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» Vol. 3, Issue 2, 2002 «



Title: Mathematical Methods for Modelling Price Fluctuations of Financial Time Series
Author: Sabyasachi Guharay, Princeton University Author Bio    
Abstract: Statistical analysis of financial time series is studied. We use wavelet analysis to study signal to noise ratios along with auto-correlation function to study correlation length for time series data of daily stock prices for specific sectors of the market. We study the "high beta" stocks versus the "low beta" stocks. We sample ten companies from both of these sectors. We find that the signal to noise ratio is not uniformly high for the "high beta" classified stocks nor is the correlation length large for the "high beta" classified stocks. We explain reasons for this and possible further applications.
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Title: Quasi p or not Quasi p? That is the Question
Author: Ben Harwood, Northern Kentucky University Author Bio    
Abstract: The question might not be as profound as Shakespeare's, but nevertheless, it is interesting. Because few people seem to be aware of quasi p-groups, we will begin with a bit of history and a definition; and then we will determine for each group of order less than 24 (and a few others) whether the group is a quasi p-group for some prime p or not. This paper is a prequel to [Hwd]. In [Hwd] we prove that (Z3 x Z3) x Z2 and Z5 x Z4 are quasi 2-groups. Those proofs now form a portion of Proposition (12.1) It should also be noted that [Hwd] may also be found in this journal.
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Title: RISKy Business: An In-Depth Look at the Game RISK
Author: Sharon Blatt, Elon University Author Bio    
Abstract: Games have been of interest to mathematicians for many years because they can be mathematical models of simple, real life situations. This paper will explore various mathematical aspects of the game RISK. By using probability theory and Markov chains, the following two questions will be answered: 1) What is the probability that if you attack a territory, you will capture that territory? and 2) If you engage in war, what is the expected number of losses based on the number of defending armies?
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Title: Investigations into the Kaprekar Process
Authors: Robert Ellis, East Tennessee State University
Jason Lewis, East Tennessee State University
Author Bio    
Author Bio    
Abstract: D.R. Kaprekar discovered an interesting phenomenon that occurs when one takes a four-digit number, such that all four digits are not equal, and computes the difference between its decreasing and increasing rearrangements. He found that within seven iterations of this process you will always reach the number 6174, and this process became known as the Kaprekar Process. In this paper we decided to investigate the results of the application of the Kaprekar Process to numbers of various digit lengths. This investigation includes new information about the Kaprekar Process, such as a statistical analysis of the Kaprekar Process on four-digit and five-digit numbers, and a description of the relationships between different four-digit numbers after the application of the Kaprekar Process. We also provide a summary of the results of the Kaprekar Process when applied to various digit lengths, and a look at the palindromic sequences which present themselves in this investigation.
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Title: Coherent System of Models for a Family of Modular Curves
Author: Tim Kneezel, University of Rochester Author Bio    
Abstract: Modular curves of the form X0(N) are intrinsically interesting curves to investigate. They contain a wealth of information and cross over the boundaries of geometric, algebraic, and analytic mathematics. We set out to compute all of the information for a specific family of related modular curves, namely X0(N) for those integers N dividing 36. In this paper, we work out the parameters for the curves, the coordinates of the important points in relation to those parameters, and then we find equations for the important maps between the curves. Also, since X0(36) has genus one, and therefore has a natural group structure, we include a brief section on the subgroup generated by its cusps.
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