We will study the spectrum of a discrete Schr ̈odinger operator called the periodic Anderson-Bernoulli operator. Because the operator is ergodic, we can use techniques in dynamical systems and apply Johnson’s Theorem to better understand this operator. These techniques involve study- ing the hyperbolic locus of SL(2, R) cocycles and the geometry of the hyperbolic locus in SL(2, R)n. This model has a spectrum that is completely pure-point, and there exist parameters such that the spectrum can be defined as the union of an infinite number of intervals, which is unexpected for multiple reasons. A result of Avila, Damanik, and Gorodetski [2] says that if the Anderson model has a background potential defined by a dynamical system with a continuous phase space, then such a result is impossible. In this model, the background potential is periodic, making that result not applicable. This thesis provides details of this work, as well as insight into where this work may progress.
Land disposal of wastewater, although not a new concept, has received widespread interest in recent years because of an increased need to conserve water and great public concern about water pollution. While there have been numerous recent research projects on the use of wastewater for irrigation, very few have dealt specifically with the economic aspects.
The Maloney Canyon Project in California has shown that greenbelt irrigation with wastewater is feasible from the biological and physical standpoints. Based on results from the above project, this research attempted to quantify the specific monetary and energy costs associated with land application renovation of wastewater, and to a lesser extent consider the long-run implications. In the first half of this study the attempt was made to see whether land application compares favorably with other forms of advanced wastewater treatment. Relationships between the fundamental characteristics of plant types such as capacity, treatment unit type, capital cost, etc., were studied by using statistical analysis such as linear regression, crosstabulations, and factor analysis. the last objective of this paper was to estimate the fixed, variable, and total cost functions of applying water through greenbelt irrigation as those functions vary relative to capacity, design, and geography.
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