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Full-Text Articles in Physical Sciences and Mathematics
Spreading Speeds And Traveling Waves In Some Population Models., Quancheng Meng
Spreading Speeds And Traveling Waves In Some Population Models., Quancheng Meng
Electronic Theses and Dissertations
Virtually every ecosystem has been invaded by exotic organisms with potentially drastic consequences for the native fauna or flora. Studying the forms and rates of invading species has been an important topic in spatial ecology. We investigate two two-species competition models with Allee effects in the forms of reaction-diffusion equations and integro-difference equations. We discuss the spatial transitions from a mono-culture equilibrium to a coexistence equilibrium or a different mono-culture equilibrium in these models. We provide formulas for the spreading speeds based on the linear determinacy and show the results on the existence of traveling waves. We also study a …
Mathematical Studies Of The Glucose-Insulin Regulatory System Models., Minghu Wang
Mathematical Studies Of The Glucose-Insulin Regulatory System Models., Minghu Wang
Electronic Theses and Dissertations
Three dynamic models are proposed to study the mechanism of glucose-insulin regulatory system and the possible causes of diabetes mellitus. The progression of diabetes comes along with the apoptosis of pancreatic beta-cells. A dynamical system model is formulated based on physiology and studied by geometric singular perturbation theory. The analytical studies reveal rich analytical features, such as persistence of solutions, Hopf bifurcation and backward bifurcation, while numerical studies successfully fit available longitudinal T2DM data of Pima Indian tribe. These studies together not only validate our model, but also point out key intrinsic factors leading to the development of T2DM. We …
The Pc-Tree Algorithm, Kuratowski Subdivisions, And The Torus., Charles J. Suer
The Pc-Tree Algorithm, Kuratowski Subdivisions, And The Torus., Charles J. Suer
Electronic Theses and Dissertations
The PC-Tree algorithm of Shih and Hsu (1999) is a practical linear-time planarity algorithm that provides a plane embedding of the given graph if it is planar and a Kuratowski subdivision otherwise. Remarkably, there is no known linear-time algorithm for embedding graphs on the torus. We extend the PC-Tree algorithm to a practical, linear-time toroidality test for K3;3-free graphs called the PCK-Tree algorithm. We also prove that it is NP-complete to decide whether the edges of a graph can be covered with two Kuratowski subdivisions. This greatly reduces the possibility of a polynomial-time toroidality testing algorithm based solely on edge-coverings …
Chaos In Semiflows., Chad Money
Chaos In Semiflows., Chad Money
Electronic Theses and Dissertations
All the common notions about dynamics in cascades - topological transitivity, periodic points, sensitive dependence, and so forth - can be formulated in the context of a general abelian semiflow. Many intricate results, such as the redundancy of Devaney chaos, remain true (with very minor qualifications) in this wider context. However, when we examine general monoid actions on a product space, it turns out that the topological and algebraic structure of N0 plays a large role in the preservation of chaotic properties. In order to obtain meaningful results in that arena, new ideas such as “directional” and “synnrec” are introduced, …
Strong Quota Pair Systems And May's Theorem On Median Semilattices., Lucas Hoots
Strong Quota Pair Systems And May's Theorem On Median Semilattices., Lucas Hoots
Electronic Theses and Dissertations
Kenneth May [16], in 1952, characterized simple majority rule in terms of three conditions: anonymity, neutrality, and positive responsiveness. In this thesis, we remove the condition of neutrality and obtain a characterization of the class of voting rules that satisfy anonymity and positive responsiveness. The key concept in this characterization is the notion of a strong quota pair system. The situation with two alternatives studied by May can be thought of as a very simple example of a finite median semilattice. The main result of this thesis is an extension of May’s theorem to the domain of all finite median …
Order Automorphisms On The Lattice Of Residuated Maps Of Some Special Nondistributive Lattices., Erika D. Foreman
Order Automorphisms On The Lattice Of Residuated Maps Of Some Special Nondistributive Lattices., Erika D. Foreman
Electronic Theses and Dissertations
The residuated maps from a lattice L to itself form their own lattice, which we denote Res(L). In this dissertation, we explore the order automorphisms on the lattice Res(L) where L is a finite nondistributive lattice. It is known that left and right composition of f ∈ Res(L) with automorphisms of L yields an order automorphism of Res(L). It begs the question, then, if all order automorphisms of Res(L) can be classified as such.
Improved Self-Consistency For Sced-Lcao., Lyle C. Smith
Improved Self-Consistency For Sced-Lcao., Lyle C. Smith
Electronic Theses and Dissertations
In this document I describe a novel implementation of the generalized bisection method for finding roots of highly non-linear functions of several variables. Several techniques were optimized to reduce computation time. The implementation of the bisection method allows for the calculation of heterogeneous systems with SCED-LCAO, since derivative-based methods often fail for these systems. Systems composed of Gallium and Nitrogen are currently receiving much interest due to their behavior as semi-conductors and their ability to form nano-wires. The methods developed here were employed to create a set of SCED-LCAO parameters for homogeneous Gallium and heterogeneous Gallium Nitride systems. These parameters …