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Articles 1 - 9 of 9
Full-Text Articles in Physical Sciences and Mathematics
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.