This thesis contains some results concerning groupoid dynamical systems and crossed products. We introduce the notion of a proper groupoid dynamical system and of its generalized fixed point algebra. We show that our notion of proper groupoid...
α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptors (AMPARs) function as paracrine and autocrine receptors throughout the body. Most studies have focused on their role in fast excitatory neuronal signaling, and learning and memory. In...
Polynomials. Finite fields (Algebra). Algebraic functions. Number theory.
The ring of univariate polynomials over a finite field shares many foundational arithmetic properties with the ring of rational integers. This similarity makes it possible for many problems in elementary number theory to be translated 'through the...
In this thesis we develop a theory of Fourier analysis and fast Fourier transforms (FFTs) for finite inverse semigroups. Our results generalize results in the theory of Fourier analysis for finite groups. There is a general method for generating...
In the late 1960s, Ihara began work that led to the Ihara zeta function, a zeta function which is defined on a finite graph. This function is an interesting graph invariant which gives information on expansion properties of the graph. It also...
Most theoretical and computational studies of turbulence in Navier-Stokes fluids and/or guiding-center plasmas have been carried out in the presence of spatially periodic boundary conditions. In view of the frequently-reproduced result that...
This thesis considers the two special sensor networks for future sensor network design: mobile sensor networks and hybrid network of sensors and robots. To investigate two types of networks, we abstract two most important aspects that are ingrained...
Experimental and theoretical aspects of macroscopic and mesoscopic elastic instability are investigated in this thesis. For the theoretical investigations we utilize a Lagrangian formulation of nonlinear continuum elasticity theory, the novel...
The LysR-type virulence regulator, AphB, initiates the Vibrio cholerae virulence cascade resulting in expression of the two critical virulence factors, toxin-coregulated pilus and cholera toxin, by activating transcription at the tcpPH promoter....
Thermodynamics, and the classic balance between entropy and enthalpy, provides a proverbial zoo of exotic phase behaviour that chemists can harness to create new materials out of simple liquids and polymers. The diversity of self-assembling...
Cyclin-dependent kinases (CDKs) and their associated cyclins are key regulators of cell cycle progression. Caenorhabditis elegans has two predicted A- type cyclins, encoded by the genes cya-1 and cya-2. Cyclin A has been shown to be required for...
Despite the array of targeted therapeutics that currently exist to combat breast cancer, disease progression leading to metastasis, and tumor recurrence still remains a significant clinical challenge. Efforts to identify novel pathways and...
In this thesis, we characterize and enumerate the permutations which are realized by the orbits of signed shifts, a family of discrete dynamical systems on words. The permutations, which are called patterns of the signed shifts, are given by the...
We prove the existence of nontrivial multiparameter isospectral deformations of metrics on the classical compact simple Lie groups SO (n) (n = 9, n ≥11), Spin(n) (n = 9, n ≥11), SU (n) (n ≥7), and Sp (n) (n ≥5). The proof breaks into three...
Motivated by quantum mechanics and geometric optics, it is a long-standing problem whether the length spectrum of a compact Riemannian manifold can be recovered from its Laplace spectrum. One route to proving that the length spectrum depends on the...
Recent technological advances have fostered the emergence of Wireless Sensor Networks (WSNs), which consist of tiny, wireless, battery-powered nodes that are expected to revolutionize the ways in which we understand and construct complex physical...
'Orthogonal modular forms are algebraic modular forms arising from lattices in quadratic spaces. In this thesis, we define orthogonal modular forms, establish their basic properties, and then apply them to a case of ternary quadratic spaces to...
Three-dimensional imaging in medicine -- Mathematical models. ; Stereoencephalotomy.
In the past, clinicians skilled at image-guided neurosurgery have relied solely on pre-operative scans for their navigational information. Often in the course of surgery, tissue is purposely retracted/resected or inadvertently moved resulting in a...
Measurement of the ionospheric thermal particle population bridges the two different communities of ground-based radar and space-based rocket studies, which have the common goal of characterizing heavy ion transport in the cusp/cleft region. We...
Human behavior -- Mathematical models. ; Web usage mining. ; Internet users.
Whom we e-mail, where we browse, what we purchase, and the things we search for on the World Wide Web all leave identifiable traces of who we are as individuals. In today's technology focused landscape, cyberspace represents the new environment in...
Free electron lasers -- Experiments. Wave guides -- Design and construction. Diffraction gratings -- Experiments. Electron beams. Infrared sources.
The far infrared region of the electromagnetic spectrum, 15-3000 Œºm in wavelength, has a paucity of narrow band laser sources. To address the issue of whether a grating based free electron laser could operate well as such a source, a grating...