Toral Algebraic Sets and Function Theory on Polydisks

A toral algebraic set $A$ is an algebraic set in \C^n whose intersection with \T^n is sufficiently large to determine the holomorphic functions on $A$. We develop the theory of these sets, and give a number of applications to function theory in several variables and operator theoretic model theory. In particular, we show that the uniqueness set for an extremal Pick problem on the bidisk is a toral algebraic set, that rational inner functions have zero sets whose irreducible components are not toral, and that the model theory for a commuting pair of contractions with finite defect lives naturally on a toral algebraic set

Dennett’s Intentional Strategy Applied to Animals

Daniel Dennett lays out what he calls the intentional strategy (or stance) and the intentional system, which proposes that we could predict the behavior of humans, non-human animals, plants or in other words, what he calls an intentional system. Roughly speaking, the intentional strategy involves attributing beliefs and desires, that a reason using object ought to have given the circumstances, to an object; with those beliefs and desires, one should be able to predict the object’s behavior. Though my goal is not to criticize Dennett’s view, I will argue that the intentional strategy works better on non-human animals than humans; a mere observation of an application of the intentional strategy. Once I have shown that the intentional strategy seems to work better on non-human animals than humans, I will argue that it is because it is in the nature of animals to make survival their highest desire and then form beliefs to secure this desire. Humans, on the other hand, form beliefs about the world, and these beliefs form their desires; they are not simply seeking survival

Implementing intersection calculations of the ray tracing algorithm with systolic arrays

Ray tracing is one technique that has been used to synthesize realistic images with a computer. Unfortunately, this technique, when implemented in software, is slow and expensive. The trend in computer graphics has been toward the use of special purpose hardware, to speed up the calculations, and, hence, the generation of the synthesized image. This paper describes the design and the operation of a systolic based architecture, tailored to speed up the intersection calculations, that must be performed as a part of the ray tracing algorithm

Relativistic Expansion of Electron-Positron-Photon Plasma Droplets and Photon Emission

The expansion dynamics of hot electron-positron-photon plasma droplets is dealt with within relativistic hydrodynamics. Such droplets, envisaged to be created in future experiments by irradiating thin foils with counter-propagating ultra-intense laser beams, are sources of flashes of gamma radiation. Warm electron-positron plasma droplets may be identified and characterized by a broadened 511 keV line

Functional Elastomeric Scaffold Development for Tissue Engineering

Scaffolds for engineering soft tissue would ideally be mechanically compliant and anisotropic while possessing inherent bioactivity and enzyme sensitivity similar to the native extracellular matrix. Biodegradable elastomers, such as cytocompatible poly(ester urethane)ureas, represent attractive alternatives to more common biodegradable polyesters utilized in tissue engineering. These materials can be processed by electrospinning into scaffolds suitable for in vivo placement and support of cellular adhesion and growth. This process, where an electric field overcomes surface tension to generate and draw nanoscale fibers, can create scaffolds with extracellular matrix-like morphologies that retain mechanical strength and flexibility while also permitting protein incorporation into spun fibers to impart bioactivity. Poly(ester urethane)urea (PEUU) was blended with collagen or urinary bladder matrix and processed with electrospinning into nanofibrous scaffolds. Protein incorporation into the matrices resulted in increased cellular adhesion and scaffold degradation rate. PEUU scaffolds were fabricated with various degrees of fiber alignment to more closely mimic soft tissue anisotropy such as that of the native pulmonary valve. The fabrication of mechanically anisotropic scaffolds is desired due to their ability to direct cell growth during tissue remodeling. PEUU elastomeric matrices could serve as mechanical support scaffolds for cell adhesion and growth but can require long seeding and culture times to achieve high density cellular in-growth. Therefore, a microintegration technique was developed where the elastomeric fibers are spun concurrently with electrospraying of cells. This process produced viable, high cell density constructs and lessened the time necessary for scaffold fabrication and seeding. The functionality of electrospun PEUU was evaluated for its ability to release bioactive basic fibroblast growth factor or the antibiotic tetracycline. These controlled release elastomeric matrices might be appropriate for application in wound repair or management. Electrospun PEUU was also evaluated in fabricating a functional tissue engineered blood vessel. Small diameter electrospun PEUU tubular conduits were implanted as rat aorta replacements and demonstrated patency and tissue remodeling at 2 wks. In addition, the cellular microintegration technology was extended as a means to incorporate cells into electrospun small diameter tubes in vitro. These materials possessed mechanical compliance similar to native vessels and demonstrated great potential for tissue engineering

Disposition and Development Strategies for Vacant Property in Petersburg, Virginia

Petersburg, Virginia has weathered decades of population and industrial decline resulting in the abundance of City-owned vacant property. As the Richmond metropolitan area continues to gain population and attract development, Petersburg is ideally positioned to capitalize on these regional growth trends. The purpose of this plan is to propose recommendations for Petersburg to establish a streamlined and proactive land disposition and development approach to reposition itself within the region. Through the study of five post-industrial cities to learn how each handle vacant property disposition and development, this plan incorporates good practices from the study cities and feedback from regional developers and community revitalization professionals to align itself with Petersburg’s revitalization goals