A problem encountered in the boundary element method is the difficulty caused by corners and/or discontinuous boundary conditions. An existing code using standard linear continuous elements is modified to overcome such problems using the multiple node method with an auxiliary boundary collocation approach. Another code is implemented applying the gradient approach as an alternative to handle such problems. Laplace problems posed on variety of domain shapes have been introduced to test the programs. For Poisson problems the programs have been developed using a transformation to a Laplace problem. This method cannot be applied to solve Poissontype equations. The dual reciprocity boundary element method (DRM) which is a generalised way to avoid domain integrals is introduced to solve such equations. The gradient approach to handle corner problems is co-opted in the program using DRM. The program is modified to solve non-linear problems using an iterative method. Newton's method is applied in the program to enhance the accuracy of the results and reduce the number of iterations. The program is further developed to solve coupled Poisson-type equations and such a formulation is considered for the biharmonic problems. A coupled pair of non-linear equations describing the ohmic heating problem is also investigated. Where appropriate results are compared with those from reference solutions or exact solutions. v

Recent work on many problems in additive combinatorics, such as Roth's Theorem, has shown the usefulness of first studying the problem in a finite field environment. Using the techniques of Bourgain to give a result in other settings such as general abelian groups, the author gives a walk through, including proof, of Roth's theorem in both the one dimensional and two dimensional cases (it would be more accurate to refer to the two dimensional case as Shkredov's Theorem). In the one dimensional case the argument is at its base Meshulam's but the structure will be essentially Green's. Let Ϝⁿ [subscript p], p ≠ 2 be the finite field of cardinality N = pⁿ. For large N, any subset A ⊂ Ϝⁿ [subscript p] of cardinality ∣A ∣≳ N ∕ log N must contain a triple of the form {x, x + d, x + 2d} for x, d ∈ Ϝⁿ [subscript p], d ≠ 0. In the two dimensional case the argument is Lacey and McClain who made considerable refinements to this argument of Green who was bringing the argument to the finite field case from a paper of Shkredov. Let Ϝ ⁿ ₂ be the finite field of cardinality N = 2ⁿ. For all large N, any subset A⊂ Ϝⁿ ₂ × Ϝⁿ ₂ of cardinality ∣A ∣≳ N ² (log n) − [superscript epsilon], ε <, 1, must contain a corner {(x, y), (x + d, y), (x, y + d)} for x, y, d ∈ Ϝⁿ₂ and d ≠ 0.

As Athapaskan-speaking people with a lifestyle distinct from other Southwestern groups, Navajos, upon entering the Southwest in the sixteenth century, are thought to have begun a process of culture change that persists to this day. The anthropological view of Navajo culture is that it is a synthesis of Athapaskan and Puebloan culture traits, and early archaeological studies of Navajo culture reinforced this view. Navajo archaeology continues to suffer from a general lack of Navajo perspectives on their own history andarchaeological record. I examine Navajo identity expressed in the built environment and the negotiation of intrusive federal Indian policies in the late nineteenth and early twentieth centuries using narratives from a ceremony called the Blessingway and theories of agency, practice, history, and structuration. Environmental, architectural, dendrochronological, artifactual, and historical data collected from 393 hogan sites recorded in the Four Corners area during the Navajo Land Claim Project in the 1950s comprise the basis for my study. Data analyses indicate that in spite of the imposition of policies designed to alter Navajo lifeways and relationships with the landscape, American colonial interactions did not dramatically alter the core of nineteenth and twentieth century Navajo culture. The dialectic between colonial policy and traditional Dine culture resulted in persistent architecture, settlement patterning, and decision making about movement over landscapes in spite of conflicts over land and water. Historically, theories and methods arising from the Western tradition have been the main avenues through which archaeologists interpret and make sense of the Indigenous past in North America. The growing body of modern literature in Indigenous archaeology now consciously includes, and often takes as its starting point, Indigenous perspectives on the past, and the practice of archaeology in America. Practitioners of Indigenous archaeology seek to strike a balance between Western perspectives and Indigenous worldviews and to increase the participation of Indigenous people in the discipline. My study is an attempt to weave together Indigenous and Western philosophies in a mutually beneficial manner.

Thesis (Ph. D. - Hydrology and Water Resources)--University of Arizona. / Includes bibliographical references.

No description available.

No description available.

The focal point of the quality of life associated with the United States is a strong economy. Growth in the economy means growth in employment. The establishment of stringent environmental legislation is now a reality. However, those responsible for enacting environmental laws, as well intentioned as they may be, must strive to assess the socio-economic consequences of their actions so that the true net benefit of the environmental legislation is established. The main effort in this research centers around the analysis of how a particular resource, energy (i.e., energy in the form of electric power derived from strip-mined coal) is embedded in the economic growth of the Southwest. The basic econometric tool that has been utilized is a regional input-output model which evolved from a California-Arizona linked input-output model developed by H. O. Carter and D. Ireri. The decision space developed, which effectively acted as a mechanism for restricting coal-fired power availability in future years, was based on a schedule of electric energy capacity additions as delineated by the U.S. Department of Interior's Southwest Energy Study. The regional economic analysis, described in Chapter 5 of this dissertation, suggests there is a definite relationship between coal-fired power availability and regional economic growth in the Southwest. Furthermore, the estimates of incremental decreases in regional economic activity associated with certain levels of decreased coal-fired power development are of such a magnitude that one could characterize the relationship as very significant.

Thesis (Ph. D. - Hydrology and Water Resources)--University of Arizona. / Includes bibliographical references.

Thesis (M Arch)--Montana State University--Bozeman, 2010. / Typescript. Chairperson, Graduate Committee: Ralph Johnson. Includes bibliographical references (leaves 104-106).

Energy developments in the Southwest have established a basis for the examination of complexities involved in environmental decision making. The coalfired generation facilities exhibit an impact potential on the social, physical, and economic surroundings of both local and distant communities. A recent seventeen-volume report directed by the U.S. Department of Interior, The Southwest Energy Study, is an indicator of the magnitude of the situation. The Four Corners Program is a team research project with emphasis placed upon technology transfer. Simulation models are used to estimate the physical, economic, and social effects of a range of decisions concerning alternate power schedules. The research results are communicated to interest groups in other than the usual report form. A workshop environment allows the participants to interact with the decisions, the models, the results, and one another. One of the simulation models is the groundwater model. The groundwater model is used to estimate head declines in the confined and unconfined portions of the Navajo Sandstone and the Mesaverde Formation on Black Mesa. The Mesaverde Formation is found to be isolated from the Navajo Sandstone by the Mancos Shale and other intervening layers. A simulation routine developed by the Illinois State Water Survey is modified and adapted to the problem. As a result of the small amount of published aquifer data, minimum or below minimum values of aquifer properties and a sensitivity analysis were incorporated into model considerations. Pumping rates and pumping durations of groundwater for slurry transfer of coal define the decision space. The mining pumpage will have a negligible effect upon the Indian wells located in recharge areas of the Navajo Sandstone. The effects of mining pumpage upon potentiometric surfaces in the artesian portion of the Navajo Sandstone will range from zero to twenty percent of the artesian head, depending upon location and aquifer properties. Theoretical effects of groundwater pumpage on four monitor locations are quantified in terms of ranges of variation. These results can help to evaluate development plans for decision makers and other interest groups. With the future acquisition of measured drawdowns, consideration of theoretical and actual results can provide additional precision to aquifer parameter estimates. The Four Corners Program has a two year duration. The goal of the first year effort was the completion of simulation modeling. Beyond technical or prejudicial hurdles, the workshop encounters will require a public relations and communications posture which is conducive to group participation. The effectiveness of simulation as a means of technology transfer to a variety of users is yet to be evaluated.