Now showing items 1-20 of 21

• #### Uniqueness implies uniqueness and existence for nonlocal boundary value problems for fourth order differential equations. ﻿

(2006-07-07)
In this dissertation, we are concerned with uniqueness and existence of solutions of certain types of boundary value problems for fourth order differential equations. In particular, we deal with uniqueness implies uniqueness ...
• #### Uniqueness implies uniqueness and existence for nonlocal boundary value problems for third order ordinary differential equations. ﻿

(2006-07-29)
For the third order ordinary differential equation, $y'''=f(x,y,y',y'')$, it is assumed that, for some $m\geq 4$, solutions of nonlocal boundary value problems satisfying $y(x_1)=y_1,\ y(x_2)=y_2,$ \[y(x_m)-\sum_{i= ...
• #### 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 ...
• #### Restarting the Lanczos algorithm for large eigenvalue problems and linear equations. ﻿

(2008-10-02)
We are interested in computing eigenvalues and eigenvectors of large matrices and in solving large systems of linear equations. Restarted versions of both the symmetric and nonsymmetric Lanczos algorithms are given. For ...
• #### 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 ...
• #### 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 ...
• #### 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 ...
• #### 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 ...
• #### 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 ...
• #### 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 ...
• #### 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 ...
• #### Orbit structures of homeomorphisms. ﻿

(, 2012-11-29)
In this dissertation we answer the following question: If X is a Cantor set and T: X → to X is a homeomorphism, what possible orbit structures can T have? The answer is given in terms of the orbit spectrum of T. If X is a ...
• #### Spectral functions for generalized piston configurations. ﻿

(, 2012-11-29)
In this work we explore various piston configurations with different types of potentials. We analyze Laplace-type operators P=-g^ij ∇^E_i ∇ ^E_j+V where V is the potential. First we study delta potentials and rectangular ...
• #### 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.
• #### 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 ...
• #### 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 ...
• #### 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 ...
• #### Quadratic Lyapunov theory for dynamic linear switched systems. ﻿

(, 2014-01-28)
In this work, a special class of time-varying linear systems in the arbitrary time scale setting is examined by considering the qualitative properties of their solutions. Building on the work of J. DaCunha and A. Ramos, ...
• #### 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 ...
• #### 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 ...