Browse Dissertations and Theses - Mathematics by Title

  • O-minimal homology 
    Woerheide, Arthur Anderson (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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  • Obstructions to the existence of displaceable Lagrangian submanifolds 
    Sirikci, Nil Ipek (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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  • On an analogue to the Grushko-Neumann theorem involving finite groups 
    Dabrowski, Walter Casimir (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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  • On congruence function fields with many rational places 
    Mak, Kit Ho (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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  • On elementary pairs ofo-minimal structures 
    Lewenberg, Adam H. (1995)
    In the first part of this thesis I prove some results on elementary pairs of o-minimal structures.
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  • On lower bounds for the betti numbers of finite length modules 
    Charalambous, Hara (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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  • On p-operator spaces and their applications 
    Lee, Jung Jin (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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  • On residues of polynomial sequences 
    Wittrig, Aaron (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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  • On semi-invariants of filtered representations of quivers and the cotangent bundle of the enhanced Grothendieck-Springer resolution 
    Im, Mee Seong (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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  • On some spaces related to weak L(p) and their duals 
    Chung, Si Kit (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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  • On subset-sum-distinct sequences of positive integers 
    Bae, Jaegug (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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  • On Tait's color-tiling problem 
    Hu, Zhu-Xin (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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  • On the coefficients of cyclotomic polynomials 
    Bachman, Gennady (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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  • On the location of zeros of solutions to w" + Aw = 0 for certain entire functions A 
    Steinbart, Enid Marguerite (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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  • On the maximum number of limit cycles of certain polynomial Lienard equations 
    Yao, Leummim (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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  • On the nilpotent injectors of the general linear groups 
    Sheu, Tsung-Luen (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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  • On the Stern sequence and a related sequence 
    Lansing, Jennifer (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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  • On vertex degrees, graph decomposition, and circular chromatic Ramsey number 
    Jao, Fang-Kai (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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  • Operators and subspaces of L(,0) 
    Faber, Richard George (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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  • Optimization on products of combinatorial structures 
    Chappell, Glenn G. (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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