# Browse Dissertations and Theses - Mathematics by Title

• (1991)
The Hanna Neumann Conjecture states that if two subgroups of a finitely generated free group have finite ranks m and n, then their intersection has rank N which satisfies $N$ $-$ 1 $\leq$ ($m$ $-$ 1)($n$ $-$ 1). The current ...
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• (1995)
We construct examples illustrating various aspects of Hodge theory on Riemannian manifolds. We consider the relationship between the harmonic forms on a product space and the harmonic forms on the factors as well as the ...
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• (2011-01-21)
This thesis is devoted to the study of the Hilbert transform and its applications in computational finance. We will show in this thesis that under some mild conditions, the Hilbert transform can be approximated by the ...
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• (2012-05-22)
Holomorphic chains on a smooth algebraic curve are tuples of vector bundles on the curve together with the homomorphisms between them. A type of a holomorphic chain is a tuple t of integers consisting of the ranks and ...
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• (1995)
In this paper, we present two new spines for ribbon disc complements. We describe Craggs's 3-dimensional spine and introduce a 2-dimensional spine ${\cal W}\sp2$ which we show satisfies the homotopy reciprocity law. We ...
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• (2013-08-22)
For a single cusped hyperbolic 3-manifold, Hodgson proved that there are only finitely many Dehn fillings of it whose trace fields have bounded degree. In this paper, we conjecture the same for manifolds with more cusps, ...
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• (1989)
A famous theorem of P. Hall gives a necessary and sufficient condition for a bipartite graph $\Gamma$ to possess a matching f. (A bipartite graph $\Gamma$ is a subset of the cartesian product of two finite sets X and Y. A ...
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• (2013-08-22)
My dissertation is mainly about various identities involving theta functions and analogues of theta functions. In Chapter 1, we give a completely elementary proof of Ramanujan's circular summation formula of theta functions ...
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• (2010-08-20)
The main goal of this work is to improve algebraic geometric/number theoretic constructions of error-correcting codes and secret sharing schemes. For both objects we define parameters that indicate their effectiveness in ...
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• (1995)
In Chapter 1 we sharpen Burkholder's inequality $\mu(\vert v\vert\geq1)\leq2\Vert u\Vert\sb1$ for two harmonic functions u and v by adjoining an extra assumption. That is, we prove the weak-type inequality $\mu(\vert ... PDF (2MB) • (1995) This thesis explores a new approach, begun by Maurice Heins and Jang-Mei Wu, to studying the near-boundary behavior of positive solutions of elliptic DE's by finding surfaces which minimize the integrals of solutions over ... PDF (2MB) • (1996) We introduce and analyze a coupled system of partial differential equations which model the interaction of shocks with a dispersive wave envelope. The system mimics the Zakharov equations from weak plasma turbulence theory ... PDF (3MB) • (1994) A digraph is an interval digraph if each vertex can be assigned a source interval and a sink interval on the real line such that there is an edge from u to v if and only if the source interval for u intersects the sink ... PDF (4MB) • (2013-05-24) In this thesis we study Deligne-Lusztig curves associated to the simple groups$\AAA$,$\BB$, and$\GG$with applications in algebraic geometry codes, hash families, and polar codes. This thesis consists of four parts, the ... PDF (833KB) • (1991) We consider proper holomorphic maps between balls that are invariant under the action of finite groups of unitary matrices. We are primarily interested in actions of groups that are fixed-point-free; for purposes of ... PDF (3MB) • (2011-08-25) For a fixed base, John H. Conway’s RATS sequences are generated by iterating the following procedure on an initial integer: Reverse the digits of the integer, Add the reversal to the original, Then Sort the resulting digits ... PDF (606KB) • (2013-02-03) Let P be a lattice polytope in R^d, the convex hull of a finite set in Z^d, and let L(P) = P intersection Z^d = {v1,..., vN}, where N = |L(P)|. We call P a distinct pair-sum or dps polytope if L(P)+L(P) contains N + N ... PDF (2MB) • (2013-08-22) This dissertation is concerned with equivalence relations on homotopy classes of curves coming from various spaces of at metrics on a genus g >1 surface. We prove an analog of a result of Randol (building on work of ... PDF (358KB) • (2014-01-16) This thesis is concerned with the restriction theory of the Fourier transform. We prove two restriction estimates for the Fourier transform. The first is a bilinear estimate for the light cone when the exponents are on a ... PDF (1MB) • (2011-08-25) We study extremal and structural problems in regular graphs involving various parameters. In Chapter 2, we obtain the best lower bound for the matching number over$n\$-vertex connected regular graphs in terms of ...
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