Physical Sciences and Mathematics Commons^™

Analytical And Computational Studies Of Magneto-Convection In Solidifying Mushy Layer, Mallikarjunaiah Siddapura Muddamallappa

Theses and Dissertations - UTB/UTPA

Natural convection in solidifying binary media is of great interest due to it's applications in material processing and crystal growth industries. Convective flows between the layers of melt during alloy solidification is known to produce mechanical imperfections such as freckle's. Hence it is important to investigate the criterion for freckling and discover the means of suppressing it. A mushy layer, which has both solid and fluid components and is formed between underlying solid and overlying liquid, is known to produce chimneys, which are narrow, vertical vents, devoid of solid. We consider the problem of magneto-convection in a horizontal mushy layer …

Reaction-Diffusion Systems With A Nonlinear Rate Of Growth, Yubing Wan

Theses and Dissertations - UTB/UTPA

In the literature there are quite a few elegant approaches which have been proposed to find (he first integrals of nonlinear differential equations. Recently, the modified Prelle-Singer method for finding the first integrals of second-order nonlinear ordinary differential equations (ODEs) has attracted considerable attention. Many researchers used this method to derive the first integrals to various systems. In this thesis, we are concerned with the first integrals for reaction-diffusion systems with a nonlinear rate of growth. Under certain parametric conditions we express the first integrals explicitly by applying an analytical method as well as the modified Prelle-Singer method.

Integrable Equations With Non-Smooth Solitons, Xianqi Li

Theses and Dissertations - UTB/UTPA

In this thesis, we present a class of integrable equations with non-smooth soliton solutions. In particular, we derive the bi-Hamiltonian structure and Lax pair of the equation pt = bux + \[{u2 — u1)p]x,p = u — uxx, which guarantee its integrability. Another interesting integrable equation we study is (=Jff!i)t = 2uux, which is exactly the first member of the negative KdV hierarchy. Through traveling wave setting arid phase step analysis, we obtain non-smooth soliton solutions of these integrable equations under different boundary condition at infinities. These equations were shown to have peaked soliton (peakon), "W/M-shape" peakon or cusped soliton …

Optimal Control Applied To Population And Disease Models, Rachael Lynn Miller Neilan

Doctoral Dissertations

This dissertation considers the use of optimal control theory in population models for the purpose of characterizing strategies of control which minimize an invasive or infected population with the least cost. Three different models and optimal control problems are presented. Each model describes population dynamics via a system of differential equations and includes the effects of one or more control methods.

The first model is a system of two ordinary differential equations describing dynamics between a native population and an invasive population. Population growth terms are functions of the control, constructed so that the value of the control may affect …

Countable Groups As Fundamental Groups Of Compacta In Four-Dimensional Euclidean Space, Ziga Virk

Doctoral Dissertations

This dissertation addresses the question of realization of countable groups as funda- mental groups of continuum. In first chapter we discuss classical realizations in the category of CW complexes. We introduce Eilenberg-Maclane spaces and their topological properties. The second chapter provides recent developments on realization question such as those of Shelah, Keesling, ... The third chapter proves the realization theorem for countable groups. The re- sulting space is compact path connected, connected subspace of four dimensional Euclidean space.

Structure And Properties Of Maximal Outerplanar Graphs., Benjamin Allgeier

Electronic Theses and Dissertations

Outerplanar graphs are planar graphs that have a plane embedding in which each vertex lies on the boundary of the exterior region. An outerplanar graph is maximal outerplanar if the graph obtained by adding an edge is not outerplanar. Maximal outerplanar graphs are also known as triangulations of polygons. The spine of a maximal outerplanar graph G is the dual graph of G without the vertex that corresponds to the exterior region. In this thesis we study metric properties involving geodesic intervals, geodetic sets, Steiner sets, different concepts of boundary, and also relationships between the independence numbers and domination numbers …

Some Congruence Modulo 2 Statements Of Primitive Conway Vassiliev Invariants., James M. Dawson

Masters Theses

Polynomial knot invariants can often be used to define Vassiliev invariants on singu- lar knots. Here Vassiliev invariants form the Conway, Jones, HOMFLY, and Kauffman polynomials are explored. Also, some explanation is given about how symbols of the Jones and Conway polynomial can evaluated on suitable chord diagrams. These in- variants are further used to find expressions that are congruent modulo 2 to some low degree invariants derived from the Primitive Conway polynomial.

Versal Deformations Of Leibniz Algebra., Ashis Mandal Dr.

Doctoral Theses

No abstract provided.

Isomorphism Of Schwartz Spaces Under Fourier Transform., Joydip Jana Dr.

Doctoral Theses

Classical Fourier analysis derives much of its power from the fact that there are three function spaces whose images under the Fourier transform can be exactly determined. They are the Schwartz space, the L2 space and the space of all C ∞ functions of compact support. The determination of the image is obtained from the definition in the case of Schwartz space, through the Plancherel theorem for the L 2space and through the Paley-Wiener theorem for the other space.In harmonic analysis of semisimple Lie groups, function spaces on various restricted set-ups are of interest. Among the multitude of these spaces …

Four-Body Problem With Collision Singularity, Duokui Yan

Theses and Dissertations

In this dissertation, regularization of simultaneous binary collision, existence of a Schubart-like periodic orbit, existence of a planar symmetric periodic orbit with multiple simultaneous binary collisions, and their linear stabilities are studied. The detailed background of those problems is introduced in chapter 1. The singularities of simultaneous binary collision in the collinear four-body problem is regularized in chapter 2. We use canonical transformations to collectively analytically continue the singularities of the simultaneous binary collision solutions in both the decoupled case and the coupled case. All the solutions are found and more importantly, we find a crucial first integral which describes …

Research On Brand Strategies Of Cdl Company, Wei Gu

World Maritime University Dissertations

No abstract provided.

Research On Value-At-Risk In International Crude Oil Shipping Market, Xiaoyin Cui

World Maritime University Dissertations

No abstract provided.

The Feasibility Analysis Of The Third Euro-Asia Continental Bridge, Tongyou Weng

World Maritime University Dissertations

No abstract provided.

Marketing Analysis Of The Chinese Coffee Market: Suggestions For A Logistic System For The Colombian Coffee Exporters, Soraya Margarita Herrera Jaramillo

World Maritime University Dissertations

No abstract provided.

New Eurasian Continental Bridgehead Lianyungang, Qiaoqiao Wu

World Maritime University Dissertations

No abstract provided.

The Research On Optimization Of Liner Route Between China To Middle East, Tingyi Chen

World Maritime University Dissertations

No abstract provided.

Economic Approach Of Piracy Along The Maritime Silk Road And Cost Analysis Of The Northern Sea Route, Petros Kelaiditis

World Maritime University Dissertations

No abstract provided.

The Construction And Development Of Shanghai International Shipping Center, Shimin Wang

World Maritime University Dissertations

No abstract provided.

The Research On Risk Evaluation Of Shanghai Lng Import Program, Chao Lin

World Maritime University Dissertations

No abstract provided.

An Application Of Armitage Trend Test To Genome-Wide Association Studies, Nigel A. Scott

Mathematics Theses

Genome-wide Association (GWA) studies have become a widely used method for analyzing genetic data. It is useful in detecting associations that may exist between particular alleles and diseases of interest. This thesis investigates the dataset provided from problem 1 of the Genetic Analysis Workshop 16 (GAW 16). The dataset consists of GWA data from the North American Rheumatoid Arthritis Consortium (NARAC). The thesis attempts to determine a set of single nucleotide polymorphisms (SNP) that are associated significantly with rheumatoid arthritis. Moreover, this thesis also attempts to address the question of whether the one-sided alternative hypothesis that the minor allele is …

Multistability In Bursting Patterns In A Model Of A Multifunctional Central Pattern Generator., Matthew Bryan Brooks

Mathematics Theses

A multifunctional central pattern generator (CPG) can produce bursting polyrhythms that determine locomotive activity in an animal: for example, swimming and crawling in a leech. Each rhythm corresponds to a specific attractor of the CPG. We employ a Hodgkin-Huxley type model of a bursting leech heart interneuron, and connect three such neurons by fast inhibitory synapses to form a ring. This network motif exhibits multistable co-existing bursting rhythms. The problem of determining rhythmic outcomes is reduced to an analysis of fixed points of Poincare mappings and their attractor basins, in a phase plane defined by the interneurons' phase differences along …

Two Problems On Bipartite Graphs, Albert Bush

Mathematics Theses

Erdos proved the well-known result that every graph has a spanning, bipartite subgraph such that every vertex has degree at least half of its original degree. Bollobas and Scott conjectured that one can get a slightly weaker result if we require the subgraph to be not only spanning and bipartite, but also balanced. We prove this conjecture for graphs of maximum degree 3.

The majority of the paper however, will focus on graph tiling. Graph tiling (or sometimes referred to as graph packing) is where, given a graph H, we find a spanning subgraph of some larger graph G that …

Advanced Statistical Methodologies In Determining The Observation Time To Discriminate Viruses Using Ftir, Shan Luo

Mathematics Theses

Fourier transform infrared (FTIR) spectroscopy, one method of electromagnetic radiation for detecting specific cellular molecular structure, can be used to discriminate different types of cells. The objective is to find the minimum time (choice among 2 hour, 4 hour and 6 hour) to record FTIR readings such that different viruses can be discriminated. A new method is adopted for the datasets. Briefly, inner differences are created as the control group, and Wilcoxon Signed Rank Test is used as the first selecting variable procedure in order to prepare the next stage of discrimination. In the second stage we propose either partial …

The Orbifold Landau-Ginzburg Conjecture For Unimodal And Bimodal Singularities, Natalie Wilde Bergin

Theses and Dissertations

The Orbifold Landau-Ginzburg Mirror Symmetry Conjecture states that for a quasihomogeneous singularity W and a group G of symmetries of W, there is a dual singularity WT and dual group GT such that the orbifold A-model of W/G is isomorphic to the orbifold B-model of WT/GT. The Landau-Ginzburg A-model is the Frobenius algebra HW,G constructed by Fan, Jarvis, and Ruan, and the B-model is the Orbifold Milnor ring of WT . The unorbifolded conjecture has been verified for Arnol'd's list of simple, unimodal and bimodal quasi-homogeneous singularities with G the maximal diagonal symmetry group by Priddis, Krawitz, Bergin, Acosta, et …

The Expectation Of Transition Events On Finite-State Markov Chains, Jeremy Michael West

Theses and Dissertations

Markov chains are a fundamental subject of study in mathematical probability and have found wide application in nearly every branch of science. Of particular interest are finite-state Markov chains; the representation of finite-state Markov chains by a transition matrix facilitates detailed analysis by linear algebraic methods. Previous methods of analyzing finite-state Markov chains have emphasized state events. In this thesis we develop the concept of a transition event and define two types of transition events: cumulative events and time-average events. Transition events generalize state events and provide a more flexible framework for analysis. We derive computable, closed-form expressions for the …

Development Of Scoring Rubrics And Pre-Service Teachers Ability To Validate Mathematical Proofs, Timothy J. Middleton

Mathematics & Statistics ETDs

The basic aim of this exploratory research study was to determine if a specific instructional strategy, that of developing scoring rubrics within a collaborative classroom setting, could be used to improve pre-service teachers facility with proofs. During the study, which occurred in a course for secondary mathematics teachers, the primary focus was on creating and implementing a scoring rubric, rather than on direct instruction about proofs. In general, the study had very mixed results. Statistically, the quantitative data indicated no significant improvement occurred in participants' ability to validate proofs. However, the qualitative results and the considerable improvement by some participants …

Some Congruence Properties Of Pell's Equation, Nathan C. Priddis

Theses and Dissertations

In this thesis I will outline the impact of Pell's equation on various branches of number theory, as well as some of the history. I will also discuss some recently discovered properties of the solutions of Pell's equation.

Evans Function Computation, Blake H. Barker

Theses and Dissertations

In this thesis, we review the stability problem for traveling waves and discuss the Evans function, an emerging tool in the stability analysis of traveling waves. We describe some recent developments in the numerical computation of the Evans function and discuss STABLAB, an interactive MATLAB based tool box that we developed. In addition, we verify the Evans function for shock layers in Burgers equation and the p-system with and without capillarity, as well as pulses in the generalized Kortweg-de Vries (gKdV) equation. We conduct a new study of parallel shock layers in isentropic magnetohydrodynamics (MHD) obtaining results consistent with stability.

Numerical Solutions For Stochastic Differential Equations And Some Examples, Yi Luo

Theses and Dissertations

In this thesis, I will study the qualitative properties of solutions of stochastic differential equations arising in applications by using the numerical methods. It contains two parts. In the first part, I will first review some of the basic theory of the stochastic calculus and the Ito-Taylor expansion for stochastic differential equations (SDEs). Then I will discuss some numerical schemes that come from the Ito-Taylor expansion including their order of convergence. In the second part, I will use some schemes to solve the stochastic Duffing equation, the stochastic Lorenz equation, the stochastic pendulum equation, and the stochastic equations which model …

Properties Of The Zero Forcing Number, Kayla Denise Owens

Theses and Dissertations

The zero forcing number is a graph parameter first introduced as a tool for solving the minimum rank problem, which is: Given a simple, undirected graph G, and a field F, let S(F,G) denote the set of all symmetric matrices A=[a_{ij}] with entries in F such that a_{ij} doess not equal 0 if and only if ij is an edge in G. Find the minimum possible rank of a matrix in S(F,G). It is known that the zero forcing number Z(G) provides an upper bound for the maximum nullity of a graph. I investigate properties of the zero forcing number, …