Browsing Department of Mathematics by Title
Now showing items 1-20 of 26
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A multigrid Krylov method for eigenvalue problems.
(2015-07-31)We are interested in computing eigenvalues and eigenvectors of matrices derived from differential equations. They are often large sparse matrices, including both symmetric and non symmetric cases. Restarted Arnoldi methods ... -
Adaptive methods for the Helmholtz equation with discontinuous coefficients at an interface.
(2008-03-03)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 ... -
Applications of full rank factorization to solving matrix equations
(1992-12)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 ... -
Asymptotic arc-components in inverse limits of dendrites.
(, 2011-09-14)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 condition dependence of spectral zeta functions.
(2015-07-14)In this work, we provide the analytic continuation of the spectral zeta function associated with the one-dimensional regular Sturm-Liouville problem and the two-dimensional Laplacian on the annulus. In the one-dimensional ... -
Boundary data smoothness for solutions of nonlocal boundary value problems.
(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 ... -
Chaotic properties of set-valued dynamical systems.
(2016-04-04)In this thesis, many classical results of topological dynamics are adapted to the set-valued case. In particular, focus is given to the notions of topological entropy and the specification property. These properties are ... -
A combinatorial property of Bernstein-Gelfand-Gelfand resolutions of unitary highest weight modules.
(, 2013-09-24)It follows from a formula by Kostant that the difference between the highest weights of consecutive parabolic Verma modules in the Bernstein-Gelfand-Gelfand-Lepowsky 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.
(, 2011-09-14)The theory of u₀-positive 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.
(2010-06-23)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 ... -
Eigenvalue comparison theorems for certain boundary value problems and positive solutions for a fifth order singular boundary value problem.
(2016-03-23)Comparison of smallest eigenvalues for certain two point boundary value problems for a fifth order linear differential equation are first obtained. The results are extended to (2n+1)-order and (3n+2)-order boundary value ... -
Existence and uniqueness of solutions of boundary value problems by matching solutions.
(, 2013-09-24)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.
(, 2013-09-16)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.
(Orlando, FL : International Publications., 2005-05)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^(n-2)(p)=y^(n-1)(1)=0, i=0,...,n-3, where p is a ... -
Glazman-Krein-Naimark theory, left-definite theory, and the square of the Legendre polynomials differential operator.
(2016-02-27)As an application of a general left-definite spectral theory, Everitt, Littlejohn and Wellman, in 2002, developed the left-definite theory associated with the classical Legendre self-adjoint second-order differential ... -
Global SL(2,R) representations of the Schrödinger equation with time-dependent potentials.
(, 2012-08-08)We study the representation theory of the solution space of the one-dimensional Schrödinger equation with time-dependent potentials that possess sl₂-symmetry. We give explicit local intertwining maps to multiplier ... -
Indecomposability in inverse limits.
(2010-10-08)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 set-valued inverse limits of arbitrary ... -
Krylov methods for solving a sequence of large systems of linear equations.
(2015-07-22)Consider solving a sequence of linear systems A_{(i)}x^{(i)}=b^{(i)}, i=1, 2, ... where A₍ᵢ₎ ϵℂⁿᵡⁿ and b⁽ⁱ⁾ϵℂⁿ using some variations of Krylov subspace methods, like GMRES. For a single system Ax=b, it is well-known that ... -
The left-definite spectral analysis of the legendre type differential equation.
(2010-02-02)Littlejohn and Wellman developed a general abstract left-definite theory for a self-adjoint operator A that is bounded below in a Hilbert space (H,(‧,‧)). More specifically, they construct a continuum of Hilbert spaces ... -
On a ring associated to F[x].
(, 2013-09-24)For a field F and the polynomial ring F [x] in a single indeterminate, we define Ḟ [x] = {α ∈ End_F(F [x]) : α(ƒ) ∈ ƒF [x] for all ƒ ∈ F [x]}. Then Ḟ [x] is naturally isomorphic to F [x] if and only if F is infinite. If F ...