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» Vol. 2, Issue 1, 2001 «



Title: River Quality Modeling Using Differential Equations
Author: Clark Bennett, University of South Dakota Author Bio    
Abstract: A mathematical model provides the ability to predict the contaminant concentration levels of a river. The advection-diffusion equation is used as a first approximation for such a model. The validity of the model's results are compared with data gathered and compiled by the Minnesota Pollution Control Agency. A portion of the Mississippi River beginning at a site in the Southeast portion of Saint Paul, Minnesota and ending at a bridge near La Crosse, Wisconsin was used. The focus was to create the mathematical model and to compare its estimations against the available data on this portion of the river. Proceeding downstream, a river's contaminant concentrations can both increase and decrease due to factors such as tributaries, weather, and agricultural runoff. To fit the assumptions of a steady state advection-diffusion model, the contaminant concentration values that were utilized for the model were monotone increasing or decreasing above and below the tributary.
Article: Downloadable PDF    
Additional Downloads: app1.doc     app1.pdf     app1.jpg     app2.xls     app3-7.xls    

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Title: The 'Flattened' Projections of Orientable Surfaces
Author: Jonathan Schneider, Walter Johnson HS Author Bio    
Abstract: When orientable surfaces having at least one edge are immersed into the plane, there often exists regions where two parts of the surface must occupy the same space in the plane. If these regions are considered overlaps rather than intersections, the surface remains embedded in three-space but appears to be flattened. This form of the surface, called a "flattening," can be subjected to certain deformations without leaving its flattened state. Called "flat deformations," these deformations can be used to show that two apparently different flattenings are sometimes just two forms of the same flattening; in that case, the two original forms are called "indistinct." This paper attempts to determine a formula relating the properties of a given surface with the number of distinct flattenings which can possibly be formed from it. Specifically, it focuses on the flattenings of tori with n disks removed. Although an explicit formula is not derived, the paper outlines a method for determining the correct number of flattenings, and charts this number against n for values up to ten.
Article: Downloadable PDF    
Additional Downloads: DOC     allfig.pdf     allfig.doc     15 figures (jpgs)    

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Title: Polynomials Over Finite Fields Whose Values Are Squares
Author: Kyle Petersen, Washington University Author Bio    
Abstract: This paper seeks to explain in the simplest terms possible a paper written by Umberto Zannier. Though Zannier says that his is "a simple elementary method," there are still steps in his paper that are quite subtle. The tools needed to follow his proof are in the hands of most Algebra students, though which tools to use and how to use them may not be obvious. This essay hopes to make the path from conception to conclusion as clear and easy as possible, with simple proofs and examples to show the way.
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