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» Vol. 1, Issue 1, 2000 «



Title: Optimization Methods Applied to and Compared Through an Academic Database
Author: Lori Giles, University of Evansville Author Bio    
Abstract: We present results and conclusions stemming from the application of various optimization methods on an academic database. The goal is to provide a tool for our client to use to predict the best prospective students based on data gathered pre-registration. We applied several optimization programs to our database. The methods will be compared and contrasted based on accuracy and transferability of results to future student data. We also analyze the general "goodness" of the database itself, and propose possible improvements that will aid in better classification.
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Additional Downloads: PS    

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Title: Turning the Lights Out in Three Dimensions
Author: J. Jacob Tawney, Denison University Author Bio    
Abstract: Tiger electronics now has an entire Lights Out series. The original version, solved by means of Linear Algebra by Feil and Anderson in October 1998 is a five by five grid of lights. Pressing a button results in a change of parity of that button and a change in parity of the north, south, east, and west neighbors of that light (if such neighbors exist). The object of the game is to get all of the lights turned off. Later, Tiger released its next version of the mind puzzle, Lights Out Cube, a cube in which the sides are three by three grids of lights. The parity-changing rule still applies, except this time if a light lies on the border of a face, pressing it will change all of its neighbors, including those on adjacent faces. Thus, in Lights Out Cube, pressing any button will always result in the change of parity of five buttons, itself and its four neighbors. Again, the game presents the user with a configuration of lights, some off and some on, and the objective is to turn all the lights out. We will present a complete solution to Lights Out Cube in a style similar to that used by Feil and Anderson; however, a lack in certain mathematical conveniences of matrices present in the original Lights Out solution will complicate the process for the cube of lights.
Article: Downloadable PDF    
Additional Downloads: PS     AppA1.mws     AppA2.mws     AppB.mws    

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Title: Sprials, Partial Sums and Continuous Images
Authors: Suzanne Reichel, University of Wisconsin
Kyen Waldron, University of Oregon
Author Bio    
Author Bio    
Abstract: In this paper a continuum is a compact connected subset of the plane. When we consider two continua X and Y, one of the basic questions we ask is whether there exists a continuous map of X onto Y. More generally, when we consider two collections of continua, we ask when there exists a continuous map of a member of one collection onto a member of the other collection. We consider a collection of continua each of which is the union of the unit circle and a ray spiralling down upon the circle in a way to be defined later. The purpose of this paper is to determine which of these continua is the continuous image of a nonseparating continuum, i. e., a continuum that has a connected complement in the plane. This work is a special case of more general work done by David Bellamy. Bellamy proves the theorem for a larger class of "compactifications of (0,1] with remainder a circle" that are not assumed to be subsets of the plane, and he determines that the nonseparating continuum can be required to have the special property of being "chainable." Naturally his proof is more involved. We believe that our special case conveys the idea behind this result in a way accessible to undergraduate mathematics majors.
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Title: A Study of Sufficient Conditions for Hamiltonian Cycles
Author: Melissa DeLeon, Seton Hall University Author Bio    
Abstract: A graph G is Hamiltonian if it has a spanning cycle. The problem of determining if a graph is Hamiltonian is well known to be NP-complete. While there are several necessary conditions for Hamiltonicity, the search continues for sufficient conditions. In their paper, "On Smallest Non-Hamiltonian Regular Tough Graphs" (Congressus Numerantium 70), Bauer, Broersma, and Veldman stated, without a formal proof, that all 4-regular, 2-connected, 1-tough graphs on fewer than 18 nodes are Hamiltonian. They also demonstrated that this result is best possible. Following a brief survey of some sufficient conditions for Hamiltonicity, Bauer, Broersma, and Veldman's result is demonstrated to be true for graphs on fewer than 16 nodes. Possible approaches for the proof of the n=16 and n=17 cases also will be discussed.
Article: Downloadable PDF    
Additional Downloads: DOC     AppA.pdf     AppB.pdf    

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Title: Symmetry and Tiling Groups for Genus 4 and 5
Author: C. Ryan Vinroot, North Carolina State University Author Bio    
Abstract: All symmetry groups for surfaces of genus 2 and 3 are known. In this paper, we classify symmetry groups and tiling groups with three branch points for surfaces of genus 4 and 5. Also, a class of symmetry groups that are not tiling groups is presented, as well as a class of odd order non-abelian tiling groups.
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