Browsing Graduate School by Author "Mathematics."
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Adaptive methods for the Helmholtz equation with discontinuous coefficients at an interface.
Rogers, James W., Jr. (20080303)In this dissertation, we explore highly efficient and accurate finite difference methods for the numerical solution of variable coefficient partial differential equations arising in electromagnetic wave applications. We ... 
Adding machines.
Jones, Leslie Braziel. (20090601)We explore the endpoint structure of the inverse limit space of unimodal maps such that the restriction of the map to the ωlimit set of the critical point is topologically conjugate to an adding machine. These maps fall ... 
Applications of full rank factorization to solving matrix equations
Sykes, Jeffery D. (199212)In the study of matrices, we are always searching for tools which allow us to simplify our investigations. Because full rank factorizations exist for all matrices and their properties often help to simplify arguments, their ... 
Applied leftdefinite theory : the Jacobi polynomials, their Sobolev orthogonality, and selfadjoint operators.
Bruder, Andrea S. (20090610)It is well known that, for –α, –β, –α – β – 1 ∉ ℕ, the Jacobi polynomials {Pn(α,β)(x)} ∞ n=0 are orthogonal on ℝ with respect to a bilinear form of the type(f,g)μ = ∫ℝfgdμ, for some measure μ. However, for negative integer ... 
Asymptotic arccomponents in inverse limits of dendrites.
Hamilton, Brent (Brent A.) (, 20110914)We study asymptotic behavior arising in inverse limit spaces of dendrites. In particular, the inverse limit is constructed with a single unimodal bonding map, for which points have unique itineraries and the critical point ... 
Boundary data smoothness for solutions of nonlocal boundary value problems.
Lyons, Jeffrey W. (Mathematical Sciences Publishers.International Publications.Academic Publications., 2011)In this dissertation, we investigate boundary data smoothness for solutions of nonlocal boundary value problems over discrete and continuous domains. Essentially, we show that under certain conditions partial derivatives ... 
A combinatorial property of BernsteinGelfandGelfand resolutions of unitary highest weight modules.
Hartsock, Gail. (, 20130924)It follows from a formula by Kostant that the difference between the highest weights of consecutive parabolic Verma modules in the BernsteinGelfandGelfandLepowsky resolution of the trivial representation is a single ... 
Comparison of smallest eigenvalues and extremal points for third and fourth order three point boundary value problems.
Neugebauer, Jeffrey T. (, 20110914)The theory of u₀positive operators with respect to a cone in a Banach space is applied to the linear differential equations u⁽⁴⁾ + λ₁p(x)u = 0 and u⁽⁴⁾ + λ₂q(x)u = 0, 0 ≤ x ≤ 1, with each satisfying the boundary conditions ... 
Diagrams and reduced decompositions for cominuscule flag varieties and affine Grassmannians.
Pruett, W. Andrew. (20100623)We develop a system of canonical reduced decompositions of minimal coset representatives of quotients corresponding to cominuscule flag varieties and affine Grassmannians. This canonical decomposition allows, in the first ... 
Existence and uniqueness of solutions of boundary value problems by matching solutions.
Liu, Xueyan, 1978. (, 20130924)In this dissertation, we investigate the existence and uniqueness of boundary value problems for the third and nth order differential equations by matching solutions. Essentially, we consider the interval [a, c] of a BVP ... 
Existence of positive solutions to right focal three point singular boundary value problems.
Sutherland, Shawn M., 1984 (, 20130916)In this dissertation, we prove the existence of positive solutions to two classes of three point right focal singular boundary value problems of at least fourth order. 
Existence of positive solutions to singular right focal boundary value problems.
Maroun, Mariette. (Orlando, FL : International Publications., 200505)In this dissetation, we seek positive solutions for the n^th order ordinary differential equation, y^(n)=f(x,y), satisfying the right focal boundary conditions, y^(i)(0)=y^(n2)(p)=y^(n1)(1)=0, i=0,...,n3, where p is a ... 
Finitary incidence algebras.
Wagner, Bradley M. (, 20140611)Let P be an arbitrary partially ordered set and I(P) its incidence space. Then F(P) is the finitary incidence algebra and I(P) is a bimodule over it. Consequently we can form D(P) = FI(P) ⊕ I(P) the idealization of I(P). ... 
A functional approach to positive solutions of boundary value problems.
Ehrke, John E. (20070523)We apply a wellknown fixed point theorem to guarantee the existence of a positive solution and bounds for solutions for second, third, fourth, and nth order families of boundary value problems. We begin by characterizing ... 
A general linear systems theory on time scales: transforms, stability, and control.
Jackson, Billy, 1978 (20071203)In this work, we examine linear systems theory in the arbitrary time scale setting by considering Laplace transforms, stability, controllability, and realizability. In particular, we revisit the definition of the Laplace ... 
Global SL(2,R) representations of the Schrödinger equation with timedependent potentials.
Franco, Jose A. (, 20120808)We study the representation theory of the solution space of the onedimensional Schrödinger equation with timedependent potentials that possess sl₂symmetry. We give explicit local intertwining maps to multiplier ... 
Indecomposability in inverse limits.
Williams, Brian R. (Brian Robert), 1982 (20101008)Topological inverse limits play an important in the theory of dynamical systems and in continuum theory. In this dissertation, we investigate classical inverse limits of Julia sets and setvalued inverse limits of arbitrary ... 
Inverse limits of setvalued functions.
Cornelius, Alexander Nelson. (20090826)Much is known about inverse limits of compact spaces with continuous bonding maps. When the requirement that the bonding maps be continuous functions is relaxed, to allow for upper semicontinuous setvalued functions, ... 
The leftdefinite spectral analysis of the legendre type differential equation.
Tuncer, Davut. (20100202)Littlejohn and Wellman developed a general abstract leftdefinite theory for a selfadjoint operator A that is bounded below in a Hilbert space (H,(‧,‧)). More specifically, they construct a continuum of Hilbert spaces ... 
Multiplicity of positive solutions of evenorder nonhomogeneous boundary value problems.
Hopkins, Britney. (20090602)In this work, we discuss multiplicity results for nonhomogeneous evenorder boundary value problems on both discrete and continuous domains. We develop a method for establishing existence of positive solutions by transforming ...