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Articles 181 - 210 of 255
Full-Text Articles in Mathematics
Quasi-Anosov Diffeomorphisms Of 3-Manifolds, Todd L. Fisher, Hertz M. Rodriguez
Quasi-Anosov Diffeomorphisms Of 3-Manifolds, Todd L. Fisher, Hertz M. Rodriguez
Faculty Publications
In 1969, Hirsch posed the following problem: given a diffeomorphism f:N → N and a compact invariant hyperbolic set Λ of f, describe the topology of Λ and the dynamics of f restricted to Λ. We solve the problem where Λ=M^3 is a closed 3-manifold: if M^3 is orientable, then it is a connected sum of tori and handles; otherwise it is a connected sum of tori and handles quotiented by involutions.
Using A Mathematical Model Of Cadherin-Based Adhesion To Understand The Function Of The Actin Cytoskeleton, J. C. Dallon, Elijah Newren, Marc Hansen
Using A Mathematical Model Of Cadherin-Based Adhesion To Understand The Function Of The Actin Cytoskeleton, J. C. Dallon, Elijah Newren, Marc Hansen
Faculty Publications
The actin cytoskeleton plays a role in cell-cell adhesion but its specific function is not clear. Actin might anchor cadherins or drive membrane protrusions in order to facilitate cell-cell adhesion. Using a mathematical model of the forces involved in cadherin-based adhesion we investigate its possible functions. The immersed boundary method is used to model the cell membrane and cortex with cadherin binding forces added as linear springs. The simulations indicate that cells in suspension can develop normal cell-cell contacts without actin-based cadherin anchoring or membrane protrusions. The cadherins can be fixed in the membrane or free to move and the …
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.
A Review Of Fibroblast Populated Collagen Lattices, J. C. Dallon, Paul H. Ehrlich
A Review Of Fibroblast Populated Collagen Lattices, J. C. Dallon, Paul H. Ehrlich
Faculty Publications
Bellaes introduction of the fibroblast populated collagen lattice (FPCL) (1) has facilitated the study of collagen-cell interactions. As a result of the numerous modifications of the casting of FPCL's, the in vivo applications of these in vitro findings has been confusing. Here experimental FPCL contraction findings are viewed in regard to three proposed mechanisms responsible for lattice contraction. The cellular mechanisms responsible for generating FPCL contraction are: cell contraction, cell tractional forces related to cell locomotion, and initial cell elongation and spreading.
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 …
Constructing Subdivision Rules From Rational Maps, J. W. Cannon, W. J. Floyd, W. R. Parry
Constructing Subdivision Rules From Rational Maps, J. W. Cannon, W. J. Floyd, W. R. Parry
Faculty Publications
This paper deepens the connections between critically finite rational maps and finite subdivision rules. The main theorem is that if f is a critically finite rational map with no periodic critical points, then for any sufficiently large integer n the iterate f is the subdivision map of a finite subdivision rule. This enables one to give essentially combinatorial models for the dynamics of such iterates.
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 $s=frac {1+i}{2}$.
Proven Cases Of A Generalization Of Serre's Conjecture, Jonathan H. Blackhurst
Proven Cases Of A Generalization Of Serre's Conjecture, Jonathan H. Blackhurst
Theses and Dissertations
In the 1970's Serre conjectured a correspondence between modular forms and two-dimensional Galois representations. Ash, Doud, and Pollack have extended this conjecture to a correspondence between Hecke eigenclasses in arithmetic cohomology and n-dimensional Galois representations. We present some of the first examples of proven cases of this generalized conjecture.
On The Combinatorics Of Certain Garside Semigroups, Christopher R. Cornwell
On The Combinatorics Of Certain Garside Semigroups, Christopher R. Cornwell
Theses and Dissertations
In his dissertation, F.A. Garside provided a solution to the word and conjugacy problems in the braid group on n-strands, using a particular element that he called the fundamental word. Others have since defined fundamental words in the generalized setting of Artin groups, and even more recently in Garside groups. We consider the problem of finding the number of representations of a power of the fundamental word in these settings. In the process, we find a Pascal-like identity that is satisfied in a certain class of Garside groups.
Fibroblast Migration And Collagen Deposition During Dermal Wound Healing: Mathematical Modelling And Clinical Implications, S. Mcdougall, J. A. Sherratt, P. K. Maini, J. C. Dallon
Fibroblast Migration And Collagen Deposition During Dermal Wound Healing: Mathematical Modelling And Clinical Implications, S. Mcdougall, J. A. Sherratt, P. K. Maini, J. C. Dallon
Faculty Publications
The extent to which collagen alignment occurs during dermal wound healing determines the severity of scar tissue formation. We have modelled this using a multiscale approach, in which extracellular materials, for example collagen and fibrin, are modelled as continua, while fibroblasts are considered as discrete units. Within this model framework, we have explored the effects that different parameters have on the alignment process, and we have used the model to investigate how manipulation of transforming growth factor-b levels can reduce scar tissue formation. We briefly review this body of work, then extend the modelling framework to investigate the role played …
Mathematically Modeling The Effects Of Counting Factor (Cf) In Dictyostelium Discoideum, J. C. Dallon, W. Jang, R. H. Gomer
Mathematically Modeling The Effects Of Counting Factor (Cf) In Dictyostelium Discoideum, J. C. Dallon, W. Jang, R. H. Gomer
Faculty Publications
Size regulation is a crucial feature in many biological systems, with misregulation leading to dysplasia or hyperplasia. The recent discovery of counting factor (CF) in Dictyostelium discoideum will lead to a greater understanding of how the system regulates the size of a group of cells. In this paper we mathematically model the known effects of CF using two different models: a cellular automata model and a discrete continuum hybrid model. With the use of these models we are able to understand how modulation of adhesion and motile forces by CF can facilitate stream breakup. In addition, the modelling suggests a …
Classifcation Of Conics In The Tropical Projective Plane, Amanda Ellis
Classifcation Of Conics In The Tropical Projective Plane, Amanda Ellis
Theses and Dissertations
This paper defines tropical projective space, TP^n, and the tropical general linear group TPGL(n). After discussing some simple examples of tropical polynomials and their hypersurfaces, a strategy is given for finding all conics in the tropical projective plane. The classification of conics and an analysis of the coefficient space corresponding to such conics is given.
Totally Real Galois Representations In Characteristic 2 And Arithmetic Cohomology, Heather Aurora Florence De Melo
Totally Real Galois Representations In Characteristic 2 And Arithmetic Cohomology, Heather Aurora Florence De Melo
Theses and Dissertations
The purpose of this paper is to provide new examples supporting a conjecture of Ash, Doud, and Pollack. This conjecture involves Galois representations taking Gal(Q bar/Q) to the general linear group of 3 x 3 matrices in characterisic 2, and our examples are where complex conjugation is mapped to the identity. Since this case has not yet been examined, the results of this paper are quite significant.
A Mathematical Model Of Adhesion Interactions Between Living Cells, Casey P. Johnson
A Mathematical Model Of Adhesion Interactions Between Living Cells, Casey P. Johnson
Theses and Dissertations
This thesis presents a simple force-based model of moving and interacting cells that incorporates a realistic description of cell adhesion and applies it to a system of spherical cells. In addition, several results in matrix theory are proved with the end of showing that the equations produced by the model uniquely determine the motion of the system or cells.
Maximal Surfaces In Complexes, Allen J. Dickson
Maximal Surfaces In Complexes, Allen J. Dickson
Theses and Dissertations
Cubical complexes are defined in a manner analogous to that for simplicial complexes, the chief difference being that cubical complexes are unions of cubes rather than of simplices. A very natural cubical complex to consider is the complex C(k_1,...,k_n) where k_1,...,k_n are nonnegative integers. This complex has as its underlying space [0,k_1]x...x[0,k_n] subset of R^n with vertices at all points having integer coordinates and higher dimensional cubes formed by the vertices in the natural way. The genus of a cubical complex is defined to be the maximum genus of all surfaces that are subcomplexes of the cubical complex. A formula …