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» Vol. 2, Issue 2, 2001 «



Title: Comparison of Centrality Estimators for Several Distributions
Author: Jamie McCreary, Tennessee Technological University Author Bio    
Abstract: The measure of central tendency is the most commonly used tool in statistical data analysis. The ability to determine an ``average'' provides a way to locate data centrality. Central tendency is usually determined by one of three methods. One can calculate the mean, median or midrange of a sample set. However, does the best method to determine the central point of a distribution vary with the types of distributions involved? In this paper we attempt to determine which methods are best used for several different distributions. Specifically we will examine the Normal, Uniform, and Cauchy distributions.
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Title: Topspin: Solvability of Sliding Number Games
Author: Eric Wilbur, St. Olaf College Author Bio    
Abstract: The puzzle Topspin is a sliding number game consisting of an oval track containing a random arrangement of numbered discs, and a small turnstile within the track. A game is of the form [t,n] if it has n total discs, and a turnstile with t discs. Using concepts of group theory, the solvability, or ordering, of the discs is determined or conjectured for all values of t and n. Furthermore, if a game is not solvable, its attainable subgroup is determined or conjectured for all values of t and n. Several notations are used in the proofs of these theorems to help the reader follow visually as well as mathematically. Solvability is difficult to prove, but in the puzzle [t,n] where t and n are both even, we reveal the complex series of flips and shifts needed to prove the solvability of the game. Finally, using the results of the [t,n] games, the solvability is determined or conjectured for multiple turnstile games.
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Title: Application of Generalized Inverses and Circulant Matrices to Iterated Functions on Integers
Author: Chantel S. Cleghorn, Angelo State University Author Bio    
Abstract: After reviewing fundamental properties of matrix generalized inverses and circulant matrices, we describe a particular application in which both of these concepts play an important role. In particular, we establish the form of the Moore-Penrose generalized inverse of a type of circulant matrix that arises naturally in the study of iterated functions on integers.
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Title: Automorphisms of Metacyclic p-Groups with Cyclic Maximal Subgroups
Author: Mark Schulte, St. Olaf College Author Bio    
Abstract: This paper deals with the determination of the automorphism group of the metacyclic p-groups, P(p,m), given by the presentation P(p,m) = where p is an odd prime number. We show that Aut(P) has a unique Sylow p-subgroup, S_p, and that Aut(P) is isomorphic to the the semidirect product of S_p and Z_(p-1).
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Title: Algebra and Matrix Normed Spaces
Author: Seth M. Hain, University of Nebraska Author Bio    
Abstract: We begin by looking at why operator spaces are necessary in the study of operator algebras and many examples of and ways to construct operator algebras. Then we examine how certain basic algebraic relationships break down when norms are placed on them. This leads to ways to correct these ideas using matrix norms.
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Title: U-factorizations in Commutative Rings with Zero Divisors
Author: Nicholas Roersma, Wabash College Author Bio    
Abstract: Let R be a commutative ring with identity. We define an alternate method of factorization, called a U-factorization, and extend several finite factorization characterizations to U-factorizations.
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