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Volumes and topology of hyperbolic 4-manifolds.
(1998)
We also consider the question of when a finite volume hyperbolic $(n + 1)$-manifold M may be embedded as a complement of a closed codimension-k submanifold A inside a closed $(n + 1)$-manifold N. We show that if this is ...
Topics in feedback control stabilization.
(1997)
In this dissertation, we first show that for a class of uncertain nonlinear systems, the robust output feedback stabilizability is equivalent to the existence of robust output Lyapunov functions with the small control ...
Regularity for systems and the angle condition.
(2000)
In this dissertation we consider weak solutions of the System A(u) + B(u) = 0 on a bounded domain W⊂ Rn where B(u) is a perturbation of critical growth, i.e. its growth exponent p equals the integrability exponent ...
The structure of injective hulls of Lie modules.
(1982)
Let N be a finite dimensional nilpotent Lie algebra over an algebraically closed field k of characteristic zero. In this paper we show that the injective hull of the 1-dimensional trivial U(N)-module (here U(N) denotes the ...
On the Existence and Stability of Filiform Nilsolitons
(2022-08)
This dissertation is concerned with the existence and stability of nilsoliton metrics on filiform Lie algebras. The results are presented in two major components. First, we give new results which preclude the existence of ...
(Multi-)Persistent Homology and Topological Robotics
(2023-05-12)
After developing the relevant background and proving some general results in the early chapters, the main novel content of this thesis is the computation of the $i$-th homology groups of the second configuration spaces of ...
Tau functions for matrix hierarchies.
(1997)
The totality of all zero curvature equations with a rational dependence of connection matrices on a spectral parameter form a hierarchy, which means that all the corresponding vector fields commute. This is the so-called ...
Transport Protocols for Wireless Sensor Networks: State-of-the-Art and Future Directions
(2007)
Characteristics of wireless sensor networks, specifically dense deployment, limited processing power, and limited power supply, provide unique design challenges at the transport layer. Message transmission between sensor ...
Building fences around the chromatic coefficients.
(1997)
Although these bounding conditions do not allow us to completely predict all chromatic polynomials, they do serve to severely limit the form of polynomials considered to be candidates for the chromatic polynomial of some graph.