Pervasive Algebras and Maximal Subalgebras.

A uniform algebra A on its Shilov boundary X is maximal if A is not C(X) and no uniform algebra is strictly contained between A and C(X) . It is essentially pervasive if A is dense in C(F) whenever F is a proper closed subset of the essential set of A. If A is maximal, then it is essentially pervasive and proper. We explore the gap between these two concepts. We show: (1) If A is pervasive and proper, and has a nonconstant unimodular element, then A contains an infinite descending chain of pervasive subalgebras on X . (2) It is possible to find a compact Hausdorff space X such that there is an isomorphic copy of the lattice of all subsets of N in the family of pervasive subalgebras of C(X). (3) In the other direction, if A is strongly logmodular, proper and pervasive, then it is maximal. (4) This fails if the word ���strongly��� is removed. We discuss examples involving Dirichlet algebras, A(U) algebras, Douglas algebras, and subalgebras of H���(D), and develop new results that relate pervasiveness, maximality, and relative maximality to support sets of representing measures.

Design and Development of an FPGA-based Distributed Computing Processing Platform

This thesis presents two frameworks- a software framework and a hardware core manager framework- which, together, can be used to develop a processing platform using a distributed system of field-programmable gate array (FPGA) boards. The software framework providesusers with the ability to easily develop applications that exploit the processing power of FPGAs while the hardware core manager framework gives users the ability to configure and interact with multiple FPGA boards and/or hardware cores. This thesis describes the design and development of these frameworks and analyzes the performance of a system that was constructed using the frameworks. The performance analysis included measuring the effect of incorporating additional hardware components into the system and comparing the system to a software-only implementation. This work draws conclusions based on the provided results of the performance analysis and offers suggestions for future work.