Browsing Pure Mathematics by Issue Date
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Classification of Nilpotent Lie Algebras of Dimension 7 (over Algebraically Closed Field and R)
(University of Waterloo, 1998)This thesis is concerned with the classification of 7dimensional nilpotent Lie algebras. Skjelbred and Sund have published in 1977 their method of constructing all nilpotent Lie algebras of dimension <i>n</i> given those ... 
The Model Theory of Algebraically Closed Fields
(University of Waterloo, 2000)Model theory can express properties of algebraic subsets of complex nspace. The constructible subsets are precisely the first order definable subsets, and varieties correspond to maximal consistent collections of ... 
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 ... 
Intervals with few Prime Numbers
(University of Waterloo, 2004)In this thesis we discuss some of the tools used in the study of the number of primes in short intervals. In particular, we discuss a large sieve density estimate due to Gallagher and two classical delay equations. ... 
Infinite Sets of Dintegral Points on Projective Algebrain Varieties
(University of Waterloo, 2005)Let <em>X</em>(<em>K</em>) ⊂ <strong>P</strong><sup><em>n</em></sup> (<em>K</em>) be a projective algebraic variety over <em>K</em>, and let <em>D</em> be a subset of <strong>P</strong><sup><em>n</em></sup><sub><em>O ... 
Gröbner Bases Theory and The Diamond Lemma
(University of Waterloo, 2006)Commutative Gröbner bases theory is well known and widely used. In this thesis, we will discuss thoroughly its generalization to noncommutative polynomial ring <em>k</em><<em>X</em>> which is also an associative free ... 
Counting points of bounded height on del Pezzo surfaces
(University of Waterloo, 2006)del Pezzo surfaces are isomorphic to either P<sup>1</sup> x P<sup>1</sup> or P<sup>2</sup> blown up <i>a</i> times, where <i>a</i> ranges from 0 to 8. We will look at lines on del Pezzo surfaces isomorphic to P<sup>2</sup> ... 
Multiplicities of Linear Recurrence Sequences
(University of Waterloo, 2006)In this report we give an overview of some of the major results concerning the multiplicities of linear recurrence sequences. We first investigate binary recurrence sequences where we exhibit a result due to Beukers and ... 
On the Similarity of Operator Algebras to C*Algebras
(University of Waterloo, 2006)This is an expository thesis which addresses the requirements for an operator algebra to be similar to a <em>C</em>*algebra. It has been conjectured that this similarity condition is equivalent to either amenability ... 
Reductions and Triangularizations of Sets of Matrices
(University of Waterloo, 2006)Families of operators that are triangularizable must necessarily satisfy a number of spectral mapping properties. These necessary conditions are often sufficient as well. This thesis investigates such properties in ... 
NonIsotopic Symplectic Surfaces in Products of Riemann Surfaces
(University of Waterloo, 2006)<html> <head> <meta httpequiv="ContentType" content="text/html;charset=iso88591"> </head> Let Σ<em><sub>g</sub></em> be a closed Riemann surface of genus <em>g</em>. Generalizing Ivan Smith's construction, ... 
Maximal Operators in R^2
(University of Waterloo, 20070813)A maximal operator over the bases $\mathcal{B}$ is defined as \[Mf(x) = \sup_{x \in B \in \mathcal{B}} \frac{1}{B}\int_B f(y)dy. \] The boundedness of this operator can be used in a number of applications including ... 
HigherDimensional Kloosterman Sums and the Greatest Prime Factor of Integers of the Form a_1a_2\cdots a_{k+1}+1
(University of Waterloo, 20070829)We consider the greatest prime factors of integers of certain form. 
Amenability for the Fourier Algebra
(University of Waterloo, 20070829)The Fourier algebra A(G) can be viewed as a dual object for the group G and, in turn, for the group algebra L1(G). It is a commutative Banach algebra constructed using the representation theory of the group, and from which ... 
On Diagonal Acts of Monoids
(University of Waterloo, 20070830)In this paper we discuss what is known so far about diagonal acts of monoids. The first results that will be discussed comprise an overview of some work done on determining whether or not the diagonal act can be finitely ... 
A kConjugacy Class Problem
(University of Waterloo, 20070907)In any group G, we may extend the definition of the conjugacy class of an element to the conjugacy class of a ktuple, for a positive integer k. When k = 2, we are forming the conjugacy classes of ordered pairs, when k ... 
On a Question of Wintner Concerning the Sequence of Integers Composed of Primes from a Given Set
(University of Waterloo, 20070927)We answer to a Wintner's question concerning the sequence of integers composed of primes from a given set. The results generalize and develop the answer to Wintner’s question due to Tijdeman. 
Posets of NonCrossing Partitions of Type B and Applications
(University of Waterloo, 20071019)The thesis is devoted to the study of certain combinatorial objects called \emph{noncrossing partitions}. The enumeration properties of the lattice ${\textsf{NC$^{\textsf{\,A}}$(n)}}\,$ of \emph{noncrossing partitions} ... 
Lehmer Numbers with at Least 2 Primitive Divisors
(University of Waterloo, 20071024)In 1878, Lucas \cite{lucas} investigated the sequences $(\ell_n)_{n=0}^\infty$ where $$\ell_n=\frac{\alpha^n\beta^n}{\alpha\beta},$$ $\alpha \beta$ and $\alpha+\beta$ are coprime integers, and where $\beta/\alpha$ is ... 
Spectral Analysis of Laplacians on Certain Fractals
(University of Waterloo, 20071206)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 ...