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A MESHLESS METHOD WITH ENRICHED BASIS FUNCTIONS FOR SINGULARITY PROBLEMS
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...
A Random Hierarchical Laplacian
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...
Diffusion Processes on Solvable Groups of Upper Triangular 3x3 matrices. Applications in Asian and Basket Options.
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...
ESTIMATES FOR THE NUMBER OF EIGENVALUES OF NON-SELF-ADJOINT OPERATORS
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...
GLOBAL CONVERGENCE AND QUASI REVERSIBILITY FOR COEFFICIENT INVERSE PROBLEMS
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...
Limit Cycles in Two Dimensional Systems of Ordinary Differential Equations
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...
On the spectral theory of 1-D Schrodinger operator with random sparse potentials
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...
Spectral theory of the Schrodinger operator on general graphs
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...