic varieties
(University of Waterloo, 2016-08-17)In this thesis we study several problems related to the representation of integers by binary forms and counting rational points on algebraic varieties. In particular, we establish an asymptotic formula for $R_F(Z)$, the ... -
Sparse Automatic Sets
(University of Waterloo, 2020-11-26)The theory of automatic sets and sequences arises naturally in many different areas of mathematics, notably in the study of algebraic power series in positive characteristic, due to work of Christol, and in Derksen's ... -
A spatial version of Wedderburn’s Principal Theorem
(Taylor & Francis, 2015)In this article we verify that ‘Wedderburn’s Principal Theorem’ has a particularly pleasant spatial implementation in the case of cleft subalgebras of the algebra of all linear transformations on a finite-dimensional vector ... -
Spectral Analysis of Laplacians on Certain Fractals
(University of Waterloo, 2007-12-06)Surprisingly, Fourier series on certain fractals can have better convergence properties than classical Fourier series. This is a result of the existence of gaps in the spectrum of the Laplacian. In this work we prove a ... -
Strong Morita Equivalence and Imprimitivity Theorems
(University of Waterloo, 2016-09-15)The purpose of this thesis is to give an exposition of two topics, mostly following the books \cite{R & W} and \cite{Wil}. First, we wish to investigate crossed product $C^*$-algebras in its most general form. Crossed ... -
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 ... -
A Survey of the Classification of Division Algebras
(University of Waterloo, 2008-09-29)For a given field F we seek all division algebras over F up to isomorphism. This question was first investigated for division algebras of finite dimension over F by Richard Brauer. We discuss the construction of the Brauer ... -
Symmetrically-Normed Ideals and Characterizations of Absolutely Norming Operators
(University of Waterloo, 2018-08-23)The primary objective of this thesis is two fold: first, it is devoted to the study of absolutely norming operators (with respect to various arbitrary symmetric norms on $\mathcal{B}(\mathcal{H})$) with an eye towards the ... -
Techniques in operator algebras: classification, dilation and non-commutative boundary theory
(University of Waterloo, 2017-08-11)In this thesis we bring together several techniques in the theory of non-self-adjoint operator algebras and operator systems. We begin with classification of non-self-adjoint and self-adjoint operator algebras constructed ... -
Topics in G₂ geometry and geometric flows
(University of Waterloo, 2020-05-15)We study three different problems in this thesis, all related to G₂ structures and geometric flows. In the first problem we study hypersurfaces in a nearly G₂ manifold. We define various quantities associated to such a ... -
Tracial and ideal structure of crossed products and related constructions
(University of Waterloo, 2022-08-17)In this thesis, we concern ourselves with asking questions about the basic structure of group C*-algebras, crossed products, and groupoid C*-algebras. Specifically, we are concerned with two main topics. One is the simplicity ...