Search results
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Title
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Number Rings and Dedekind Domains
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Author
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Harrison, Mary
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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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In this paper, we study number rings and their factorization properties. We begin with an introduction to number fields and number rings. Then we consider the ring Z[i], which is a unique factorization domain, where each element factors uniquely i...
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Title
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Numerical models of COVID-19
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Author
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Cung, Benjamin
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Date Created
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2021
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Subjects--Topical
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Mathematics
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Description
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COVID-19 is an ongoing infectious disease where individuals progress through the following four stages: susceptible (S), exposed (E), infected (I), and recovered (R). The standard mathematical model for the spread of such diseases through a large ...
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Title
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OPTION VALUATION UNDER A REGIME-SWITCHING MODEL USING THE FAST FOURIER TRANSFORM
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Author
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Sohrabi, Elham
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Date Created
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2018
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Subjects--Topical
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Finance, Mathematics
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Description
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In this dissertation, we consider European-style commodity options and futures options where the logarithm of the underlying commodity price dynamics is governed by the regime-switching Ornstein-Uhlenbeck model. A semi-analytical approach to value...
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Title
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Neumann functions and image systems of the Laplacian in the spheroidal geometry
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Author
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Edmiston, Robert
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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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We apply the method of image charges from electrostatics to the study of the Neumannfunction for the Laplace operator, equivalent to the Green's function with a Neumannboundary condition imposed. Such an analysis has previously been given for the ...
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Title
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Multivariate Functional Predictor Selection
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Author
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Mahzarnia, Ali
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Date Created
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2021
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Subjects--Topical
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Mathematics, Statistics
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Description
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We propose methods for functional predictor selection and the estimation of smooth functional coefficients simultaneously in a scalar-on-function regression problem under a high-dimensional multivariate functional data setting. In particular, we d...
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Title
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Optimal multiple stopping: theory and applications
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Author
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Crosby, Gary
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Date Created
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2017
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Subjects--Topical
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Mathematics
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Description
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The classical secretary problem was an optimal selection thought experiment for a decision process where candidates with independent and identically distributed values to the observer appear in a random order and the observer must attempt to choos...
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Title
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On the Structure and Invariants of Cubical Complexes
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Author
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Birdsong, Sarah
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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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This dissertation introduces two new results for cubical complexes. The first is a simple statistic on noncrossing partitions that expresses each coordinate of the toric h-vector of a cubical complex, written in the basis of the Adin h-vector entr...
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Title
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On lambda-quantile dependent convex risk measures
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Author
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Xia, Lihong
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Date Created
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2011
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Subjects--Topical
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Mathematics, Finance
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Description
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We define a class of convex measures of risk whose values depend on the random variables only up to the lambda-quantiles for some given constant lambda in (0,1). For this class of convex risk measures, the assumption of Fatou property can be stren...
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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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ON THE DISCRETE SPECTRUM OF EXTERIOR ELLIPTIC PROBLEMS.
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Author
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Puri, Rajan
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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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In this dissertation, we present three new results in the exterior elliptic problems with the variable coefficients that describe the process in inhomogeneous media in the presence of obstacles. These results concern perturbations of the operator ...
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Title
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Nonparametric Pricing Kernel Models
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Author
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Sun, Linman
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Date Created
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2011
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Subjects--Topical
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Mathematics
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Description
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The capital asset pricing model (CAPM) and the arbitrage asset pricingtheory (APT) have been the cornerstone in theoretical and empirical finance for the recent few decades. The classical CAPM usually assumes a simple and stable linear relationshi...
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Title
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PARALLEL COMPUTING FOR MARKOV CHAINS WITH ISLANDS AND PORTS
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Author
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Basnet, Amod
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Date Created
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2017
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Subjects--Topical
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Mathematics
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Description
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We present recursive algorithms to calculate invariant distributions and fundamental matrices of Markov chains specified by the "Islands & Ports'" (IP) model. The state space of the IP model can be partitioned into "islands'" and "ports". An islan...
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Title
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Risk Minimizing Portfolio Optimization and Hedging with Conditional Value-at-Risk
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Author
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Li, Jing
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Date Created
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2009
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Subjects--Topical
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Mathematics
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Description
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This thesis looks at the problem of finding the optimal investment strategy of a self-financing portfolio in a dynamic complete market setting so that the risk measured by Conditional Value-at-Risk (CVaR) is minimized under the condition that the ...
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Title
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SCHWARZ METHODS FOR FOURTH-ORDER PROBLEMS CONTAINING SINGULARITIES
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Author
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Palta, Birce
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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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We develop numerical methods for analysis of fourth-order partial differential equations on domains with angular corners. For the finite element analysis of fourth-order partial differential equations, we have to use smoother basis functions whose...
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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...
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Title
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Understanding the Probability Literacy of High School Students
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Author
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Coon, Fred
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Date Created
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2019
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Subjects--Topical
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Mathematics--Study and teaching, Education, Mathematics
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Description
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This multi-case study examined high school students’ probability literacy, with focus on randomness, independence, and sample space. Task-based interviews were used with ten high school students. A Levels of Understanding Matrix (LUM), that was cr...
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Title
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The general non-stationary Anderson Parabolic Model with correlated white noise
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Author
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Chen, Xiaoyun
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Date Created
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2022
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Subjects--Topical
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Mathematics
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Description
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This dissertation contains the analysis of the general lattice non-stationary Anderson parabolic model with correlated white noise. It starts form the brief description of known results about parabolic problem with local Laplacian and the detailed...
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Title
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THE BRAID INDICES OF ALTERNATING LINKS
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Author
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Liu, Pengyu
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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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It is well known in knot theory that any link can be represented by a closed braid and the braid index of a link is the invariant defined as the minimum number of strands in any closed braid representing the link. It is difficult in general to det...
