As part of the national observance of Math Awareness Week, the Department of Mathematics at North Carolina A&T State University is pleased to sponsor the following events on Friday, April 25, 1997 and invites you to join our second annual celebration of the beauty of mathematics.

The themes of the day's activities include mathematics and the internet, and mathematics and other disciplines.

8:00 -- 10:00 AM: Applied Mathematics Session--Graduate Students Presentations (120 Marteena Hall)

Chair: P. Varatharajah

10:30 -- 12:00 PM: Interdisciplinary Session (120 Marteena Hall)

Chair: G. Gibson

Abstracts of the Talks in Applied Mathematics Session

• Numerical Investigation of the Singular-Value Decomposition of Various Tomographic Operators
Nerissa Felder (This work is directed by Dr. Paramanathan Varatharajah)
Abstract: The goals of this study are to understand the random transform, the singogram, the full angle problem, the limited angle problem, the interior problem, the exterior problem, SVD, measurement and null components of an object, etc. The following four tomographic operators will be considered in our study: the random transform over full angular range, the random transform over limited angular range, the random transform of the interior problem, and the random transform of the exterior problem.
• Simplex and Integer Linear Programming
Perry L. Gillespie, Jr. (This work is directed by Dr. Bolindra Borah)
Abstract: This presentation discusses the history of the Simplex Algorithm, and an application of it. We also discuss the new algorithm known as Karmakar Algorithm which is ten times faster than Simplex Algorithm. We also look at an example dealing with another area of linear and nonlinear programming, and integer linear programming.
• Converse of the Intermediate Value Theorem
Wm. Randolph Harrison (This work is directed by Dr. James Chew)
Abstract: The Intermediate Value Theorem states that a continuous real-valued function f defined on a closed interval [a,b] assumes values between f(a) and f(b). We use the Darboux Property to strengthen this theorem by considering not just values at the endpoints, but every value between f(p) and f(q) on [p,q] contained in [a,b]. We then consider the converse problem: if a function has the Darboux Property, is the function necessarily continuous?
• Probabilities in Some Common Games of Chance
Shelia Littlejohn (This work is directed by Dr. A. Giles Warrack)
Abstract: Probabilities are computed for the ways one can win in various popular Casino Games, in particular Craps and Roulette. The concept of expectation is used to show that in the long run the casino will invariably make money.
• A Statistical Model of Cladding Degradation
Makia S. Moore
Abstract: The purpose of this project is to create a statistical model showing how strain of a cladding rod is affected by temperature, time, and stress. This is done by using a statistical package called S-Plus.
• Analysis of Relative Motion on a Time-Dependent Hypersurface in R^3
Anthony Segers
Abstract: Relative motion is analyzed on a time-dependent hypersurface in R^3. Given an unlimited number of particles in C^infinite smooth motion on one or more surfaces and three-dimensional observers that travel with the particles, a notation and a formula are developed to readily determine the paths of the particles in the coordinate system of any selected observer.
• Forced Vibrations of A Two-Degree-of-Freedom Mechanical System
Barbara Tankersley (This work is directed by Dr. Guoqing Tang)
Abstract: We consider an example of forced vibrations of a two-degree-of-freedom mechanical system arising from a uniform slender rod with two vertical spring supports. First, we derive the system of differential equations governing the force vibrations using the Newton's law. Then we outline the general procedure for finding the system response for forced but undamped mechanical vibrations using the Principal Coordinate method to decouple the system into a set of second order linear nonhomogeneous equations. Once that is done, finally, we go back to the application problem and use the algorithm developed to solve the example of forced vibrations of a two-degree-of -freedom mechanical system completely.
• Free and Undamped Mechanical Vibrations
Andre L. Williams (This work is directed by Dr. Guoqing Tang)
Abstract: We present the general procedure for finding the system response of free and undamped mechanical vibrations through an example of a three-degree-of-freedom mechanical system which is obtained from a slide on frictionless surface. By using the Newton Second Law, we derive the differential equations governing free and undamped vibrations using x_1, x_2, and x_3 as generalized coordinates. We then consider the problem of finding the system response for general free and undamped mechanical vibrations of n-degree-of-freedom mechanical systems and discuss the algorithm for computing the natural frequencies and normal modes. The developed algorithm is then applied to solve the application problem. Three normal modes are illustrated by Maple graphing utilities.

• An Optimal Estimation Scheme for Subsurface Contaminant Transport Model using Kalman-Bucy Filtering
Shoou-Yuh Chang, Professor of Environmental Engineering
Abstract: A methodology for developing a data assimilation scheme using Kalman-Bucy (KB) filter for an applicable subsurface model is proposed and illustrated. A numerical scheme was constructed using C language and MATLAB routines. Preliminary results of a hypothetical two-dimensional contaminant plume indicate that the numerical model with KB filter reduces the deviation of model predictions by 60%. Sensitivity tests were also conducted to demonstrate the robustness of the estimation scheme.
• Traveling Waves in Lattice Dynamical Systems
Mingxiang Chen, Assistant Professor of Mathematics
Abstract: Applications in electrical circuit theory, material science and biology require studies of lattice dynamical systems (LDS). Among the topics of studies are spatial pattern formations, spatial chaos, and traveling waves etc. This talk gives a brief introduction of current researches and progresses in the study of traveling waves in LDS.
• The Existence of Homoclinic Manifolds in a Model for Chaotic Oscillations of a Buckled Elastic Beam
Joseph Gruendler, Associate Professor of Mathematics
Abstract: Previous work has studied the case with a center manifold of codimension two and reduced to Duffing's equation. Increasing the axial load increases the codimension of the center manifold. In our case this codimension is four and reduces to an equation in R^4 with a hyperbolic equilibrium and two homoclinic solutions along which the invariant manifolds meet in dimension two. We address the problem of showing that these two orbits lie on a homoclinic manifold.
• Using Differential Equations to Describe Physical Systems
Sekazi K. Mtingwa, Professor of Physics
Abstract: Differential equations are indispensable tools for constructing theories to describe physical systems. In fact, the true beauty of physics lies in the solutions of such equations. To illustrate this point, we consider the mathematics of a simple system consisting of a mass attached to a spring. We then proceed to generalize to circuit analysis and the propagation of electromagnetic waves.
• Regression Model of Income in North Carolina Counties
Belinda Brewster-Clemence, An Economics Major Student
Abstract: We use linear regression analysis to model the relevance of certain structural and personal characteristics on income levels among counties in North Carolina in 1989. Our particular interest is how race influences income differentials. A surprising result of the study is that the per capita income of a county is independent of the proportion of the labor force employed in white collar jobs.
• Fourier Series of a Triangular Wave
David Charters, A Physics Major Student
Abstract: Fourier series are used to express functions in terms of an infinite sum of sines and cosines. We compute the generalized series for a periodic triangular wave. To get an approximation of the triangular wave, the Fourier series must be carried out to several terms. The more terms the series is expanded into, the closer the series resembles the triangular wave itself. We then prepare plots of the Fouries series carried out to a range of one to eleven terms. Analysis of these plots clearly shows the series more closely approximates the triangular wave with more terms expanded.

Coordinated by Janis Oldham and the Student Chapter of MAA

Coordinated by Errol Rowe and Neil Sigmon

Coordinated by James Chew, Robert Mers (Chair), Janis Oldham, and Gloria Phoenix

Coordinated by James Chew, Robert Mers, Janis Oldham, and Gloria Phoenix

Addison-Wesley Publishing Company

Coordinated by Thomas Clarke and A. Giles Warrack

Refreshment will be served in the Faculty Lounge in Marteena Hall during breaks at 10:00-10:30 AM, and 2:30-2:45 PM. There will be a lunch gathering in the William Cafeteria. Anyone who is interested in participating in the lunch gathering please contact either of the two coordinators at 334-7822 so that a seat can be reserved.

NC A&T SU Math Awareness Committee