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Title: Spectral theory of the Schrodinger operator on general graphs
Author: Zheng, Lukun
Date Created: 2015
Subjects--Topical: 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...

Title: Spectral Theory of Schrödinger Type Operator on Spider Type Quantum Graphs
Author: Paul, Madhumita
Date Created: 2023
Subjects--Topical: Mathematics
Description: The dissertation consists of chapter 1: Introduction, this chapter contains some definitions and examples of quantum graphs, symplectic analysis and its representation on spider graph. Chapter 2-Brownian motion on the spider like quantum graph, th...

Title: On the spectral theory of 1-D Schrodinger operator with random sparse potentials
Author: Cook, Thomas
Date Created: 2019
Subjects--Topical: 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: Limit Cycles in Two Dimensional Systems of Ordinary Differential Equations
Author: Rowe, Ashley
Date Created: 2018
Subjects--Topical: 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: GLOBAL CONVERGENCE AND QUASI REVERSIBILITY FOR COEFFICIENT INVERSE PROBLEMS
Author: Kuzhuget, Andrey
Date Created: 2011
Subjects--Topical: 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: ESTIMATES FOR THE NUMBER OF EIGENVALUES OF NON-SELF-ADJOINT OPERATORS
Author: Hulko, Artem
Date Created: 2018
Subjects--Topical: Mathematics
Description: In this dissertation we find estimates for the total number of eigenvalues of non-self-adjoint operators. We consider five different operators, three of them discrete and two continuous. Discrete operators are as follows: Schrödinger operator defi...

Title: Diffusion Processes on Solvable Groups of Upper Triangular 3x3 matrices. Applications in Asian and Basket Options.
Author: Simonsen, Julia
Date Created: 2020
Subjects--Topical: Mathematics
Description: One of the questions in algebraic groups is about the asymptotic behavior of the probability of return of a random walk, which closely related on the growth rate of a group. Upper-triangular matrices form a group. Solvable groups have an exponenti...

Title: A Random Hierarchical Laplacian
Author: Ray, Elijah
Date Created: 2013
Subjects--Topical: Mathematics
Description: The Hierarchical Laplacian, proposed in Dyson's theory of one-dimensional 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: A MESHLESS METHOD WITH ENRICHED BASIS FUNCTIONS FOR SINGULARITY PROBLEMS
Author: Hong, Won-Tak
Date Created: 2009
Subjects--Topical: 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...