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Math 495 Presentations          Tuesday, December 13, 2005          

Time: 11:05-11:25, UNH2337           Speaker: Tade Souaiaia
Title: A mathematical model of the effect of environmental effects on long jump performance of world class athletes.
Abstract: In the 1968 Mexico Olympic games, in a warm climate at high altitude many world records were set in both the sprints and the long jumps. Most famous was the long jump by record set by Bob Beamon at over 29 feet. This record eclipsed the previous by more than a foot, an astronomical amount in the long jump. Statistical analysis of the performances in Mexico city proved the breaking performances statistically improbable. Years later, with the advent of computing power athletic models began to be created that analyzed both sprint and jump performances. Ward-Smith a pioneer in the field published analysis of the effects of altitude and wind speed on both the long jump and the sprint performances. Mureika published further models that analyzed not only the effect of altitude on sprint performance but also barometric pressure, humidity and temperature. This analysis of the long jump analyzes the difference in performance uses parameters similar to Mureika, but also attempts to look at examine gravity as a parameter that varies with altitude and latitude. This long jump model finds similar variation in performance to Ward-Smith's findings when examining only wind speed and altitude fluctuations, but suggests the performances are further affected by the environment. The outdoor track and field events have been scrutinized by physical and mathematical models.


Time: 11:30-11:50, UNH2337           Speaker: Jeannine Abiva
Title: Is college age drinking becoming a problem? - A mathematical analysis
Abstract: Drinking and its negative effects to the community have stirred up much discussion throughout the whole world. In the past, there have been efforts to diminish the negative effects by focusing on the individual drinker. Now research is being focused on the communities that have an influence on drinkers. Since it is believed that the drinking habits acquired during college will continue after college, our research will be focused on the communities in a college environment. Students who abuse alcohol not only have the potential to harm themselves but also those around them. Other effects include low GPA, crime, physical assault, drunk driving, and even death. In order to better understand college drinking, the college population will be divided into six compartments: abstainers, social non-bingers, moderate non-bingers, problem drinkers, social bingers, and moderate bingers. By understanding the flow of students from one compartment into the next, there will be a better understanding of drinking in college and thus of drinking in the entire community. We will discuss several models of the college population as students flow from one compartment into another. We will develop various mathematical models and analyze them using the framework from population dynamics.


Time: 11:55-12:15, UNH2337           Speaker: Katie Tyler
Title: Is the Varicella-Zoster Vaccination Really Working??
Abstract: Varicella-Zoster virus (VZV) is an alpha-herpesvirus which causes varicella (chickenpox) and zoster (shingles) if the virus is later reactivated. Varicella-Zoster is a highly contagious disease that is found all over the world. Varicella is experience by nearly every human being, and the only available control for the disease is with widespread vaccination. This model will study the prior works of Herbert Hethcote and the model for transmission of varicella-zoster done by Matthew Schuette. It includes the addition of a vaccinated class and investigates its overall effectiveness on the population.


Time: 12:20-12:40, UNH2337           Speaker: Paul Schroeder
Title: Modeling the Spread of Rumors
Abstract: TBA


Time: 12:45-1:05, UNH2337           Speaker: Miguel Aceves
Title: How the African elephant population is beginning to stabilize.
Abstract: The African elephant population was at a substantial low during the 1980's even though land available to them was greater. The effect which caused this downward shift in African elephant population was due to poaching. Then in 1989 came the ban on poaching which has resurrected the African elephant population. Now a new threat has been posed to the elephant population which is that of a decrease in land available to them due to the growth of human population in Africa. We will analyze a system of equations relating the elephant population and the fertile land from which they feed. The equations will allow us to view mathematically the conditions which the African elephants face nowadays and make predictions. Since the elephant and the fertile land grow in two different time scales, we will do a separate analysis for the steady states of the elephant population and the fertile land. We will then analyze them together and find the equilibrium points and determine their stability. Furthermore, a bifurcation analysis will also be done on each equation and the results will show what happens when the parameters vary in value.