» Vol. 1, Issue 2, 2000 «

Title: The Interpolation of Hydraulic Head Contours Author: Kelly Knapp, Ursinus College Author Bio     Abstract: We looked at methods of interpolation for calculating the hydraulic head contour lines from wells located throughout a region. One method we chose to investigate was a relaxation or finite-difference method. This method required that the hydraulic heads be located on a square grid and can be derived using elementary numerical analysis. An initial guess was made for the unknown hydraulic head values, and then passes were repeatedly made through the grid to determine the unknown head values. The calculations were done using a spreadsheet. Ten methods of initializing the data were tested that simulate varying boundary and interior date conditions. The resulting hydraulic head values were then used to create hydraulic head contour maps in Maple. We also obtained data from sites in New Jersey from the NJ Department of Environmental Protection Division of Hazardous Site Mitigation and ran our model on this data. Article: Downloadable PDF     Additional Downloads: DOC     » BACK TO TOP Title: Basins of Roots and Periodicity in Newton's Method for Cubic Polynomials Author: Amy Smith, Davidson College Author Bio     Abstract: Newton's method is a useful tool for finding roots of functions when analytical methods fail. The goal of our research was to understand the dynamics of Newton's method on cubic polynomials with real coefficients. Usually iterations will converge quickly to the root. However, there are more interesting things that can happen. When we allow initial values to be chosen from the complex plane, we find that the points that converge are bounded by fractals. For some polynomials we found interesting phenomena including chaos and attracting periodic cycles. We classified which polynomials could have attracting periodic cycles. Article: Downloadable PDF     Additional Downloads: DOC     App.pdf     App.doc     » BACK TO TOP Title: Theory and Implementation of a Functional Programming Language Author: Ari Lamstein, University of Michigan Author Bio     Abstract: The goal of this research is to design and implement a small functional programming language that incorporates some of the features that arise from the theoretical study of programming language semantics. We begin with the study of the lambda-calculus, an idealized mathematical language. We present the language PPL, a strongly typed, call-by-name language which supports recursion and polymorphism. We describe a compiler of PPL into a low-level assembly language. The compilation is based on an abstract machine interpretation and includes a type inference algorithm. Article: Downloadable PDF     Additional Downloads: PS     » BACK TO TOP