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Enabling And Threatening Factors Affecting Persistence. A Qualitative And Quantitative Study On Rural First-Generation Stem Students’ And Stem Faculty's Perspectives., Travis A. Miller

Graduate Theses, Dissertations, and Problem Reports

This study focuses on the factors that enable and threaten rural first-generation STEM students’ persistence. Limited empirical studies are available that focus on rural first-generation STEM majors’ persistence. Quantitative analysis was conducted using Kruskal Wallis H and Mann-Whitney U tests to determine any significant differences with the survey results. Content and thematic analysis was conducted on the student and faculty interviews to determine themes of enabling and threatening factors affecting persistence.

Enabling factors affecting persistence were found to be: Drive or Motivation, Experiences and skills, and Support. These were both faculty and student interview themes whereas a …

From Graph Coloring To Receptor Clustering, Ye Chen

Graduate Theses, Dissertations, and Problem Reports

1. Hued colorings for planar graphs, graphs of higher genus and K4-minor free graphs.;For integers k, r > 0, a (k,r) -coloring of a graph G is a proper coloring of the vertices of G with k colors such that every vertex v of degree d(v) is adjacent to vertices with at least min{lcub}d(v) ,r{rcub} different colors. The r-hued chromatic number, denoted by Xr (G), is the smallest integer k for which a graph G has a ( k,r)-coloring. A list assignment L of G is a function that assigns to every vertex v of G a set L(v) of positive …

Continuities On Subspaces, Timothy James Glatzer

Graduate Theses, Dissertations, and Problem Reports

We define a generalized continuity by declaring that for any family S of subsets of a topological space X, a function f : X → Y is S -continuous if for each S∈ S , the function f ↾ S : S → Y is continuous. This is easily seen to generalize such well known concepts as separate continuity and linear continuity. Using this definition as a way to unify several disparate results, we attempt to create a theory of S -continuity. As a part of this program, we give constructions for S -continuous functions for several natural classes S …

Circuits, Perfect Matchings And Paths In Graphs, Wenliang Tang

Graduate Theses, Dissertations, and Problem Reports

We primarily consider the problem of finding a family of circuits to cover a bidgeless graph (mainly on cubic graph) with respect to a given weight function defined on the edge set. The first chapter of this thesis is going to cover all basic concepts and notations will be used and a survey of this topic.;In Chapter two, we shall pay our attention to the Strong Circuit Double Cover Conjecture (SCDC Conjecture). This conjecture was verified for some graphs with special structure. As the complement of two factor in cubic graph, the Berge-Fulkersen Conjecture was introduced right after SCDC Conjecture. …

Connectivity And Spanning Trees Of Graphs, Xiaofeng Gu

Graduate Theses, Dissertations, and Problem Reports

This dissertation focuses on connectivity, edge connectivity and edge-disjoint spanning trees in graphs and hypergraphs from the following aspects.;1. Eigenvalue aspect. Let lambda2(G) and tau( G) denote the second largest eigenvalue and the maximum number of edge-disjoint spanning trees of a graph G, respectively. Motivated by a question of Seymour on the relationship between eigenvalues of a graph G and bounds of tau(G), Cioaba and Wong conjectured that for any integers d, k ≥ 2 and a d-regular graph G, if lambda 2(G)) < d -- 2k-1d+1 , then tau(G) ≥ k. They proved the conjecture for k = 2, 3, and presented evidence for the cases when k ≥ 4. We propose a more general conjecture that for a graph G with minimum degree delta ≥ 2 k ≥ 4, if lambda2(G) < delta -- 2k-1d+1 then tau(G) ≥ k. We prove the conjecture for k = 2, 3 and provide partial results for k ≥ 4. We also prove that for a graph G with minimum degree delta ≥ k ≥ 2, if lambda2( G) < delta -- 2k-1d +1 , then the edge connectivity is at least k. As corollaries, we investigate the Laplacian and signless Laplacian eigenvalue conditions on tau(G) and edge connectivity.;2. Network reliability aspect. With graphs considered as natural models for many network design problems, edge connectivity kappa'(G) and maximum number of edge-disjoint spanning trees tau(G) of a graph G have been used as measures for reliability and strength in communication networks modeled as graph G. Let kappa'(G) = max{lcub}kappa'(H) : H is a subgraph of G{rcub}. We present: (i) For each integer k > 0, a characterization for graphs G with the property that kappa'(G) ≤ k but for any additional …

Group Connectivity Of Graphs, Senmei Yao

Graduate Theses, Dissertations, and Problem Reports

Tutte introduced the theory of nowhere-zero flows and showed that a plane graph G has a face k-coloring if and only if G has a nowhere-zero A-flow, for any Abelian group A with |A| ≥ k. In 1992 Jaeger et al. [16] extended nowhere-zero flows to group connectivity of graphs: given an orientation D of a graph G, if for any b: V (G) A with sumv∈ V(G ) b(v) = 0, there always exists a map ƒ: E(G) A - {lcub}0{rcub}, such that at each v ∈ V(G), e=vw isdirectedfrom vtow fe- e=uvi sdirectedfrom utov fe=b v in A, …

Optimal Portfolio And Consumption With Transaction Costs, Zheng Zhang

Graduate Theses, Dissertations, and Problem Reports

In Chapter 1, we study optimal portfolio and consumption with both fixed and proportional transaction costs. For a power utility function we find an explicit solution to the HJB equation governing the no-transaction region. Based on the explicit solution, we formulate a combined stochastic and impulse control problem as a quasi-variational inequality and find the transaction regions, the no-transaction region, and the boundary curves separating them. We show that the explicit solution we find satisfies the verification theorem and it is also a viscosity solution for the quasi-variational inequality. We present numerical results where we compare the various cases of …

Integer Flows And Modulo Orientations, Yezhou Wu

Graduate Theses, Dissertations, and Problem Reports

Tutte's 3-flow conjecture (1970's) states that every 4-edge-connected graph admits a nowhere-zero 3-flow. A graph G admits a nowhere-zero 3-flow if and only if G has an orientation such that the out-degree equals the in-degree modulo 3 for every vertex. In the 1980ies Jaeger suggested some related conjectures. The generalized conjecture to modulo k-orientations, called circular flow conjecture, says that, for every odd natural number k, every (2k-2)-edge-connected graph has an orientation such that the out-degree equals the in-degree modulo k for every vertex. And the weaker conjecture he made, known as the weak 3-flow conjecture where he suggests that …

Perfect Matching And Circuit Cover Of Graphs, Dong Ye

Graduate Theses, Dissertations, and Problem Reports

The research of my dissertation is motivated by the Circuit Double Cover Conjecture due to Szekeres and independently Seymour, that every bridgeless graph G has a family of circuits which covers every edge of G twice. By Fleischner's Splitting Lemma, it suffices to verify the circuit double cover conjecture for bridgeless cubic graphs.;It is well known that every edge-3-colorable cubic graph has a circuit double cover. The structures of edge-3-colorable cubic graphs have strong connections with the circuit double cover conjecture. In chapter two, we consider the structure properties of a special class of edge-3-colorable cubic graphs, which has an …

Cycles, Disjoint Spanning Trees And Orientations Of Graphs, Yanting Liang

Graduate Theses, Dissertations, and Problem Reports

A graph G is hamiltonian-connected if any two of its vertices are connected by a Hamilton path (a path including every vertex of G); and G is s-hamiltonian-connected if the deletion of any vertex subset with at most s vertices results in a hamiltonian-connected graph. We prove that the line graph of a (t + 4)-edge-connected graph is (t + 2)-hamiltonian-connected if and only if it is (t + 5)-connected, and for s ≥ 2 every (s + 5)-connected line graph is s-hamiltonian-connected.;For integers l and k with l > 0, and k ≥ 0, Ch( l, k) denotes the collection …

Cycles And Bases Of Graphs And Matroids, Ping Li

Graduate Theses, Dissertations, and Problem Reports

The objective of this dissertation is to investigate the properties of cycles and bases in matroids and in graphs. In [62], Tutte defined the circuit graph of a matroid and proved that a matroid is connected if and only if its circuit graph is connected. Motivated by Tutte's result, we introduce the 2nd order circuit graph of a matroid, and prove that for any connected matroid M other than U1,1, the second order circuit graph of M has diameter at most 2 if and only if M does not have a restricted minor isomorphic to U2,6.;Another research conducted in this …

Mathematical Modeling And Analysis Of Epidemiological And Chemical Systems, Calistus N. Ngonghala

Graduate Theses, Dissertations, and Problem Reports

This dissertation focuses on three interdisciplinary areas of applied mathematics, mathematical biology/epidemiology, economic epidemiology and mathematical physics, interconnected by the concepts and applications of dynamical systems.;In mathematical biology/epidemiology, a new deterministic SIS modeling framework for the dynamics of malaria transmission in which the malaria vector population is accounted for at each of its developmental stages is proposed. Rigorous qualitative and quantitative techniques are applied to acquire insights into the dynamics of the model and to identify and study two epidemiological threshold parameters reals* and R0 that characterize disease transmission and prevalence, and that can be used for disease control. It …

Group Colorability And Hamiltonian Properties Of Graphs, Hao Li

Graduate Theses, Dissertations, and Problem Reports

The research of my dissertation was motivated by the conjecture of Thomassen that every 4-connected line graph is hamiltonian and by the conjecture of Matthews and Sumner that every 4-connected claw-free graph is hamiltonian. Towards the hamiltonian line graph problem, we proved that every 3-edge-connected, essentially 4-edge-connected graph G has a spanning eulerian subgraph, if for every pair of adjacent vertices u and v, dG(u) + dG(v) ≥ 9. A straight forward corollary is that every 4-connected, essentially 6-connected line graph with minimum degree at least 7 is hamiltonian.;We also investigate graphs G such that the line graph L(G) is …

Reduced Order Model Of A Spouted Fluidized Bed Utilizing Proper Orthogonal Decomposition, Stephanie R. Beck-Roth

Graduate Theses, Dissertations, and Problem Reports

A reduced order model utilizing proper orthogonal decomposition for approximation of gas and solids velocities as well as pressure, solids granular temperature and gas void fraction for use in multiphase incompressible fluidized beds is developed and presented. The methodology is then tested on data representing a flat-bottom spouted fluidized bed and comparative results against the software Multiphase Flow with Interphase eXchanges (MFIX) are provided. The governing equations for the model development are based upon those implemented in the (MFIX) software. The three reduced order models explored are projective, extrapolative and interpolative. The first is an extension of the system solution …

Graph Coloring And Flows, Xiaofeng Wang

Graduate Theses, Dissertations, and Problem Reports

Part 1. The Fulkerson Conjecture states that every cubic bridgeless graph has six perfect matchings such that every edge of the graph is contained in exactly two of these perfect matchings. In this paper, we verify the conjecture for some families of snarks (Goldberg snarks, flower snarks) by using a technical lemma.;Part 2. A star coloring of an undirected graph G is a proper vertex coloring of G such that any path of length 3 in G is not bi-colored. The star chromatic number of a family of graphs G , denoted by chis( G ), is the minimum number …

Hamiltonian Line Graphs And Claw -Free Graphs, Huiya Yan

Graduate Theses, Dissertations, and Problem Reports

The research of my dissertation was motivated by the conjecture of Thomassen that every 4-connected line graph is hamiltonian and by the conjecture of Matthews and Sumner that every 4-connected claw-free graph is hamiltonian. Towards the hamiltonian line graph problem, we proved that every 3-connected claw-free Z8-free graph is hamiltonian, where Z8 is obtained by identifying one end-vertex of P9 with one vertex of a triangle; let hc( G) denote the least integer m such that the iterated line graph Lm(G) is Hamilton-connected, we showed that k -- 1 ≤ hc( G) ≤ max{lcub}diam(G), k -- 1{rcub}, where k is …

Numerical Solutions Of Boundary Inverse Problems For Some Elliptic Partial Differential Equations, Suxing Zeng

Graduate Theses, Dissertations, and Problem Reports

In this dissertation, we study boundary inverse problems for some elliptic partial differential equations. These are problems arising from quantitative analysis of various non-destructive testing techniques in applications. In such a problem, we are interested in using boundary measurements of the solution to recover either an unknown coefficient function in the boundary condition, or a portion of the boundary, or an unknown interior interface. We first introduce formulations of the boundary value problems into integral equations, then design numerical algorithms for solving each of these inverse problems. Numerical implementation and examples are presented to illustrate the feasibility and effectiveness of …

Pierce-Engel Hybrid Expansions, Andrea Sutyak

Graduate Theses, Dissertations, and Problem Reports

Pierce and Engel expansions are representations of numbers between 0 and 1 as sums of unitary fractions (of alternating signs in the case of Pierce) whose denominators are built multiplicatively, choosing the successive factors greedily. We show some results for Pierce expansions, and investigate the idea of hybrid expansions, which are built similarly but without regard to the signs of the terms.

Cycles In Graph Theory And Matroids, Ju Zhou

Graduate Theses, Dissertations, and Problem Reports

A circuit is a connected 2-regular graph. A cycle is a graph such that the degree of each vertex is even. A graph G is Hamiltonian if it has a spanning circuit, and Hamiltonian-connected if for every pair of distinct vertices u, v ∈ V( G), G has a spanning (u, v)-path. A graph G is s-Hamiltonian if for any S ⊆ V (G) of order at most s, G -- S has a Hamiltonian-circuit, and s-Hamiltonian connected if for any S ⊆ V( G) of order at most s, G -- S is Hamiltonian-connected. In this dissertation, we investigated …

Solutions For 2-Dimensional Stabilized Kuramoto -Sivashinsky System, Maomao Cai

Graduate Theses, Dissertations, and Problem Reports

We study a stabilized Kuramoto-Sivanshinsky system in two-dimensional space. A model consists of a mixed Kuramoto-Sivanshinsky-Korteweg-de Vires equation, linearly coupled to an extra linear dissipative equation. The model is proposed to describe the surface waves on multi-layered liquid films. In this work, we investigate the stability of the solution to this system by establishing a priori energy estimate for the linearized problem of this non-linear system. We use linear iteration to prove the local existence of the solution to this system. Based on a weak global priori energy estimate, we further prove the global existence and uniqueness of classical solution …

Nonlinear Approximation Using Blaschke Polynomials, Daniel Van Vliet

Graduate Theses, Dissertations, and Problem Reports

This dissertation, entitled Nonlinear Approximation Using Blaschke Polynomials, is motivated by questions arising from Empirical Mode Decomposition (EMD). EMD is a signal processing method which decomposes input signals into components called intrinsic mode functions (IMFs). These IMFs often have the desirable property that the instantaneous frequency of their analytic signals is positive. However, this is not always the case.;The first two chapters are introductions to approximation in general, and Empirical Mode Decomposition, respectively.;The third chapter presents a characterization of which analytic signals have the property of non-negative instantaneous frequency. These 'analytic signals with non-negative instantaneous frequency' (ASNIFs) are described using …

Integer Flow And Petersen Minor, Taoye Zhang

Graduate Theses, Dissertations, and Problem Reports

Tutte [45] conjectured that every bridgeless Petersen-minor free graph admits a nowhere-zero 4-flow. Let P10 m&d1; ) be the graph obtained from the Petersen graph by contracting mu edges from a perfect matching. In chapter 1 we prove that every bridgeless P10 3&d1; -minor free graph admits a nowhere-zero 4-flow.;Walton and Welsh [48] proved that if a coloopless regular matroid M does not have a minor in {lcub}M(K 3,3), M*(K5){rcub}, then M admits a nowhere zero 4-flow. Lai et al [27] proved that if M does not have a minor in {lcub}M( K5), M*(K5){rcub}, then M admits a nowhere zero …

Asymptotic Solutions Of Almost Diagonal Differential And Difference Systems, Fei Xue

Graduate Theses, Dissertations, and Problem Reports

New methods for both asymptotic integration of the linear differential systems Y'(t) = [D( t) + R(t)]Y( t) and asymptotic summation of the linear difference systems Y(t + 1) = [D(t)+ R(t)]Y(t) are derived. The fundamental solution Y(t) = phi( t)[I+P(t)] for differential and difference systems is constructed in terms of a product. The first matrix function phi(t) is decided by the diagonal matrix D(t) and the second matrix I + P(t) is a perturbation of the identity matrix I. Another fundamental solution Y( t) = [I + Q(t)]phi( t) is also constructed for difference systems. Conditions are given on …

Some New Methods For Image Compression, Muhammad Aslam

Graduate Theses, Dissertations, and Problem Reports

The vanishing moment of wavelets and associated multi-resolution framework yield an efficient representation of smooth functions with wavelet approximation. However as pointed out in many papers, the similar result cannot be expected for the piecewise smooth functions with large jumps. In other words, wavelet approximation cannot achieve the same approximation order in the vicinity of jumps as in the smooth regions. Large wavelet coefficients associated with jumps are generated and consequently produce oscillations near discontinuities in the reconstructed signal. This is the so-called Gibbs phenomenon or a Ringing effect. In this thesis, we develop a technique which reduces the Gibbs …

Maximum Size T-Cross-Intersecting And Intersecting Families With Degree Conditions, Yongbin Ou

Graduate Theses, Dissertations, and Problem Reports

We present four main results: (1) A solution to the problem of finding two set systems A and B such that A is r1-intersecting, B is r2-intersecting, A,B are t-cross-intersecting and A+ B is a maximum; (2) A solution to the problem of finding two set systems A and B such that A,B are Sperner, t-cross-intersecting and A+ B is a maximum; (3) A solution to the problem of finding the maximum size of an intersecting set system F such that the complementary degree c( F ) = s for a specified value s; (4) An asymptotic result on the …

Claw -Free Graphs And Line Graphs, Yehong Shao

Graduate Theses, Dissertations, and Problem Reports

The research of my dissertation is motivated by the conjecture of Thomassen that every 4-connected line graph is hamiltonian and by the conjecture of Tutte that every 4-edge-connected graph has a no-where-zero 3-flow. Towards the hamiltonian line graph problem, we proved that every 3-connected N2-locally connected claw-free graph is hamiltonian, which was conjectured by Ryjacek in 1990; that every 4-connected line graph of an almost claw free graph is hamiltonian connected, and that every triangularly connected claw-free graph G with |E( G)| ≥ 3 is vertex pancyclic. Towards the second conjecture, we proved that every line graph of a 4-edge-connected …

The Hyperspace Graph Of Connected Subgraphs, Likin C. Simon Romero

Graduate Theses, Dissertations, and Problem Reports

Given a connected graph G, the hyperspace graph of connected subgraphs C (G) is defined. The graph C (G) is such that every vertex represents a connected subgraph of G. It is shown that every connected graph G has a unique graph C (G). A characterization of a path, a cycle and the 3-star by their corresponding hyperspace graphs of connected subgraphs is shown. A special geometric representation R (G) of C (G) in an euclidean space is presented. A set P (G) is constructed based on R (G). When G is a topological tree, P (G) and the hyperspace …

Applications Of The Covering Property Axiom, Andres Millan Millan

Graduate Theses, Dissertations, and Problem Reports

The purpose of this work is two-fold. First, we present some consequences of the Covering Property Axiom CPA of Ciesielski and Pawlikowski which captures the combinatorial core of the Sacks' model of the set theory. Second, we discuss the assumptions in the formulation of different versions of CPA.;As our first application of CPA we prove that under the version CPAgamecube of CPA there are uncountable strong gamma-sets on R . It is known that Martin's Axiom (MA) implies the existence of a strong gamma-set on R . Our result is interesting since that CPAgamecube implies the negation of MA.;Next, we …

Enumeration Of The Generalized Catalan Numbers, Steven L. Richardson Jr.

Graduate Theses, Dissertations, and Problem Reports

The sequence of numbers given by the equation Cn=1n +12nn are widely known as the Catalan numbers, because they were first studied by Catalan. The ways to enumerate these numbers are similarly widely known and studied, as can be seen in Gould's catalog of Catalan numbers. Our objective is to find ways to enumerate this larger and generalized set of sequences, using multiple methods that will build on known enumerations of the Catalan numbers.

Graph Minor, Jianbing Niu

Graduate Theses, Dissertations, and Problem Reports

In this paper, we present three results: (1) Let G be a (k + 2)-connected non-(k - 3)-apex graph where k ≥ 2. If G contains three k-cliques, say L 1, L2, L3, such that |Li ∩ Lj| ≤ k - 2 (1 ≤ i < j ≤ 3), then G contains a Kk +2 as a minor. (2) Let G be a 6-connected claw-free graph. If delta(G) ≥ 7 and G contains three disjoint 5-cliques, say Ll, L2, L3, then G contains a K7 as a minor. (3) There is a function h : N → N, such that, for every 4-connected graph G with minimum degree at least five embedded in a surface with Euler genus g and face-width at least h(g), every longest circuit of the graph G has a chord.