# Browse Dissertations and Theses - Mathematics by Title

• (1996)
The purpose of this dissertation is to define homology functors for the category of definable sets and definable continuous maps in an o-minimal expansion of an ordered field. Both simplicial and singular homology functors ...
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• (2012-06-27)
We utilize Floer theory and an index relation relating the Maslov index, Morse index and Conley-Zehnder index for a periodic orbit of the flow of a specific Hamiltonian function to state and prove some nonexistence results ...
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• (1996)
Let C be a class of finite groups closed under the operations of taking subgroups, quotients, and extensions. Let H and K be pro-C-groups and let $G=H*K$ be their free pro-C-product. An open question in the theory of ...
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• (2012-09-18)
In this thesis, we study congruence function fields, in particular those with many rational places. This thesis consists of three parts, the first two parts present our results in two different aspects of function fields ...
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• (1995)
In the first part of this thesis I prove some results on elementary pairs of o-minimal structures.
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• (1990)
In this manuscript we consider multigraded modules. Chapter 1 gives the necessary definitions and examples that develop the theory of multigraded modules. A multigraded module has a multigraded minimal resolution. We give ...
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• (2010-08-20)
There have been a lot of research done on the relationship between locally compact groups and algebras associated with them. For example, Johnson proved that a locally compact group G is amenable if and only if the ...
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• (2012-09-18)
Given $f(x)\in\Q[x]$, graphing the doubly infinite sequence $f\big|_{\Z}$ mod 1 can often produce interesting and even surprising results. In this paper, we will give some examples of such sequences, introduce some ...
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• (2014-05-30)
We introduce the notion of filtered representations of quivers, which is related to usual quiver representations, but is a systematic generalization of conjugacy classes of $n\times n$ matrices to (block) upper triangular ...
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• (1993)
In Cwikel's paper "On the dual of Weak $L\sp{p}$", it is shown that (Weak $L\sp{p})\sp\prime = L(p\sp\prime, 1)\oplus S\sb0\oplus S\sb\infty.$ For non-atomic measure spaces, Cwikel obtains a representation of elements in ...
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• (1995)
An SSD-sequence of integers is one in which each subset is uniquely determined by its sum. Such sequences are "sparse". Ryavec used a generating function technique to show that the sum of the reciprocals of the terms of ...
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• (1996)
In this thesis, we study a problem that generalizes a color tiling problem studied by the Scottish mathematician P. G. Tait in 1883, which has been of interest in China for many decades.
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• (1991)
Let $\Phi\sb{n}(z)$ denote the $n$th cyclotomic polynomial, given by$$\Phi\sb{n}(z) = {\prod\limits\sbsp{a=1\atop(a,n)=1}{n}}\ (z - \exp(2\pi ia/n)) = {\sum\limits\sbsp{m=0}{\phi(n)}} a(m,n)z\sp{m}.$$It is easily verified ...
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• (1989)
Consider the differential equation $(\*)$ $w\sp{\prime\prime}$ + $Aw$ = 0 where $A$ is of the form $A$($z$) = $\sum\sbsp{j=1}{m}Q\sb{j}(z)$exp$P\sb{j}(z)$ with $Q\sb{j}$ and $P\sb{j}$ polynomials in $z$. We study the ...
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• (1995)
We consider the Lienard equation of the form$$\ddot x + \epsilon f(x)\dot x + x\sp{2m+1} = 0,\eqno(1)\cr$$which is equivalent to the planar system\eqalignno{\dot x &= y&\enspace\cr \dot{y} &= -x\sp{2m+1} - \epsilon ...
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• (1989)
A nilpotent injector in an arbitrary finite group G is defined to be a maximal nilpotent subgroup of G, containing a subgroup H of G of maximal order satisfying class(H) $\leq$ 2. Among other results the nilpotent injectors ...
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• (2014-05-30)
In this dissertation, we discuss properties of the Stern sequence, denoted by s(n), and define a related sequence. First, we give a brief historical background and known results. We then discuss the second and third ...
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• (2013-05-24)
In this thesis, we study extremal problems about vertex degrees and a variant of Ramsey number of graphs, and also structural problems about graph decomposition. In a list (d_1,...,d_n) of positive integers, let r and ...
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• (1995)
We prove linear and non-linear lifting theorems for locally convex subspaces of $L\sb0,$ and we give a characterization for locally bounded subspaces of $L\sb0.$ For every closed locally convex subspace E of $L\sb0$ and ...
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• (1996)
We consider optimization problems on combinatorial structures with a product form. The independence number of a graph G, denoted $\alpha (G)$, is the size of the largest independent set in G, where a subset S of the vertex ...
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