Search results


Title

A MESHLESS METHOD WITH ENRICHED BASIS FUNCTIONS FOR SINGULARITY PROBLEMS

Author

Hong, WonTak

Date Created

2009

SubjectsTopical

Mechanical engineering, Mechanics, Mathematics

Description

For the last several decades, the Finite Element Method (FEM) has been a powerful tool in solving challenging science and engineering problems, especially when solution domains have complex geometry. However the mesh refinements and construction o...


Title

A Random Hierarchical Laplacian

Author

Ray, Elijah

Date Created

2013

SubjectsTopical

Mathematics

Description

The Hierarchical Laplacian, proposed in Dyson's theory of onedimensional ferromagnetic phase transitions, has a discrete spectrum with each isolated eigenvalue having infinite multiplicity. As a result, the integrated density of states is piecewi...


Title

ESTIMATES FOR THE NUMBER OF EIGENVALUES OF NONSELFADJOINT OPERATORS

Author

Hulko, Artem

Date Created

2018

SubjectsTopical

Mathematics

Description

In this dissertation we find estimates for the total number of eigenvalues of nonselfadjoint operators. We consider five different operators, three of them discrete and two continuous. Discrete operators are as follows: SchrÃ¶dinger operator defi...


Title

GLOBAL CONVERGENCE AND QUASI REVERSIBILITY FOR COEFFICIENT INVERSE PROBLEMS

Author

Kuzhuget, Andrey

Date Created

2011

SubjectsTopical

Mathematics

Description

An inverse problem of the determination of an initial condition in ahyperbolic equation from the lateral Cauchy data is considered. Thisproblem has applications to the thermoacoustic tomography, as wellas to linearized coefficient inverse problems...


Title

Limit Cycles in Two Dimensional Systems of Ordinary Differential Equations

Author

Rowe, Ashley

Date Created

2018

SubjectsTopical

Mathematics

Description

This thesis concerns cycles, i.e., topological ovals, in the phase portraits of systems of first order ordinary differential equationsin the plane, with an emphasis on limit cycles, cycles that are isolated from all other cycles. These are of fund...


Title

On the spectral theory of 1D Schrodinger operator with random sparse potentials

Author

Cook, Thomas

Date Created

2019

SubjectsTopical

Mathematics

Description

The goal of this dissertation is to develop a spectral theory for the Schr\"odinger operator with sparse random potential. To do this, we will first reformulate theories for sparse deterministic potentials. This includes a general development of t...


Title

Spectral theory of the Schrodinger operator on general graphs

Author

Zheng, Lukun

Date Created

2015

SubjectsTopical

Mathematics, Physics

Description

The goal of this dissertation is to give the sufficient conditions for the absence of a.c.spectrum or existence of the pure point (p.p.) spectrum for the deterministic or random Schrodinger operators on the general graphs. For the particular situa...