The Department of Energy`s program for disposing of nuclear High-Level Waste (HLW) and transuranic (TRU) waste has been impeded by overwhelming political opposition fueled by public perceptions of actual risk. Analysis of these perceptions shows them to be deeply rooted in images of fear and dread that have been present since the discovery of radioactivity. The development and use of nuclear weapons linked these images to reality and the mishandling of radioactive waste from the nations military weapons facilities has contributed toward creating a state of distrust that cannot be erased quickly or easily. In addition, the analysis indicates that even the highly educated technical community is not well informed on the latest technology involved with nuclear HLW and TRU waste disposal. It is not surprising then, that the general public feels uncomfortable with DOE`s management plans for with nuclear HLW and TRU waste disposal. Postponing the permanent geologic repository and use of Monitored Retrievable Storage (MRS) would provide the time necessary for difficult social and political issues to be resolved. It would also allow time for the public to become better educated if DOE chooses to become proactive.

In the United States we generate greater than 500 million tons of toxic waste per year which pose a threat to human health and the environment. Some of the most toxic of these wastes are those that are radioactively contaminated. This thesis explores the need for permanent disposal facilities to isolate radioactive waste materials that are being stored temporarily, and therefore potentially unsafely, at generating facilities. Because of current controversies involving the interstate transfer of toxic waste, more states are restricting the flow of wastes into - their borders with the resultant outcome of requiring the management (storage and disposal) of wastes generated solely within a state`s boundary to remain there. The purpose of this project is to study nuclear waste storage issues and public perceptions of this important matter. Temporary storage at generating facilities is a cause for safety concerns and underscores, the need for the opening of permanent disposal sites. Political controversies and public concern are forcing states to look within their own borders to find solutions to this difficult problem. Permanent disposal or retrievable storage for radioactive waste may become a necessity in the near future in Colorado. Suitable areas that could support - a nuclear storage/disposal …

The differential geometry on a Hopf algebra is constructed, by using the basic axioms of Hopf algebras and noncommutative differential geometry. The space of generalized derivations on a Hopf algebra of functions is presented via the smash product, and used to define and discuss quantum Lie algebras and their properties. The Cartan calculus of the exterior derivative, Lie derivative, and inner derivation is found for both the universal and general differential calculi of an arbitrary Hopf algebra, and, by restricting to the quasitriangular case and using the numerical R-matrix formalism, the aforementioned structures for quantum groups are determined.