Thesis (M. Phil.)--University of Hong Kong, 2002. / Includes bibliographical references (leaves 112-116).

published_or_final_version / Mathematics / Master / Master of Philosophy

Thesis (Ph.D.)--Auburn University, 2005. / Abstract. Vita. Includes bibliographic references (ℓ. )

First published in the Bulletin of the American Mathematical Society in 1963, published by the American Mathematical Society

In this paper, we use the techniques of plethystic substitution to reformulate the difference raising operators presented by Di Francesco and Kedem. A connection between these operators and Shimozono and Zabrocki's parabolic Jing operators is presented. In particular, we find that these operators are a renormalization of a particular case of the parabolic Jing operators. / Master of Science

For the last decade, practical limitations have prevented processor speeds from increasing significantly. To increase throughput, the computing industry has turned to multiprocessing; that is, executing computations in parallel on separate processing units. Making use of these additional units requires support from the operating system (OS). Indeed, most modern operating systems do have the capability of recognizing and utilizing multiprocessor hardware. Pintos is an instructional operating system used by many institutions to teach important operating systems concepts. Pintos aims to increase student engagement by providing challenging programming projects in which students personally implement many core functionalities of an operating system. However, prior to this work, Pintos was a uniprocessor OS. This makes it difficult for Pintos to expose students to the same synchronization challenges that most modern kernel developers face. In addition, the first structured project, aimed at teaching scheduling policies, requires students to implement an uniprocessor variant of MLFQS scheduler which is no longer used in modern systems. We implemented Symmetric MultiProcessing (SMP) support in Pintos. We also created a new scheduling assignment to expose students to a multiprocessor proportional-share scheduling policy called Completely Fair Scheduler and to introduce them to the concept of load balancing. Finally, we evaluate the effectiveness of our new Pintos framework in augmenting students’ knowledge of OS scheduling and enhancing their ability to code and debug in a low-level environment. / Master of Science

published_or_final_version / Mathematics / Doctoral / Doctor of Philosophy

This thesis explores the geometry at infinity for certain hermitian locally symmetric spaces. Let Gamma < SU(r + 1, r) be a maximal nonuniform arithmetic lattice determined by automorphisms of a hermitian form on k^{2 r + 1}, where k is an imaginary quadratic field. We give a formula for the number of cusps of X / Gamma, where X is the hermitian symmetric space on which SU(r + 1, r) acts. If r > 1 and 2 r + 1 is prime, this completely determines the number of cusps for minimal finite volume orbifolds with X-geometry, and there are only finitely many commensurability classes of noncompact finite volume quotients of X containing a one-cusped orbifold. In the case r = 1, which corresponds to the complex hyperbolic plane, we show that this holds for any N: there are only finitely many commensurability classes of arithmetic lattices in SU(2, 1) which contain an N-cusped orbifold. / text

No description available.

RC4 is one of the most widely used ciphers in practical software applications. In this thesis we examine security and design aspects of RC4. First we describe the functioning of RC4 and present previously published analyses. We then present a new cipher, Chameleon which uses a similar internal organization to RC4 but uses different methods. The remainder of the thesis uses ideas from both Chameleon and RC4 to develop design strategies for new ciphers. In particular, we develop a new cipher, RC4B, with the goal of greater security with an algorithm comparable in simplicity to RC4. We also present design strategies for ciphers and two new ciphers for 32-bit processors. Finally we present versions of Chameleon and RC4B that are implemented using playing-cards.