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Hausdorff, Packing and Capacity Dimensions

Description: In this thesis, Hausdorff, packing and capacity dimensions are studied by evaluating sets in the Euclidean space R^. Also the lower entropy dimension is calculated for some Cantor sets. By incorporating technics of Munroe and of Saint Raymond and Tricot, outer measures are created. A Vitali covering theorem for packings is proved. Methods (by Taylor and Tricot, Kahane and Salem, and Schweiger) for determining the Hausdorff and capacity dimensions of sets using probability measures are discussed… more
Date: August 1989
Creator: Spear, Donald W.
Item Type: Refine your search to only Thesis or Dissertation
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Hermitian Jacobi Forms and Congruences

Description: In this thesis, we introduce a new space of Hermitian Jacobi forms, and we determine its structure. As an application, we study heat cycles of Hermitian Jacobi forms, and we establish a criterion for the existence of U(p) congruences of Hermitian Jacobi forms. We demonstrate that criterion with some explicit examples. Finally, in the appendix we give tables of Fourier series coefficients of several Hermitian Jacobi forms.
Date: August 2014
Creator: Senadheera, Jayantha
Item Type: Refine your search to only Thesis or Dissertation
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Hochschild Cohomology and Complex Reflection Groups

Description: A concrete description of Hochschild cohomology is the first step toward exploring associative deformations of algebras. In this dissertation, deformation theory, geometry, combinatorics, invariant theory, representation theory, and homological algebra merge in an investigation of Hochschild cohomology of skew group algebras arising from complex reflection groups. Given a linear action of a finite group on a finite dimensional vector space, the skew group algebra under consideration is the se… more
Date: August 2012
Creator: Foster-Greenwood, Briana A.
Item Type: Refine your search to only Thesis or Dissertation
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Hochschild Cohomology of Finite Cyclic Groups Acting on Polynomial Rings

Description: The Hochschild cohomology of an associative algebra records information about the deformations of that algebra, and hence the first step toward understanding its deformations is an examination of the Hochschild cohomology. In this dissertation, we use techniques from homological algebra, invariant theory, and combinatorics to analyze the Hochschild cohomology of skew group algebras arising from finite cyclic groups acting on polynomial rings over fields of arbitrary characteristic. These algebr… more
Date: May 2023
Creator: Lawson, Colin M.
Item Type: Refine your search to only Thesis or Dissertation

Hyperbolic Monge-Ampère Equation

Description: In this paper we use the Sobolev steepest descent method introduced by John W. Neuberger to solve the hyperbolic Monge-Ampère equation. First, we use the discrete Sobolev steepest descent method to find numerical solutions; we use several initial guesses, and explore the effect of some imposed boundary conditions on the solutions. Next, we prove convergence of the continuous Sobolev steepest descent to show local existence of solutions to the hyperbolic Monge-Ampère equation. Finally, we prov… more
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Date: August 2006
Creator: Howard, Tamani M.
Item Type: Refine your search to only Thesis or Dissertation
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Infinitary Combinatorics and the Spreading Models of Banach Spaces

Description: Spreading models have become fundamental to the study of asymptotic geometry in Banach spaces. The existence of spreading models in every Banach space, and the so-called good sequences which generate them, was one of the first applications of Ramsey theory in Banach space theory. We use Ramsey theory and other techniques from infinitary combinatorics to examine some old and new questions concerning spreading models and good sequences. First, we consider the lp spreading model problem which asks… more
Date: May 2019
Creator: Krause, Cory A.
Item Type: Refine your search to only Thesis or Dissertation
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Infinite Planar Graphs

Description: How many equivalence classes of geodesic rays does a graph contain? How many bounded automorphisms does a planar graph have? Neimayer and Watkins studied these two questions and answered them for a certain class of graphs. Using the concept of excess of a vertex, the class of graphs that Neimayer and Watkins studied are extended to include graphs with positive excess at each vertex. The results of this paper show that there are an uncountable number of geodesic fibers for graphs in this exte… more
Date: May 2000
Creator: Aurand, Eric William
Item Type: Refine your search to only Thesis or Dissertation
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Infinitely Many Solutions of Semilinear Equations on Exterior Domains

Description: We prove the existence and nonexistence of solutions for the semilinear problem ∆u + K(r)f(u) = 0 with various boundary conditions on the exterior of the ball in R^N such that lim r→∞u(r) = 0. Here f : R → R is an odd locally lipschitz non-linear function such that there exists a β > 0 with f < 0 on (0, β), f > 0 on (β, ∞), and K(r) \equiv r^−α for some α > 0.
Date: August 2018
Creator: Joshi, Janak R
Item Type: Refine your search to only Thesis or Dissertation
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Invariant Differential Derivations for Modular Reflection Groups

Description: The invariant theory of finite reflection groups has rich connections to geometry, topology, representation theory, and combinatorics. We consider finite reflection groups acting on vector spaces over fields of arbitrary characteristic, where many arguments of classical invariant theory break down. When the characteristic of the underlying field is positive, reflections may be nondiagonalizable. A group containing these so-called transvections has order which is divisible by the characteristic … more
Date: May 2023
Creator: Hanson, Dillon James
Item Type: Refine your search to only Thesis or Dissertation
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Invariants of Polynomials Modulo Frobenius Powers

Description: Rational Catalan combinatorics connects various Catalan numbers to the representation theory of rational Cherednik algebras for Coxeter and complex reflection groups. Lewis, Reiner, and Stanton seek a theory of rational Catalan combinatorics for the general linear group over a finite field. The finite general linear group is a modular reflection group that behaves like a finite Coxeter group. They conjecture a Hilbert series for a space of invariants under the action of this group using (q,t)-… more
Date: May 2020
Creator: Drescher, Chelsea
Item Type: Refine your search to only Thesis or Dissertation
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Invertible Ideals and the Strong Two-Generator Property in Some Polynomial Subrings

Description: Let K be any field and Q be the rationals. Define K^1[X] = {f(X) e K[X]| the coefficient of X in f(X) is zero} and Q^1β[X] = {f(X) e Q[X]| the coefficent of β1(X) in the binomial expansion of f(X) is zero}, where {β1(X)}^∞ i=0 are the well-known binomial polynomials. In this work, I establish the following results: K^1[X] and Q^1β[X] are one-dimensional, Noetherian, non-Prüfer domains with the two-generator property on ideals. Using the unique factorization structure of the overrings K[X] and Q… more
Date: May 1987
Creator: Chapman, Scott T. (Scott Thomas)
Item Type: Refine your search to only Thesis or Dissertation
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Irreducible Modules for Yokonuma-Type Hecke Algebras

Description: Yokonuma-type Hecke algebras are a class of Hecke algebras built from a Type A construction. In this thesis, I construct the irreducible representations for a class of generic Yokonuma-type Hecke algebras which specialize to group algebras of the complex reflection groups and to endomorphism rings of certain permutation characters of finite general linear groups.
Date: August 2016
Creator: Dave, Ojas
Item Type: Refine your search to only Thesis or Dissertation
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Iterative Solution of Linear Boundary Value Problems

Description: The investigation is initially a continuation of Neuberger's work on linear boundary value problems. A very general iterative procedure for solution of these problems is described. The alternating-projection theorem of von Neumann is the mathematical starting point for this study. Later theorems demonstrate the validity of numerical approximation for Neuberger's method under certain conditions. A sampling of differential equations within the scope of our iterative method is given. The numerical… more
Date: August 1983
Creator: Walsh, John Breslin
Item Type: Refine your search to only Thesis or Dissertation
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Kleinian Groups in Hilbert Spaces

Description: The theory of discrete groups acting on finite dimensional Euclidean open balls by hyperbolic isometries was borne around the end of 19th century within the works of Fuchs, Klein and Poincaré. We develop the theory of discrete groups acting by hyperbolic isometries on the open unit ball of an infinite dimensional separable Hilbert space. We present our investigations on the geometry of limit sets at the sphere at infinity with an attempt to highlight the differences between the finite and infin… more
Date: August 2012
Creator: Das, Tushar
Item Type: Refine your search to only Thesis or Dissertation
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Level Curves of the Angle Function of a Positive Definite Symmetric Matrix

Description: Given a real N by N matrix A, write p(A) for the maximum angle by which A rotates any unit vector. Suppose that A and B are positive definite symmetric (PDS) N by N matrices. Then their Jordan product {A, B} := AB + BA is also symmetric, but not necessarily positive definite. If p(A) + p(B) is obtuse, then there exists a special orthogonal matrix S such that {A, SBS^(-1)} is indefinite. Of course, if A and B commute, then {A, B} is positive definite. Our work grows from the following quest… more
Date: December 2009
Creator: Bajracharya, Neeraj
Item Type: Refine your search to only Thesis or Dissertation
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Localized Radial Solutions for Nonlinear p-Laplacian Equation in RN

Description: We establish the existence of radial solutions to the p-Laplacian equation ∆p u + f(u)=0 in RN, where f behaves like |u|q-1 u when u is large and f(u) < 0 for small positive u. We show that for each nonnegative integer n, there is a localized solution u which has exactly n zeros. Also, we look for radial solutions of a superlinear Dirichlet problem in a ball. We show that for each nonnegative integer n, there is a solution u which has exactly n zeros. Here we give an alternate proof to tha… more
Date: May 2008
Creator: Pudipeddi, Sridevi
Item Type: Refine your search to only Thesis or Dissertation
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Maximum Likelihood Estimation of Logistic Sinusoidal Regression Models

Description: We consider the problem of maximum likelihood estimation of logistic sinusoidal regression models and develop some asymptotic theory including the consistency and joint rates of convergence for the maximum likelihood estimators. The key techniques build upon a synthesis of the results of Walker and Song and Li for the widely studied sinusoidal regression model and on making a connection to a result of Radchenko. Monte Carlo simulations are also presented to demonstrate the finite-sample perform… more
Date: December 2013
Creator: Weng, Yu
Item Type: Refine your search to only Thesis or Dissertation
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The Maximum Size of Combinatorial Geometries Excluding Wheels and Whirls as Minors

Description: We show that the maximum size of a geometry of rank n excluding the (q + 2)-point line, the 3-wheel W_3, and the 3-whirl W^3 as minor is (n - 1)q + 1, and geometries of maximum size are parallel connections of (q + 1)-point lines. We show that the maximum size of a geometry of rank n excluding the 5-point line, the 4-wheel W_4, and the 4-whirl W^4 as minors is 6n - 5, for n ≥ 3. Examples of geometries having rank n and size 6n - 5 include parallel connections of the geometries V_19 and PG(2,3).
Date: August 1989
Creator: Hipp, James W. (James William), 1956-
Item Type: Refine your search to only Thesis or Dissertation
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Maximum-Sized Matroids with no Minors Isomorphic to U2,5, F7, F7¯, OR P7

Description: Let M be the class of simple matroids which do not contain the 5-point line U2,5 , the Fano plane F7 , the non-Fano plane F7- , or the matroid P7 , as minors. Let h(n) be the maximum number of points in a rank-n matroid in M. We show that h(2)=4, h(3)=7, and h(n)=n(n+1)/2 for n>3, and we also find all the maximum-sized matroids for each rank.
Date: May 2000
Creator: Mecay, Stefan Terence
Item Type: Refine your search to only Thesis or Dissertation
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Measurable Selection Theorems for Partitions of Polish Spaces into Gδ Equivalence Classes

Description: Let X be a Polish space and Q a measurable partition of X into Gδ equivalence classes. In 1978, S. M. Srivastava proved the existence of a Borel cross section for Q. He asked whether more can be concluded in case each equivalence class is uncountable. This question is answered here in the affirmative. The main result of the author is a proof that shows the existence of a Castaing Representation for Q.
Date: May 1980
Creator: Simrin, Harry S.
Item Type: Refine your search to only Thesis or Dissertation
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Minimality of the Special Linear Groups

Description: Let F denote the field of real numbers, complex numbers, or a finite algebraic extension of the p-adic field. We prove that the special linear group SLn(F) with the usual topology induced by F is a minimal topological group. This is accomplished by first proving the minimality of the upper triangular group in SLn(F). The proof for the upper triangular group uses an induction argument on a chain of upper triangular subgroups and relies on general results for locally compact topological groups, q… more
Date: December 1997
Creator: Hayes, Diana Margaret
Item Type: Refine your search to only Thesis or Dissertation
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Multifractal Measures

Description: The purpose of this dissertation is to introduce a natural and unifying multifractal formalism which contains the above mentioned multifractal parameters, and gives interesting results for a large class of natural measures. In Part 2 we introduce the proposed multifractal formalism and study it properties. We also show that this multifractal formalism gives natural and interesting results when applied to (nonrandom) graph directed self-similar measures in Rd and "cookie-cutter" measures in R. I… more
Date: May 1994
Creator: Olsen, Lars
Item Type: Refine your search to only Thesis or Dissertation
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