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Articles 481 - 510 of 548
Full-Text Articles in Mathematics
Four-Body Problem With Collision Singularity, Duokui Yan
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 …
The Expectation Of Transition Events On Finite-State Markov Chains, Jeremy Michael West
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 …
The Orbifold Landau-Ginzburg Conjecture For Unimodal And Bimodal Singularities, Natalie Wilde Bergin
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 …
Some Congruence Properties Of Pell's Equation, Nathan C. Priddis
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
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
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
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, …
Fusion Of The Parastrophic Matrix And Weak Cayley Table, Nathan C. Perry
Fusion Of The Parastrophic Matrix And Weak Cayley Table, Nathan C. Perry
Theses and Dissertations
The parastrophic matrix and Weak Cayley Tables are matrices that have close ties to the character table. Work by Ken Johnson has shown that fusion of groups induces a relationship between the character tables of the groups. In this paper we will demonstrate a similar induced relationship between the parastrophic matrices and Weak Cayley Tables of the fused groups.
Topics In Analytic Number Theory, Kevin James Powell
Topics In Analytic Number Theory, Kevin James Powell
Theses and Dissertations
The thesis is in two parts. The first part is the paper “The Distribution of k-free integers” that my advisor, Dr. Roger Baker, and I submitted in February 2009. The reader will note that I have inserted additional commentary and explanations which appear in smaller text. Dr. Baker and I improved the asymptotic formula for the number of k-free integers less than x by taking advantage of exponential sum techniques developed since the 1980's. Both of us made substantial contributions to the paper. I discovered the exponent in the error term for the cases k=3,4, and worked the case k=3 …
Alternating Links And Subdivision Rules, Brian Craig Rushton
Alternating Links And Subdivision Rules, Brian Craig Rushton
Theses and Dissertations
The study of geometric group theory has suggested several theorems related to subdivision tilings that have a natural hyperbolic structure. However, few examples exist. We construct subdivision tilings for the complement of every nonsingular, prime alternating link and all torus links, and explore some of their properties and applications. Several examples are exhibited with color coding of tiles.
Creating Multi Objective Value Functions From Non-Independent Values, Christopher D. Richards
Creating Multi Objective Value Functions From Non-Independent Values, Christopher D. Richards
Theses and Dissertations
Decisions are made every day and by everyone. As these decisions become more important, involve higher costs and affect a broader group of stakeholders it becomes essential to establish a more rigorous strategy than simply intuition or "going with your gut". In the past several decades, the concept of Value Focused Thinking (VFT) has gained much acclaim in assisting Decision Makers (DMs) in this very effort. By identifying and organizing what a DM values VFT is able to decompose the original problem and create a mathematical model to score and rank alternatives to be chosen. But what if the decision …
Dynamics And Rheology Of Biaxial Liquid Crystal Polymers, Sarthok K. Sircar
Dynamics And Rheology Of Biaxial Liquid Crystal Polymers, Sarthok K. Sircar
Theses and Dissertations
In this thesis we derive a hydrodynamical kinetic theory to study the orientational response of a mesoscopic system of nematic liquid crystals in the presence of an external flow field. Various problems have been attempted in this direction. First, we understand the steady-state behavior of uniaxial LCPs under an imposed elongational flow, electric and magnetic field respectively. We show that (1) the Smoluchowski equation can be cast into a generic form, (2) the external field is parallel to one of the eigenvectors of the second moment tensor, and (3) the steady state probability density function is of the Boltzmann type. …
Lyapunov Exponents And Invariant Manifold For Random Dynamical Systems In A Banach Space, Zeng Lian
Lyapunov Exponents And Invariant Manifold For Random Dynamical Systems In A Banach Space, Zeng Lian
Theses and Dissertations
We study the Lyapunov exponents and their associated invariant subspaces for infinite dimensional random dynamical systems in a Banach space, which are generated by, for example, stochastic or random partial differential equations. We prove a multiplicative ergodic theorem. Then, we use this theorem to establish the stable and unstable manifold theorem for nonuniformly hyperbolic random invariant sets.
The Tropical Jacobian Of A Tropical Elliptic Curve Is S^1(Q), Darryl Gene Wade
The Tropical Jacobian Of A Tropical Elliptic Curve Is S^1(Q), Darryl Gene Wade
Theses and Dissertations
We establish consistent definitions for divisors, principal divisors, and Jacobians of a tropical elliptic curve and show that for a tropical elliptic cubic C , the associated Jacobian (or zero divisor class group) is the group S^1(Q).
Complete Tropical Bezout's Theorem And Intersection Theory In The Tropical Projective Plane, Gretchen Rimmasch
Complete Tropical Bezout's Theorem And Intersection Theory In The Tropical Projective Plane, Gretchen Rimmasch
Theses and Dissertations
In this dissertation we prove a version of the tropical Bezout's theorem which is applicable to all tropical projective plane curves. There is a version of tropical Bezout's theorem presented in other works which applies in special cases, but we provide a proof of the theorem for all tropical projective plane curves. We provide several different definitions of intersection multiplicity and show that they all agree. Finally, we will use a tropical resultant to determine the intersection multiplicity of points of intersection at infinite distance. Using these new definitions of intersection multiplicity we prove the complete tropical Bezout's theorem.
Rational Schur Rings Over Abelian Groups, Brent L. Kerby
Rational Schur Rings Over Abelian Groups, Brent L. Kerby
Theses and Dissertations
In 1993, Muzychuk showed that the rational S-rings over a cyclic group Z_n are in one-to-one correspondence with sublattices of the divisor lattice of n, or equivalently, with sublattices of the lattice of subgroups of Z_n. This idea is easily extended to show that for any finite group G, sublattices of the lattice of characteristic subgroups of G give rise to rational S-rings over G in a natural way. Our main result is that any finite group may be represented as the automorphism group of such a rational S-ring over an abelian p-group. In order to show this, we first …
Homomorphisms Into The Fundamental Group Of One-Dimensional And Planar Peano Continua, Curtis Andrew Kent
Homomorphisms Into The Fundamental Group Of One-Dimensional And Planar Peano Continua, Curtis Andrew Kent
Theses and Dissertations
Let X be a planar or one-dimensional Peano continuum. Let E be a Hawaiian Earring with fundamental group H. We show that every homomorphism from H to the fundamental group of X is conjugate to a homomorphism which is induced by a continuous function.
Fusion Of Character Tables And Schur Rings Of Dihedral Groups, Long Pham Bao Nguyen
Fusion Of Character Tables And Schur Rings Of Dihedral Groups, Long Pham Bao Nguyen
Theses and Dissertations
A finite group H is said to fuse to a finite group G if the class algebra of G is isomorphic to an S-ring over H which is a subalgebra of the class algebra of H. We will also say that G fuses from H. In this case, the classes and characters of H can fuse to give the character table of G. We investigate the case where H is the dihedral group. In many cases, G can be completely determined. In general, G can be proven to have many interesting properties. The theory is developed in terms of S-ring …
Lifting Galois Representations In A Conjecture Of Figueiredo, Wayne Bennett Rosengren
Lifting Galois Representations In A Conjecture Of Figueiredo, Wayne Bennett Rosengren
Theses and Dissertations
In 1987, Jean-Pierre Serre gave a conjecture on the correspondence between degree 2 odd irreducible representations of the absolute Galois group of Q and modular forms. Letting M be an imaginary quadratic field, L.M. Figueiredo gave a related conjecture concerning degree 2 irreducible representations of the absolute Galois group of M and their correspondence to homology classes. He experimentally confirmed his conjecture for three representations arising from PSL(2,3)-polynomials, but only up to a sign because he did not lift them to SL(2,3)-polynomials. In this paper we compute explicit lifts and give further evidence that his conjecture is accurate.
Modeling The Hydrolyzing Action Of Secretory Phospholipase A2 With Ordinary Differential Equations And Monte Carlo Methods, Zijun Lan Dozier
Modeling The Hydrolyzing Action Of Secretory Phospholipase A2 With Ordinary Differential Equations And Monte Carlo Methods, Zijun Lan Dozier
Theses and Dissertations
Although cell membranes normally resist the hydrolysis of secretory phospholipase A2, a series of current investigations demonstrated that the changes in lipid order caused by increased calcium has a relationship with the susceptibility to phospholipase A2. To further explore this relationship, we setup ordinary differential equations models, statistic models and stochastic models to compare the response of human erythrocytes to the hydrolyzing action of secretory phospholipase A2 and the relationship between the susceptibility of hydrolysis and the physical properties of secretory phospholipase A2. Furthermore, we use models to determine the ability of calcium ionophore to increased membrane susceptibility.
Analysis And Implementation Of High-Order Compact Finite Difference Schemes, Jonathan G. Tyler
Analysis And Implementation Of High-Order Compact Finite Difference Schemes, Jonathan G. Tyler
Theses and Dissertations
The derivation of centered compact schemes at interior and boundary grid points is performed and an analysis of stability and computational efficiency is given. Compact schemes are high order implicit methods for numerical solutions of initial and/or boundary value problems modeled by differential equations. These schemes generally require smaller stencils than the traditional explicit finite difference counterparts. To avoid numerical instabilities at and near boundaries and in regions of mesh non-uniformity, a numerical filtering technique is employed. Experiments for non-stationary linear problems (convection, heat conduction) and also for nonlinear problems (Burgers' and KdV equations) were performed. The compact solvers were …
The Minimum Rank Problem Over Finite Fields, Jason Nicholas Grout
The Minimum Rank Problem Over Finite Fields, Jason Nicholas Grout
Theses and Dissertations
We have two main results. Our first main result is a sharp bound for the number of vertices in a minimal forbidden subgraph for the graphs having minimum rank at most 3 over the finite field of order 2. We also list all 62 such minimal forbidden subgraphs and show that many of these are minimal forbidden subgraphs for any field. Our second main result is a structural characterization of all graphs having minimum rank at most k for any k over any finite field. This characterization leads to a very strong connection to projective geometry and we apply projective …
Infinite Product Group, Keith G. Penrod
Infinite Product Group, Keith G. Penrod
Theses and Dissertations
The theory of infinite multiplication has been studied in the case of the Hawaiian earring group, and has been seen to simplify the description of that group. In this paper we try to extend the theory of infinite multiplication to other groups and give a few examples of how this can be done. In particular, we discuss the theory as applied to symmetric groups and braid groups. We also give an equivalent definition to K. Eda's infinitary product as the fundamental group of a modified wedge product.
Pipe Diagrams For Thompson's Group F, Aaron L. Peterson
Pipe Diagrams For Thompson's Group F, Aaron L. Peterson
Theses and Dissertations
We review the definition and standard description of Thompson's Group F. We define the set of pipe diagrams and show that this set forms a group isomorphic to F. We use pipe diagrams to prove two theorems about giving a minimal representation for an arbitrary element of F.
On Connections Between Univalent Harmonic Functions, Symmetry Groups, And Minimal Surfaces, Stephen M. Taylor
On Connections Between Univalent Harmonic Functions, Symmetry Groups, And Minimal Surfaces, Stephen M. Taylor
Theses and Dissertations
We survey standard topics in elementary differential geometry and complex analysis to build up the necessary theory for studying applications of univalent harmonic function theory to minimal surfaces. We then proceed to consider convex combination harmonic mappings of the form f=sf_1+(1-s) f_2 and give conditions on when f lifts to a one-parameter family of minimal surfaces via the Weierstrauss-Enneper representation formula. Finally, we demand two minimal surfaces M and M' be locally isometric, formulate a system of partial differential equations modeling this constraint, and calculate their symmetry group. The group elements generate transformations that when applied to a prescribed harmonic …
The Relationship Between The Minimal Rank Of A Tree And The Rank-Spreads Of The Vertices And Edges, John Henry Sinkovic
The Relationship Between The Minimal Rank Of A Tree And The Rank-Spreads Of The Vertices And Edges, John Henry Sinkovic
Theses and Dissertations
Let F be a field, G = (V,E) be an undirected graph on n vertices, and let S(F,G) be the set of all symmetric n × n matrices whose nonzero off-diagonal entries occur in exactly the positions corresponding to the edges of G. Let mr(F,G)be the minimum rank over all matrices in S(F,G). We give a field independent proof of a well-known result that for a tree the sum of its path cover number and minimal rank is equal to the number of vertices in the tree. The rank-spread of a vertex v of G is the difference between the …
Knots Not For Naught, Sharleen Adrienne Roberts
Knots Not For Naught, Sharleen Adrienne Roberts
Theses and Dissertations
The goal of this paper is to find the Homfly polynomial for each knot in a specific family of knots. This family of knots is generated from placing the Whitehead link into a solid torus, slicing the torus at a spot where the Whitehead has no crossings and then twisting the torus 360 degrees in either direction an integral number of times. Let L(n) denote the knot obtained by twisting the torus 360 degrees, n times. Note that n is an integer. Let the twists be towards the center of the torus for positive n and away from the center …
On The N-Body Problem, Zhifu Xie
On The N-Body Problem, Zhifu Xie
Theses and Dissertations
In this thesis, central configurations, regularization of Simultaneous binary collision, linear stability of Kepler orbits, and index theory for symplectic path are studied. The history of their study is summarized in section 1. Section 2 deals with the following problem: given a collinear configuration of 4 bodies, under what conditions is it possible to choose positive masses which make it central. It is always possible to choose three positive masses such that the given three positions with the masses form a central configuration. However, for an arbitrary configuration of 4 bodies, it is not always possible to find positive masses …
Conjugacy Classes Of The Piecewise Linear Group, Matthew L. Housley
Conjugacy Classes Of The Piecewise Linear Group, Matthew L. Housley
Theses and Dissertations
The piecewise linear group is the set of all piecewise linear orientation preserving homeomorphisms from the interval to itself under the operation of composition. We present here a complete set of invariants to classify the conjugacy classes of this group. Our approach to this problem relies on the factorization of elements into elements having only a single breakpoint.
Topics On The Spectral Theory Of Automorphic Forms, Dustin David Belt
Topics On The Spectral Theory Of Automorphic Forms, Dustin David Belt
Theses and Dissertations
We study the analytic properties of the Eisenstein Series of $frac {1}{2}$-integral weight associated with the Hecke congruence subgroup $Gamma_0(4)$. Using these properties we obtain asymptotics for sums of certain Dirichlet $L$-series. We also obtain a formula reducing the study of Selberg's Eigenvalue Conjecture to the study of the nonvanishing of the Eisenstein Series $E(z,s)$ for Hecke congruence subgroups $Gamma_0(N)$ at $s=frac {1+i}{2}$.