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  • Thesis

  • Authors: Velasquez, Maria Elena (2006)

  • The aim of this thesis is to present an overview of the Fourier transform, including the continuous Fourier transform, the l2(Z) transform (Fourier series), the discrete Fourier transform, and the windowed Fourier transform. The shortcomings of these has led to the recently discovered wavelet transform, which has corresponding continuous and discrete versions. I present the theory behind these wavelet transforms, and present some of their relevant applications. Multiresolution Analysis (MRA) will be highlighted as a tool of great potential utility in other fields such as Physics, Biology, Geology, Computer Science, Medicine, and Engineering. I conclude this thesis with a discussion of three "signature" recognition applications of the discrete wavelet transform MRA to gamma-ray spect...

  • Thesis

  • Authors: Jiang, Yongbin (2006)

  • In algebraic number theory, the study of Galois groups is one of the subjects mathematicians are most interested in. A fruitful set of results have been obtained in this field. Class field theory and some of its consequent theorems are certainly an important part of these results. In [1], E.Artin and Tate used the notion of class formations to reinterpret class field theory and proposed another interesting object, which is called the Weil group and has a strong relation with class formations, for us to study. Recently, research shows that Weil groups deserve more investigation and they behave better than the classical Galois groups in some cases. Lichtenbaum's paper [11] showed us evidence for the above mentioned opinion. In his paper, Lichtenbaum gave the definition of Weil-kale t...

  • Thesis

  • Authors: Zhang, Yuting (2006)

  • Streaming multimedia applications such as live webcasts and interactive distance learning require real-time constraints for data capture and transmission in keeping with end-user QoS requirements. Meanwhile, they can also tolerate some packets being discarded or serviced late, as long as the consecutive number of such losses is limited. Likewise, other soft real-time applications, such as data generation applications in sensor networks and in embedded systems, also have similar delay and loss constraints. To deal with the above classes of applications, this thesis presents window-constrained resource management models and polices to guarantee a fraction of their required service in every finite time window. For the single server case, the Virtual Deadline Scheduling (VDS) algorithm...

  • Thesis

  • Authors: Lee, Yangsoo (2006)

  • Centrifuges are used in geotechnical earthquake engineering to simulate complicated phenomena such as nonlinear soil-structure interaction and liquefaction induced by earthquakes. Cost efficient alternatives to large scale testing, centrifuge modeling has become widely accepted to analyze experimentally all kinds of geotechnical problems. This thesis explores the use of wireless technologies to improve data transfer and control remotely data acquisition systems of centrifuges. These improvements greatly reduce electrical noises and increase the high-frequency performance of data acquisition. This thesis also contributes to the introduction of metadata for documenting the experimental results and processes of centrifuge testing. The first part of the research work consisted of re-a...

  • Thesis

  • Authors: Silberstein, Rebecca Lynn Braynard (2006)

  • The scenario of wireless devices deployed in an ad hoc network is a compelling one. For the system to support its assigned tasks, nodes must cooperate to forward data packets through the network. The act of forwarding, however, is directly linked to node lifetime. The more a node forwards data packets, the sooner it depletes its battery through use of its high energy-consuming radio. Once forwarding nodes deplete their batteries, the network may partition and fail to provide its designated services. To reduce the burden on nodes maintaining network connectivity, we propose to balance energy consumption among all participating networked nodes, so they all fail at approximately the same time. We do this through our Medium Access Control (MAC) layer protocol, SEESAW, which offloads com...

  • Thesis

  • Authors: Gouraige, Rony (2006)

  • Two elements in a finite-dimensional central simple algebra are said to be z-equivalent if the corresponding centralizers are conjugate. We determine in this thesis the invariants which characterize z-equivalence.

  • Thesis

  • Authors: Desai, Angela (2006)

  • In this paper we discuss subsystem and coding results in Zd symbolic dynamics for d > 1. We prove that any Zd shift of finite type with positive topological entropy has a family of subsystems of finite type whose entropies are dense in the interval from zero to the entropy of the original shift. We show a similar result for Zd sofic shifts, and also show every Zd sofic shift can be covered by a Zd shift of finite type arbitrarily close in entropy. We also show that if a Z2 shift of finite type with entropy greater than log N satisfies a certain mixing condition, then it must factor onto the full N-shift.