Browsing Pure Mathematics by Issue Date
Now showing items 61-80 of 165
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Generalisations of Roth's theorem on finite abelian groups
(University of Waterloo, 2012-12-18)Roth's theorem, proved by Roth in 1953, states that when A is a subset of the integers [1,N] with A dense enough, A has a three term arithmetic progression (3-AP). Since then the bound originally given by Roth has been ... -
The Prouhet-Tarry-Escott problem
(University of Waterloo, 2013-01-15)Given natural numbers n and k, with n>k, the Prouhet-Tarry-Escott (PTE) problem asks for distinct subsets of Z, say X={x_1,...,x_n} and Y={y_1,...,y_n}, such that x_1^i+...+x_n^i=y_1^i+...+y_n^i\] for i=1,...,k. ... -
The Eberlein Compactification of Locally Compact Groups
(University of Waterloo, 2013-01-24)A compact semigroup is, roughly, a semigroup compactification of a locally compact group if it contains a dense homomorphic image of the group. The theory of semigroup compactifications has been developed in connection ... -
The Cohomology Ring of a Finite Abelian Group
(University of Waterloo, 2013-01-25)The cohomology ring of a finite cyclic group was explicitly computed by Cartan and Eilenberg in their 1956 book on Homological Algebra. It is surprising that the cohomology ring for the next simplest example, that of a ... -
Digraph Algebras over Discrete Pre-ordered Groups
(University of Waterloo, 2013-01-25)This thesis consists of studies in the separate fields of operator algebras and non-associative algebras. Two natural operator algebra structures, A ⊗_max B and A ⊗_min B, exist on the tensor product of two given unital ... -
Geometrical frustration and static correlations in hard-sphere glass formers
(American Institute of Physics, 2013-03-28)We analytically and numerically characterize the structure of hard-sphere fluids in order to review various geometrical frustration scenarios of the glass transition. We find generalized polytetrahedral order to be correlated ... -
Maximal ideal space techniques in non-selfadjoint operator algebras
(University of Waterloo, 2013-04-26)The following thesis is divided into two main parts. In the first part we study the problem of characterizing algebras of functions living on analytic varieties. Specifically, we consider the restrictions M_V of the ... -
Complexity of Classes of Structures
(University of Waterloo, 2013-08-28)The main theme of this thesis is studying classes of structures with respect to various measurements of complexity. We will briefly discuss the notion of computable dimension, while the breadth of the paper will focus on ... -
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 ... -
Dimensional dependence of the Stokes-Einstein relation and its violation
(American Institute of Physics, 2013-10-28)We generalize to higher spatial dimensions the Stokes-Einstein relation (SER) as well as the leading correction to diffusivity in finite systems with periodic boundary conditions, and validate these results with numerical ... -
Asymptotic Distributions for Block Statistics on Non-crossing Partitions
(University of Waterloo, 2014-01-23)The set of non-crossing partitions was first studied by Kreweras in 1972 and was known to play an important role in combinatorics, geometric group theory, and free probability. In particular, it has a natural embedding ... -
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 ... -
Families of Thue Inequalities with Transitive Automorphisms
(University of Waterloo, 2014-06-17)A family of parameterized Thue equations is defined as F_{t,s,...}(X, Y ) = m, m ∈ Z where F_{t,s,...}(X,Y) is a form in X and Y with degree greater than or equal to 3 and integer coefficients that are parameterized by ... -
Generalized Complex Structures on Kodaira Surfaces
(University of Waterloo, 2014-08-05)In this thesis, we study generalized complex structures on Kodaira surfaces, which are non-K\"ahler surfaces that admit holomorphic symplectic structures. We show, in particular, that the moduli space of even-type generalized ... -
Interpolation Sets For Compact Abelian Groups
(University of Waterloo, 2014-09-04)We will study various properties of I_0 and \epsilon-Kronecker sets. We show that most infinite sets in the discrete dual group contain infinite interpolation sets. -
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 ... -
On the local positivity of line bundles on algebraic surfaces
(University of Waterloo, 2015-01-09)In this thesis, we define a measure for how `positive' an effective line bundle is at a point on a variety, and prove that it is linear on the numerically effective subcone on a smooth, complete, toric surface. -
K-theory for C*-Algebras and for Topological Spaces
(University of Waterloo, 2015-04-27)K-theory is the study of a collection of abelian groups that are invariant to C*-algebras or to locally compact Hausdorff spaces. These groups are useful for distinguishing C*-algebras and topological spaces, and they are ... -
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. ... -
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 ...