Search results
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Title
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A MESHLESS METHOD WITH ENRICHED BASIS FUNCTIONS FOR SINGULARITY PROBLEMS
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Author
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Hong, Won-Tak
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Date Created
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2009
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Subjects--Topical
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Mechanical engineering, Mechanics, Mathematics
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Description
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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...
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Title
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A Random Hierarchical Laplacian
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Author
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Ray, Elijah
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Date Created
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2013
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Subjects--Topical
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Mathematics
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Description
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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...
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Title
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ESTIMATES FOR THE NUMBER OF EIGENVALUES OF NON-SELF-ADJOINT OPERATORS
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Author
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Hulko, Artem
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Date Created
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2018
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Subjects--Topical
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Mathematics
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Description
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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...
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Title
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Limit Cycles in Two Dimensional Systems of Ordinary Differential Equations
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Author
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Rowe, Ashley
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Date Created
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2018
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Subjects--Topical
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Mathematics
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Description
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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...
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Title
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On the spectral theory of 1-D Schrodinger operator with random sparse potentials
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Author
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Cook, Thomas
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Date Created
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2019
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Subjects--Topical
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Mathematics
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Description
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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...
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Title
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Spectral Theory of Schrödinger Type Operator on Spider Type Quantum Graphs
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Author
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Paul, Madhumita
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Date Created
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2023
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Subjects--Topical
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Mathematics
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Description
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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...
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Title
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Spectral theory of the Schrodinger operator on general graphs
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Author
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Zheng, Lukun
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Date Created
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2015
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Subjects--Topical
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Mathematics, Physics
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Description
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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...