Digital Commons Network^™

Using Character Varieties: Presentations, Invariants, Divisibility And Determinants, Jeffrey Allan Hall

Doctoral Dissertations

If G is a finitely generated group, then the set of all characters from G into a linear algebraic group is a useful (but not complete) invariant of G . In this thesis, we present some new methods for computing with the variety of SL2C -characters of a finitely presented group. We review the theory of Fricke characters, and introduce a notion of presentation simplicity which uses these results. With this definition, we give a set of GAP routines which facilitate the simplification of group presentations. We provide an explicit canonical basis for an invariant ring associated with a symmetrically …

Dynamic Analysis Of Unevenly Sampled Data With Applications To Statistical Process Control, Laura Ann Mcsweeney

Doctoral Dissertations

Dynamic analysis involves describing how a process changes over time. Applications of this type of analysis can be implemented in industrial settings in order to control manufacturing processes and recognize when they have changed significantly. The primary focus of this work is to construct methods to detect the onset of periodic behavior in a process which is being monitored using a scheme where data is sampled unevenly.

Techniques that can be used to identify statistically significant periodic structure using the periodogram will be reviewed and developed. The statistical properties of the periodogram for unevenly sampled data will be calculated. These …

The Word Problem And The Ideal Membership Problem, Damon Anthony Demas

Doctoral Dissertations

This dissertation concerns two problems from computational algebra, the word problem for semigroups and the ideal membership problem for noncommutative polynomial rings. Historically, the word problem provided one of the first examples of an algorithmically unsolvable problem from outside of logic and computability theory. In terms of solvability, the word problem is equivalent to a restricted version of the membership problem.

For ideals whose membership problem is solvable, computational techniques such as Grobner basis methods often can be used to solve the problem, but not always. In Chapter two, we develop a method which can be used to solve the …

Central Sequences And C*-Algebras, Hemant Pendharkar

Doctoral Dissertations

We study central sequences of C*-algebras. We find connections of the central sequences of a C*-algebra and its representations. More specifically, we prove the following results: (a) Characterization of central sequences in certain C*-subalgebras of C(X, Mn), where X is a compact Hausdorff space. We also state the conditions under which central sequences are trivial/hypercentral. (b) A representation of the C*-algebra is in the point norm closure of the set of all equivalence classes of irreducible representation if and only if it is multiplicity free. (c) For a C*-algebra A, all of whose representations are bounded by some fixed number, …

Topics In Chaotic Secure Communication, Andrew Thomas Parker

Doctoral Dissertations

Results in nonlinear dynamics and chaos during this decade have been applied to problems in secure communications with limited success. Most of these applications have been based on the chaotic synchronization property discovered by Pecora and Carroll in 1989 [37]. Short [44, 45, 48] demonstrated the effectiveness of nonlinear dynamic (NLD) forecasting methods in breaking this class of communication schemes. In response, investigators have proposed enhancements to the basic synchronization technique in an attempt to improve the security properties. In this work two of these newer communication systems will be analyzed using NLD forecasting and other techniques to determine the …