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Physical Sciences and Mathematics Commons™
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Articles 1 - 7 of 7
Full-Text Articles in Physical Sciences and Mathematics
Labeled Trees And Spanning Trees: Computational Discrete Mathematics And Applications, Demet Yalman
Labeled Trees And Spanning Trees: Computational Discrete Mathematics And Applications, Demet Yalman
Electronic Theses and Dissertations
In this thesis, we examine two topics. In the first part, we consider Leech tree which is a tree of order n with positive integer edge weights such that the weighted distances between pairs of vertices are exactly from 1 to n choose 2. Only five Leech trees are known and some non-existence results have been presented through the years. Variations of Leech trees such as the minimal distinct distance trees and modular Leech trees have been considered in recent years. In this thesis, such Leech-type questions on distances between leaves are studied as well as some other labeling questions …
Graphs Of Classroom Networks, Rebecca Holliday
Graphs Of Classroom Networks, Rebecca Holliday
Electronic Theses and 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 …
Bayesian Inference Of The Weibull-Pareto Distribution, James Dow
Bayesian Inference Of The Weibull-Pareto Distribution, James Dow
Electronic Theses and Dissertations
The Weibull distribution has many applications in various topics. Some of these topics include survival analysis, reliability engineering, general insurance, electrical engineering, and industrial engineering. The Weibull distribution was further extended by the Weibull-Pareto distribution. A desirable property this distribution has is its shape can skew being able to better model left or right skewed data. Examples of skewed data include human longevity and actuarial data. In this work a hierarchical Bayesian model was developed using the Weibull-Pareto distribution.
Improved Full-Newton-Step Infeasible Interior-Point Method For Linear Complementarity Problems, Mustafa Ozen
Improved Full-Newton-Step Infeasible Interior-Point Method For Linear Complementarity Problems, Mustafa Ozen
Electronic Theses and Dissertations
In this thesis, we present an improved version of Infeasible Interior-Point Method (IIPM) for monotone Linear Complementarity Problem (LCP). One of the most important advantages of this version in compare to old version is that it only requires feasibility steps. In the earlier version, each iteration consisted of one feasibility step and some centering steps (at most three in practice). The improved version guarantees that after one feasibility step, the new iterated point is feasible and close enough to central path. Thus, the centering steps are eliminated. This improvement is based on the Lemma(Roos, 2015). Thanks to this lemma, proximity …
Automorphisms Of Graph Curves On K3 Surfaces, Joshua C. Ferrerra
Automorphisms Of Graph Curves On K3 Surfaces, Joshua C. Ferrerra
Electronic Theses and Dissertations
We examine the automorphism group of configurations of rational curves on $K3$ surfaces. We use the properties of finite automorphisms of $\PP^1$ to examine what restrictions a given elliptic fibration imposes on the possible finite order non-symplectic automorphisms of the $K3$ surface. We also examine the fixed loci of these automorphisms, and construct an explicit fibration to demonstrate the process.
Enumerating Graphs Using Integrals From Quantum Field Theory, William A. Coggins
Enumerating Graphs Using Integrals From Quantum Field Theory, William A. Coggins
Electronic Theses and 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.
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
Electronic Theses and 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 …