» Vol. 3, Issue 1, 2002 «

Title: An Analysis of the Belousov-Zhabotinskii Reaction Author: Casey Gray, Calhoun HS, Port Lavaca, TX Author Bio     Abstract: In this survey paper, we begin with a brief history of the celebrated Belousov-Zhabotinskii (BZ) reaction. In particular, we consider the BZ reaction in a continuously stirred, closed vessel in the presence of a ferroin indicator. We examine the underlying chemical kinetics of the most significant reactions involved. This leads to the Oregonator model and an associated 3 x 3 system of nonlinear ordinary differential equations. We nondimensionalize this system and further reduce it to a 2 x 2 stiff system. Relaxation oscillations are expected and an analysis of the phase plane confirms this. Finally, we solve the system numerically for a certain set of system parameters and compare our computations with experimental results. Article: Downloadable PDF     Additional Downloads: Quicktime Movies:   limit cycle     parametric     spirals     » BACK TO TOP Title: Two Quasi p-Groups Author: Ben Harwood, Northern Kentucky University Author Bio     Abstract: Recently, I set out to find and classify all the quasi p-groups of order less than 24. For most groups of order less than 24, it was easy to check whether or not the group was a quasi p-group for some prime p. But there were two of these groups, one of order 18 and one of order 20, that required much more thought and analysis. The analysis of these two groups explores the interesting structure of the semidirect product. The purpose of this paper is to examine these two groups and show that they are both quasi 2-groups. Article: Downloadable PDF     Additional Downloads: » BACK TO TOP Title: Geodesics Using Mathematica Authors: Jacob Lewis, Columbia University Author Bio     Abstract: We describe surfaces and geodesics without assuming prior knowledge of differential geometry. This involves selecting and presenting basic definitions and theorems. Included in this discussion are definitions of surface, coordinate patch, curvature, geodesic, etc. This summary closes with a proof of the length-minimizing properties of geodesics. Examples of surfaces of constant gaussian curvature are given and plotted in Mathematica. We also describe geodesics on these surfaces and plot select examples. Article: Downloadable PDF     Additional Downloads: DOC     » BACK TO TOP Title: Three Term Identities for the Coefficients of Certain Infinite Products Author: Wei Ren, Colgate University Author Bio     Abstract: In their recent paper, Farkas and Kra proved five three-term identities for the coefficient of certain finite products. In this paper we will show that each of the five identities is just one special case of an infinite family of identities. We will briefly introduce modular forms, and show that the coefficients of these products are closely related to the coefficients of certain modular form. Consequently in our proof we will use the properties of modular forms, specifically the Hecke operators. Article: Downloadable PDF     Additional Downloads: » BACK TO TOP Title: Iterated Perpendicular Constructions from Interior Points on N-gons Author: Ivan Corwin, Arlington HS, Poughkeepsie, NY Author Bio     Abstract: Two years ago I came across a very beautiful geometric construction (Figure 1), on a tee-shirt I received from the Upstate New York math team. Written on the shirt was a surprising result of iterating a certain construction multiple times. The coaches told me that the proof for the result which they had was very long and very complex. Such a beautiful problem deserves a beautiful answer. So, I came up with a very nice proof which took less than a minute to present to the team the following year. Since then I have delved further into the construction, arriving at some very interesting results. This paper proves some of those results which arise from iterating the geometric construction. Article: Downloadable PDF     Additional Downloads: DOC     » BACK TO TOP