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Articles 1 - 14 of 14
Full-Text Articles in Physical Sciences and Mathematics
The Existence Of A Discontinuous Homomorphism Requires A Strong Axiom Of Choice, Michael Steven Andersen
The Existence Of A Discontinuous Homomorphism Requires A Strong Axiom Of Choice, Michael Steven Andersen
Theses and Dissertations
Conner and Spencer used ultrafilters to construct homomorphisms between fundamental groups that could not be induced by continuous functions between the underlying spaces. We use methods from Shelah and Pawlikowski to prove that Conner and Spencer could not have constructed these homomorphisms with a weak version of the Axiom of Choice. This led us to define and examine a class of pathological objects that cannot be constructed without a strong version of the Axiom of Choice, which we call the class of inscrutable objects. Objects that do not need a strong version of the Axiom of Choice are scrutable. We …
Pro-Covering Fibrations Of The Hawaiian Earring, Nickolas Brenten Callor
Pro-Covering Fibrations Of The Hawaiian Earring, Nickolas Brenten Callor
Theses and Dissertations
Let H be the Hawaiian Earring, and let H denote its fundamental group. Assume (Bi) is an inverse system of bouquets of circles whose inverse limit is H. We give an explicit bijection between finite normal covering spaces of H and finite normal covering spaces of Bi. This bijection induces a correspondence between a certain family of inverse sequences of these covering spaces. The correspondence preserves the inverse limit of these sequences, thus offering two methods of constructing the same limit. Finally, we characterize all spaces that can be obtained in this fashion as a particular type of fibrations of …
A Covering System With Minimum Modulus 42, Tyler Owens
A Covering System With Minimum Modulus 42, Tyler Owens
Theses and Dissertations
We construct a covering system whose minimum modulus is 42. This improves the previous record of 40 by P. Nielsen.
Transposing Noninvertible Polynomials, Nathan Cordner
Transposing Noninvertible Polynomials, Nathan Cordner
Library Research Grants
In the class of invertible polynomials, the notion of dual polynomials W and WT, as well as dual groups G and GT is well-understood. In this paper we investigate finding dual pairs W and WT for noninvertible polynomials. We find that in many instances, our intuition that stems from invertible polynomials does not extend to the noninvertible case.
Connecting Galois Representations With Cohomology, Joseph Allen Adams
Connecting Galois Representations With Cohomology, Joseph Allen Adams
Theses and Dissertations
In this paper, we examine the conjecture of Avner Ash, Darrin Doud, David Pollack, and Warren Sinnott relating Galois representations to the mod p cohomology of congruence subgroups of the general linear group of n dimensions over the integers. We present computational evidence for this conjecture (the ADPS Conjecture) for the case n = 3 by finding Galois representations which appear to correspond to cohomology eigenclasses predicted by the ADPS Conjecture for the prime p, level N, and quadratic nebentype. The examples include representations which appear to be attached to cohomology eigenclasses which arise from D8, S3, A5, and S5 …
Hecke Eigenvalues And Arithmetic Cohomology, William Leonard Cocke
Hecke Eigenvalues And Arithmetic Cohomology, William Leonard Cocke
Theses and Dissertations
We provide algorithms and documention to compute the cohomology of congruence subgroups of the special linear group over the integers when n=3 using the well-rounded retract and the Voronoi decomposition. We define the Sharbly complex and how one acts on a k-sharbly by the Hecke operators. Since the norm of a sharbly is not preserved by the Hecke operators we also examine the reduction techniques described by Gunnells and present our implementation of said techniques for n=3.
Hölder Extensions For Non-Standard Fractal Koch Curves, Joshua Taylor Fetbrandt
Hölder Extensions For Non-Standard Fractal Koch Curves, Joshua Taylor Fetbrandt
Theses and Dissertations
Let K be a non-standard fractal Koch curve with contraction factor α. Assume α is of the form α = 2+1/m for some m ∈ N and that K is embedded in a larger domain Ω. Further suppose that u is any Hölder continuous function on K. Then for each such m ∈ N and iteration n ≥ 0, we construct a bounded linear operator Πn which extends u from the prefractal Koch curve Kn into the whole of Ω. Unfortunately, our sequence of extension functions Πnu are not bounded in norm in the limit because the upper bound is …
Convolutions And Convex Combinations Of Harmonic Mappings Of The Disk, Zachary M. Boyd
Convolutions And Convex Combinations Of Harmonic Mappings Of The Disk, Zachary M. Boyd
Theses and Dissertations
Let f_1, f_2 be univalent harmonic mappings of some planar domain D into the complex plane C. This thesis contains results concerning conditions under which the convolution f_1 ∗ f_2 or the convex combination tf_1 + (1 − t)f_2 is univalent. This is a long-standing problem, and I provide several partial solutions. I also include applications to minimal surfaces.
A New Public-Key Cryptosystem, Christopher James Hettinger
A New Public-Key Cryptosystem, Christopher James Hettinger
Theses and Dissertations
Public key cryptosystems offer important advantages over symmetric methods, but the most important such systems rely on the difficulty of integer factorization (or the related discrete logarithm problem). Advances in quantum computing threaten to render such systems useless. In addition, public-key systems tend to be slower than symmetric systems because of their use of number-theoretic algorithms. I propose a new public key system which may be secure against both classical and quantum attacks, while remaining simple and very fast. The system's action is best described in terms of linear algebra, while its security is more naturally explained in the context …
Algebraic And Combinatorial Properties Of Schur Rings Over Cyclic Groups, Andrew F. Misseldine
Algebraic And Combinatorial Properties Of Schur Rings Over Cyclic Groups, Andrew F. Misseldine
Theses and Dissertations
In this dissertation, we explore the nature of Schur rings over finite cyclic groups, both algebraically and combinatorially. We provide a survey of many fundamental properties and constructions of Schur rings over arbitrary finite groups. After specializing to the case of cyclic groups, we provide an extensive treatment of the idempotents of Schur rings and a description for the complete set of primitive idempotents. We also use Galois theory to provide a classification theorem of Schur rings over cyclic groups similar to a theorem of Leung and Man and use this classification to provide a formula for the number of …
A Volume Bound For Montesinos Links, Kathleen Arvella Finlinson
A Volume Bound For Montesinos Links, Kathleen Arvella Finlinson
Theses and Dissertations
The hyperbolic volume of a knot complement is a topological knot invariant. Futer, Kalfagianni, and Purcell have estimated the volumes of Montesinos link complements for Montesinos links with at least three positive tangles. Here we extend their results to all hyperbolic Montesinos links.
The Minimum Rank Of Schemes On Graphs, William Nelson Sexton
The Minimum Rank Of Schemes On Graphs, William Nelson Sexton
Theses and Dissertations
Let G be an undirected graph on n vertices and let S(G) be the class of all real-valued symmetric n × n matrices whose nonzero off-diagonal entries occur in exactly the positions corresponding to the edges of G. Let V = {1, 2, . . . , n} be the vertex set of G. A scheme on G is a function f : V → {0, 1}. Given a scheme f on G, there is an associated class of matrices Sf (G) = {A ∈ S(G)|aii = 0 if and only if f(i) = 0}. A scheme f is said …
Representations Associated To The Group Matrix, Joseph Aaron Keller
Representations Associated To The Group Matrix, Joseph Aaron Keller
Theses and Dissertations
For a finite group G = {g_0 = 1, g_1,. . ., g_{n-1}} , we can associate independent variables x_0, x_1, . . ., x_{n-1} where x_i = x_{g_i}. There is a natural action of Aut(G) on C[x_0, . . . ,x_{n-})]. Let C_1, . . . , C_r be the conjugacy classes of G. If C = {g_{i_1}, g_{i_2}, . . . , g_{i_u }} is a conjugacy class, then let x(C) = x_{i_1} + x_{i_2} + . . . + x_{i_u}. Let ρG be the representation of Aut(G) on C[x_0, . . . , x_(n-1)]/〈x(C_1), . . . …
A Mathematical Model Of Collagen Lattice Contraction, J. C. Dallon, Emily J. Evans, H Paul Erhlich
A Mathematical Model Of Collagen Lattice Contraction, J. C. Dallon, Emily J. Evans, H Paul Erhlich
Faculty Publications
Two mathematical models for fibroblast-collagen interaction are proposed which reproduce qualitative features of fibroblast populated collagen lattice contraction in time. Both models are force based and model the cells as individual entities with discrete attachment sites however the collagen lattice is modeled differently for each model. In the collagen lattice model the lattice is more interconnected and formed by triangulating nodes to form the fibrous structure. In the collagen fiber model the nodes are not triangulated, are less interconnected, and the collagen fibers are modeled as a string of nodes. Both models suggest that the overall increase in stress of …