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Full-Text Articles in Other Applied Mathematics
Solutions Of Inequality Constrained Spline Optimization Problems With The Active Set Method, Joshua A. Holloway
Solutions Of Inequality Constrained Spline Optimization Problems With The Active Set Method, Joshua A. Holloway
College of Graduate Studies: Theses & Dissertations
We solve the problem of finding a near-interpolant curve, subject to constraints, which minimizes the bending energy of the curve. Using B-splines as our tools, we give a brief overview of spline properties and develop several different cases of inequality constrained optimization problems of this type. In particular, we develop the active set method and use it to solve these problems, emphasizing the fact that this algorithm will converge to a solution in finite iterations. Our solution will solve an open problem regarding near-interpolant spline curves. Furthermore, we supplement this with an iterative technique for better choosing data sites so …
Graphs Of Classroom Networks, Rebecca Holliday
Graphs Of Classroom Networks, Rebecca Holliday
College of Graduate Studies: Theses & Dissertations
In this work, we use the Havel-Hakimi algorithm to visualize data collected from students to investigate classroom networks. The Havel-Hakimi algorithm uses a recursive method to create a simple graph from a graphical degree sequence. In this case, the degree sequence is a representation of the students in a classroom, and we use the number of peers with whom a student studied or collaborated to determine the degree of each. We expand upon the Havel-Hakimi algorithm by coding a program in MATLAB that generates random graphs with the same degree sequence. Then, we run another algorithm to find the isomorphism …
Enumerating Graphs Using Integrals From Quantum Field Theory, William A. Coggins
Enumerating Graphs Using Integrals From Quantum Field Theory, William A. Coggins
College of Graduate Studies: Theses & Dissertations
Enumerating graphs is a relatively new subfield of mathematics. In this thesis, we will discuss a enumerative method that derives from Quantum Field Theory. We begin with the basic ideas of Calculus and extend them into a enumerative method that will allow us to classify graphs embedded on surfaces.
Generating Surfaces Of Variable Eccentricity Within A Ray Tracer, Joshua A. Smith
Generating Surfaces Of Variable Eccentricity Within A Ray Tracer, Joshua A. Smith
College of Graduate Studies: Theses & Dissertations
Polynomial surfaces used in ray tracing have recently been improved upon allowing for three dimensional applications. Among these are surfaces that have a varying eccentricity. This paper will discuss a method for finding real roots of polynomials [allowing us to create these surfaces]. First, we will give the reader a basic comprehension of the workings of a ray tracer, a general understanding of three dimensional polynomial surfaces, how this newly implemented root finder functions, and how these concepts enable us to create surfaces of variable eccentricity. Then, examples will be provided to demonstrate the capabilities of the program.
Structure Vs. Properties Using Chemical Graph Theory, Tabitha N. Williford
Structure Vs. Properties Using Chemical Graph Theory, Tabitha N. Williford
College of Graduate Studies: Theses & Dissertations
Chemical graph theory began as a way for mathematicians to bring together the areas of the Physical Sciences and Mathematics. Through its use, mathematicians are able to model chemical systems, predict their properties as well as structure-property relationships. In this dissertation, we consider two questions involving chemical graph theory and its applications. We first look at tree-like polyphenyl systems, which form an important family of compounds in Chemistry, particularly in Material Science. The importance can be seen in LEDs, transmitters, and electronics. In recent years, many extremal results regarding such systems under specific constraints have been reported. More specifically are …