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Browsing Theses/Dissertations - Mathematics by Title

Browsing Theses/Dissertations - Mathematics by Title

Now showing items 1-13 of 13

Adaptive methods for the Helmholtz equation with discontinuous coefficients at an interface.

Rogers, James W., Jr.

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 ...
Asymptotic arc-components in inverse limits of dendrites.

Hamilton, Brent (Brent A.) (, )

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., )

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.

Neugebauer, Jeffrey T. (, )

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.

Pruett, W. Andrew.

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 ...
Global SL(2,R) representations of the Schrödinger equation with time-dependent potentials.

Franco, Jose A. (, )

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.

Williams, Brian R. (Brian Robert), 1982-

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 ...
The left-definite spectral analysis of the legendre type differential equation.

Tuncer, Davut.

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 ...
Orbit structures of homeomorphisms.

Sherman, Casey L. (, )

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 ...
Restarting the Lanczos algorithm for large eigenvalue problems and linear equations.

Nicely, Dywayne A.

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 ...
Spectral functions for generalized piston configurations.

Morales-Almazán, Pedro Fernando. (, )

In this work we explore various piston configurations with different types of potentials. We analyze Laplace-type operators $P=-g^{ij}\nabla^E_i\nabla^E_j+V$ where $V$ is the potential. First we study delta potentials and ...
Uniqueness implies uniqueness and existence for nonlocal boundary value problems for fourth order differential equations.

Ma, Ding.

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.

Gray, Michael Jeffery.

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= ...