Session Chair: Dr. Peter Greim, The Citadel
2:15-2:30 Debra Knisley, East Tennessee State University
Using Domination Numbers in Trees to Analyze Secondary RNA Structure
Identifying the range of RNA's structural possibilities is an essential component in contemporary genomic research. Researchers at the Courant Institute of Mathematical Sciences recently used graph theory to model secondary RNA structures as trees in a new and novel way in a project they call RAGS (Rna As GraphS). Using the model of this project, we show that three parameters based on selected domination numbers provide information that identifies the trees that are known to represent RNA molecules.
2:35-2:50 Rao Li, University of South Carolina Aiken
Graphs having equal domination and independent domination numbers
Allan and Laskar have shown that every claw-free graph has equal domination and independent domination numbers. In this paper the result of Allan and Laskar is extended. In particular, It is shown that every S-free and quasi-claw-free graph has equal domination and independent domination numbers, where S is set of graphs such that every graph in S has at least two induced claws and it is specified explicitly in the paper.
2:55-3:10 Michael Freeze, UNC Wilmington
Application of Coding Theory to Factorization in Number Rings
Factorization of elements as products of irreducibles in rings generalized from the rational integers is often not unique. In this talk, we consider the use of combinatorial methods from elementary coding theory in quantifying uniqueness of factorization in number rings.
3:15-3:30 James Solazzo, Coastal Carolina University
Interpolation and Balls in Ck
In this talk we will compare and classify different properties that Banach algebra norms on Ck can possess in order to provide some insight into a number of problems. One of our primary motivations is to gain a deeper understanding of the geometry of the balls that arise as the solutions to various interpolation problems. The other problems include an attempt to characterize the Banach algebras that can be represented isometrically as algebras of operators on a Hilbert space, questions about the computability of various interpolation problems for uniform algebras, and questions about the failure of the multi-variable von Neumann inequality for three or more contractions on a Hilbert space.
3:35-3:50 Yaw Chang, UNC Wilmington
A Genetic Algorithm for the Vehicle Routing Problem with Time Windows
The objective of vehicle routing problem (VPR) is to deliver a set of customers with known demands on minimum-cost vehicle routes originating and terminating at the same deport. A vehicle routing problem with time windows (VPRTW) requires the delivery made in s specific time window given by the customers. Prins (2004) recently proposed a simple and effective genetic algorithm (GA) for VPR. In terms of average solution cost, it outperforms most published tabu search results. We implement this hybrid GA to handle VPRTW. Both the implementation and computational results will be discussed.
3:55-4:10 Zhenheng Li, University of South Carolina Aiken
Mathematics in Recognizing Freehand Sketches Using Pen and Tablet
We describe the mathematical techniques and research challenges in recognizing freehand 2D sketches drawn suing pen and tablet that were experienced during the implementation of sketch based mechanical design prototype application. This includes segmentation methods, geometrical shape recognition algorithms, and future research issues. Since the purpose of developing the prototype was to ascertain the issues, different segmentation and geometrical shape recognition algorithms were compared, and the best approach is terms of performance was then adopted in the prototype. A segmented stroke can be recognized as a line, circle, ellipse, elliptic arc, or a Bezier curve. We explore the solutions and research issues in segmenting and recognizing sketches based on mathematical accuracy and human cognition process.