Browse Dissertations and Theses - Mathematics by Title

• (1964)

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• (1990)
Given a semisimple linear algebraic group G over an algebraically closed field K, we fix a Borel subgroup B and a maximal torus T. This determines a root system $\Phi$, and a set of simple roots $\Delta$. The subgroups ...

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• (1981)
This thesis presents a classification up to topological equivalence of those flows on the torus satisfying: (1) all singular points and closed orbits are hyperbolic; and (2) there are no saddle connections. Such flows are ...

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• (1972)

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• (2015-07-15)
Given a $G$-toric, folded-symplectic manifold with co-orientable folding hypersurface, we show that its orbit space is naturally a manifold with corners $W$ equipped with a smooth map $\psi: W \to \frak{g}^*$, where ...

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• (2014-09-16)
In the first part of this thesis, we study the application of a clearing mechanism of a financial network to a specific type of financial network, which is established upon an abstract underlying asset. In particular, we ...

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• (2009)
This work attempts to explain the relationships between natural selection, information theory, and statistical inference. In particular, a geometric formulation of information theory known as information geometry and its ...

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• (1976)

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• (2010-08-20)
In this thesis, we explore a chain-level construction in smooth Deligne cohomology that produces data for extended topological field theories. For closed oriented manifolds $\Sigma$, this construction takes the form of a ...

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• (1970)

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• (1970)

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• (1971)

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• (1974)

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• (2006)
The second main result identifies Gromov-Hausdorff limits of certain sequences of manifolds-with-boundary as Alexandrov spaces of curvature bounded below.

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• (2015-07-06)
We consider questions regarding the existence of graphs and hypergraphs with certain coloring properties and other structural properties. In Chapter 2 we consider color-critical graphs that are nearly bipartite and have ...

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• (2004)
Then, we consider packing problems for d-degenerate graphs. Two graphs G1 and G 2 pack if G1 is a subgraph of the complement G¯2 of G 2. We disprove one of the conjecture of Bollobas and Eldridge and prove an extension of ...

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• (2004)
We also show that lambda(G) = q 2 + q = Delta2 - Delta for the incidence graph G of the projective plane PG (2, q). To prove this result, we convert the problem to a problem of packing of bipartite graphs into a complete ...

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• (2001)
An r-edge-coloring of Kn is (r, m)-splittable if V (Kn) can then be r-colored to avoid totally monochromatic m-cliques (introduced by Erdo&huml;s and Gyarfas. We interpret such colorings using a two-round game against an ...

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• (2012-05-22)
In this thesis we study some extremal problems related to colorings and list colorings of graphs and hypergraphs. One of the main problems that we study is: What is the minimum number of edges in an $r$-uniform hypergraph ...

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• (1994)
Combinatorial methods are used to prove several results in number theory. The chapters may be read independently, and are briefly discussed below.

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