Physical Sciences and Mathematics Commons^™

The Strong Law Of Large Numbers For U-Statistics Under Random Censorship, Jan Höft

Theses and Dissertations

We introduce a semi-parametric U-statistics estimator for randomly right censored data. We will study the strong law of large numbers for this estimator under proper assumptions about the conditional expectation of the censoring indicator with re- spect to the observed life times. Moreover we will conduct simulation studies, where the semi-parametric estimator is compared to a U-statistic based on the Kaplan- Meier product limit estimator in terms of bias, variance and mean squared error, under different censoring models.

Dynamic Pricing With Variable Order Sizes For A Model With Constant Demand Elasticity, Nyles Kirk Breecher

Theses and Dissertations

We investigate a dynamic pricing model under constant demand elasticity which accounts for customers ordering multiple items at once. A closed form expression for the optimal expected revenue and pricing strategy is found. Models with the same demand are shown to have asymptotically similar expected revenue and pricing strategies, even if the order size distributions of the customers are different. Surprisingly, the relative difference between comparable models is shown to be independent of time and the magnitude of demand. Variations of the model are considered, including different low inventory behavior as well as the effect of advertising. Some numerical simulations …

Triebel-Lizorkin Spaces Estimates For Evolution Equations With Structure Dissipation, Jingchun Chen

Theses and Dissertations

This work is concerned with the long time decay estimates of the generalized heat equations and the generalized wave equations in the homogeneous Triebel-Lizorkin spaces. We first extend the known results for the generalized heat equations in the real Hardy spaces. We also extend the known results for the generalized wave equations with structure dissipation in the real Hardy spaces.

The main tools employed are the decomposition of the unit, duality property in Triebel-Lizorkin spaces and the multiplier theorems in different function spaces such as Lebesgue spaces, real Hardy spaces and Triebel-Lizorkin spaces.

Identities For Partitions Of N With Parts From A Finite Set, Acadia Larsen

Theses and Dissertations

We show for a prime power number of parts m that the first differences of partitions into at most m parts can be expressed as a non-negative linear combination of partitions into at most m – 1 parts. To show this relationship, we combine a quasipolynomial construction of p(n,m) with a new partition identity for a finite number of parts. We prove these results by providing combinatorial interpretations of the quasipolynomial of p(n,m) and the new partition identity. We extend these results by establishing conditions for when partitions of n with parts coming from …

Blow-Up Solutions Of Wave Map Equations With Periodic In Time Speed Of Propagation, Nathalie M. Luna-Rivera

Theses and Dissertations

We study the initial value problem for the wave map equation with time-dependent speed of propagation. In particular, for arbitrary, small, and smooth initial data we construct blow-up solutions of the wave map with coefficients that are periodic in time. For the proof we use Lyapunov-Floquet theory and Borg’s theorem.

Asymptotic Quantization For A Condensation System Associated With A Discrete Distribution, Shankar Parajulee

Theses and Dissertations

Let P := (1/3)P ○ S1–1 + (1/3)P ○ S2–1 + (1/3)v be a condensation measure on R, where S1(x) = (1/5)x, S2(x) = (1/5)x + 4/5 for all x ∈ R , and v is a discrete distribution on R with the support of v equals C := {(2/5), (3/5)}. For such a measure P we determine the optimal sets of n–means and the nth quantization errors for all n ≥ 2. In addition, we show that the quantization dimension of the condensation measure P exists and equals …

Contact Numbers For Packing Of Spherical Particles, Eduardo Alejandro Ramirez Martinez

Theses and Dissertations

This thesis covers packings of spherical particles. The main object of this investigation is the contact number of a packing. New bounds for contact numbers of certain families of sphere packings in dimension 3 are obtained as the outcome of this research.

Generalized &Thetas;-Parameter Peakon Solutions For A Cubic Camassa-Holm Model, Michael Rippe

Theses and Dissertations

In this paper we outline a method for obtaining generalized peakon solutions for a cubic Camassa-Holm model originally introduced by Fokas (1995) and recently shown to have a Lax pair representation and bi-Hamiltonian structure by Qiao et al (2012). By considering an amended signum function—denoted sgn &thetas;(x)—where sgn(0) = &thetas; for a constant &thetas;, we explore new generalized peakon solutions for this model. In this context, all previous peakon solutions are of the case &thetas; = 0. Further, we aim to analyze the algebraic quadratic equation resulting from a substitution of the single-peakon ansatz equipped with our amended …

The Mathematical Aspects Of Theoretical Physics, Hassan Kesserwani

Theses and Dissertations

The aim of this thesis is to outline the mathematical machinery of general relativity, quantum gravity, cosmology and an introduction to string theory under one body of work. We will flesh out tensor algebra and the formalism of differential geometry. After deriving the Einstein field equation, we will outline its traditional applications. We then linearize the field equation by a perturbation method and describe the mathematics of gravitational waves and their spherical harmonic analysis. We then transition into the derivation of the Schwarzschild metric and the Kruskal coordinate transformation, in order to set the stage for quantum gravity. This sets …

Clean Indices Of Common Rings, Benjamin L. Schoonmaker

Theses and Dissertations

Lee and Zhou introduced the clean index of rings in 2004. Motivated by this work, Basnet and Bhattacharyya introduced both the weak clean index of rings and the nil clean index of rings and Cimpean and Danchev introduced the weakly nil clean index of rings. In this work, we calculate each of these indices for the rings ℤ/nℤ and matrix rings with entries in ℤ/nℤ. A generalized index is also introduced.

Thermodynamically Consistent Hydrodynamic Phase Field Models And Numerical Approximation For Multi-Component Compressible Viscous Fluid Mixtures, Xueping Zhao

Theses and Dissertations

Material systems comprising of multi-component, some of which are compressible, are ubiquitous in nature and industrial applications. In the compressible fluid flow, the material compressibility comes from two sources. One is the material compressibility itself and another is the mass-generating source. For example, the compressibility in the binary fluid flows of non-hydrocarbon (e.g. Carbon dioxide) and hydrocarbons encountered in the enhanced oil recovery (EOR) process, comes from the compressibility of the gas-liquid mixture itself. Another example of the mixture of compressible fluids is growing tissue, in which cell proliferation and cell migration make the material volume changes so that it …

Time Sensitive Functionals Of Marked Random Measures In Real Time, Kizza M. Nandyose Frisbee

Theses and Dissertations

In this dissertation, we study marked random measures that model stochastic networks (under attacks), status of queueing systems during vacation modes, responses to cancer treatments (such as chemotherapy and radiation), hostile actions in economics and warfare. We extend the recently developed time sensitivity technique for investigating the processes’ behavior about a fixed threshold to a novel time sensitive technique in three important directions: (1) real-time monotone stochastic processes; (2) two-dimensional signed random measures; and (3) antagonistic stochastic games with two active players and one passive player. The need for the time sensitive feature in our study (i.e., an analytical association …

Internal And External Harmonic Functions In Flat-Ring Coordinates, Lijuan Bi

Theses and Dissertations

The goal of this dissertation is to derive expansions for a fundamental solution of Laplace's equation in flat-ring coordinates in three-dimensional Euclidean space. These expansions are in terms of harmonic functions in the interior and the exterior of two different types of regions, "flat rings" and "peanuts" according to their shapes. We solve Laplace's equation in the interior and the exterior of these regions using the method of separation of variables. The internal and external "flat-ring" and "peanut" harmonic functions are expressed in terms of Lamé functions.

Compactifications Of Manifolds With Boundary, Shijie Gu

Theses and Dissertations

This dissertation is concerned with compactifications of high-dimensional manifolds.

Siebenmann's iconic 1965 dissertation \cite{Sie65} provided necessary and

sufficient conditions for an open manifold $M^{m}$ ($m\geq6$) to be

compactifiable by addition of a manifold boundary. His theorem extends easily

to cases where $M^{m}$ is noncompact with compact boundary; however when

$\partial M^{m}$ is noncompact, the situation is more complicated. The goal

becomes a \textquotedblleft completion\textquotedblright\ of $M^{m}$, ie, a

compact manifold $\widehat{M}^{m}$ containing a compactum $A\subseteq\partial

M^{m}$ such that $\widehat{M}^{m}\backslash A\approx M^{m}$. Siebenmann did

some initial work on this topic, and O'Brien \cite{O'B83} extended that work

to an important special case. …

Z-Structures And Semidirect Products With An Infinite Cyclic Group, Brian Walter Pietsch

Theses and Dissertations

Z-structures were originally formulated by Bestvina in order to axiomatize the properties that an ideal group boundary should have. In this dissertation, we prove that if a given group admits a Z-structure, then any semidirect product of that group with an infinite cyclic group will also admit a Z-structure. We then show how this can be applied to 3-manifold groups and strongly polycyclic groups.

Model Predictive Linear Control With Successive Linearization, Jesse Robert Friedbaum

Theses and Dissertations

Robots have been a revolutionizing force in manufacturing in the 20th and 21st century but have proven too dangerous around humans to be used in many other fields including medicine. We describe a new control algorithm for robots developed by the Brigham Young University Robotics and Dynamics and Robotics Laboratory that has shown potential to make robots less dangerous to humans and suitable to work in more applications. We analyze the computational complexity of this algorithm and find that it could be a feasible control for even the most complicated robots. We also show conditions for a system which guarantee …

Adding Limit Points To Bass-Serre Graphs Of Groups, Alexander Jin Shumway

Theses and Dissertations

We give a brief overview of Bass-Serre theory and introduce a method of adding a limit point to graphs of groups. We explore a basic example of this method, and find that while the fundamental theorem of Bass-Serre theory no longer applies in this case we still recover a group action on a covering space of sorts with a subgroup isomorphic to the fundamental group of our new base space with added limit point. We also quantify how much larger the fundamental group of a graph of groups becomes after this construction, and discuss the effects of adding and identifying …

Euclidean Domains, Vandy Jade Tombs

Theses and Dissertations

In the usual definition of a Euclidean domain, a ring has a norm function whose codomain is the positive integers. It was noticed by Motzkin in 1949 that the codomain could be replaced by any well-ordered set. This motivated the study of transfinite Euclidean domains in which the codomain of the norm function is replaced by the class of ordinals. We prove that there exists a (transfinitely valued) Euclidean Domain with Euclidean order type for every indecomposable ordinal. Modifying the construction, we prove that there exists a Euclidean Domain with no multiplicative norm. Following a definition of Clark and Murty, …

Congruences For Fourier Coefficients Of Modular Functions Of Levels 2 And 4, Eric Brandon Moss

Theses and Dissertations

We give congruences modulo powers of 2 for the Fourier coefficients of certain level 2 modular functions with poles only at 0, answering a question posed by Andersen and Jenkins. The congruences involve a modulus that depends on the binary expansion of the modular form's order of vanishing at infinity. We also demonstrate congruences for Fourier coefficients of some level 4 modular functions.

Finding Torsion-Free Groups Which Do Not Have The Unique Product Property, Lindsay Jennae Soelberg

Theses and Dissertations

This thesis discusses the Kaplansky zero divisor conjecture. The conjecture states that a group ring of a torsion-free group over a field has no nonzero zero divisors. There are situations for which this conjecture is known to hold, such as linearly orderable groups, unique product groups, solvable groups, and elementary amenable groups. This paper considers the possibility that the conjecture is false and there is some counterexample in existence. The approach to searching for such a counterexample discussed here is to first find a torsion-free group that has subsets A and B such that AB has no unique product. We …

Data Assimilation In The Boussinesq Approximation For Mantle Convection, Shane Alexander Mcquarrie

Theses and Dissertations

Many highly developed physical models poorly approximate actual physical systems due to natural random noise. For example, convection in the earth's mantle—a fundamental process for understanding the geochemical makeup of the earth's crust and the geologic history of the earth—exhibits chaotic behavior, so it is difficult to model accurately. In addition, it is impossible to directly measure temperature and fluid viscosity in the mantle, and any indirect measurements are not guaranteed to be highly accurate. Over the last 50 years, mathematicians have developed a rigorous framework for reconciling noisy observations with reasonable physical models, a technique called data assimilation. …

The Arithmetic Of Modular Grids, Grant Steven Molnar

Theses and Dissertations

Let M_k^(∞) (Gamma, nu) denote the space of weight k weakly holomorphic weight modular forms with poles only at the cusp (∞), and let widehat M_k^(∞) (Gamma, nu) subseteq M_k^(∞) (Gamma, nu) denote the space of weight k weakly holomorphic modular forms in M_k^(∞) (Gamma, nu) which vanish at every cusp other than (∞). We construct canonical bases for these spaces in terms of Maass--Poincaré series, and show that the coefficients of these bases satisfy Zagier duality.

Robust Estimation Of Parametric Models For Insurance Loss Data, Chudamani Poudyal

Theses and Dissertations

Parametric statistical models for insurance claims severity are continuous, right-skewed, and frequently heavy-tailed. The data sets that such models are usually fitted to contain outliers that

are difficult to identify and separate from genuine data. Moreover, due to commonly used actuarial “loss control strategies,” the random variables we observe and wish to model are affected by truncation (due to deductibles), censoring (due to policy limits), scaling

(due to coinsurance proportions) and other transformations. In the current practice, statistical inference for loss models is almost exclusively likelihood (MLE) based, which typically results in non-robust parameter estimators, pricing models, and risk measures. …

Network Specializations, Symmetries, And Spectral Properties, Dallas C. Smith

Theses and Dissertations

In this dissertation, we introduce three techniques for network sciences. The first of these techniques is a series of new models for describing network growth. These models, called network specialization models, are built with the idea that networks grow by specializing the function of subnetworks. Using these models we create theoretical networks which exhibit well-known properties of real networks. We also demonstrate how the spectral properties are preserved as the models grow. The second technique we describe is a method for decomposing networks that contain automorphisms in a way that preserves the spectrum of the original graph. This method …

Fitting A Complex Markov Chain Model For Firm And Market Productivity, Julia Ruth Valder

Theses and Dissertations

This thesis develops a methodology of estimating parameters for a complex Markov chain model for firm productivity. The model consists of two Markov chains, one describing firm-level productivity and the other modeling the productivity of the whole market. If applicable, the model can be used to help with optimal decision making problems for labor demand. The need for such a model is motivated and the economical background of this research is shown. A brief introduction to the concept of Markov chains and their application in this context is given. The simulated data that is being used for the estimation is …

Numerical Solution Of Stochastic Control Problems Using The Finite Element Method, Maritn Gerhard Vieten

Theses and Dissertations

Based on linear programming formulations for infinite horizon stochastic control problems, a numerical technique in fashion of the finite element method is developed. The convergence of the approximate scheme is shown and its performance is illustrated on multiple examples. This thesis begins with an introduction of stochastic optimal control and a review of the

theory of the linear programming approach. The analysis of existence and uniqueness of solutions to the linear programming formulation for fixed controls represents the first contribution of this work. Then, an approximate scheme for the linear programming formulations is established. To this end, a novel discretization …

Optimal Insurance With Background Risk: An Analysis In The Presence Of Moderate Negative Dependence, Julian Johannes Dursch

Theses and Dissertations

As an individual or a corporation, there are various types of risks one faces. For many of these risks, there are insurance policies available for purchase that provide some protection against potential losses. However, there are also risks that are not insurable. These risks remain present as a background factor and affect the insured's final wealth. Consequentially, they have an impact on the optimal insurance for the insurable risk through the dependence structure between the insurable and uninsurable risk.

In this thesis, we take a look at the optimal insurance problem given an insurable risk Xand a background risk Y …

Optimal Deductibles: A Theoretical Analysis From An Insured's Perspective, Alexander Kreienbring

Theses and Dissertations

A stop-loss policy as a tool for protection against a large loss is one of the most common insurance forms. For fixed premiums and therefore a uniquely determined insurance deductible, it has been well-established that the stop-loss form is superior to all other common

insurance forms (Arrow, 1963). Using the expected premium principal, one can relax the assumption of a fixed premium and allow the insured to choose an arbitrary deductible that fits their needs.

This thesis presents a stop-loss insurance policy model from an insured's perspective for a flexible premium. It shows the existence and uniqueness of an optimal …

Exact Sampling And Prefix Distributions, Sebastian Oberhoff

Theses and Dissertations

This thesis explores some new means to generate random numbers without incurring any numerical

inaccuracies along the way. In the context of continuous distributions this leads to the discussion of

prex distributions { discrete distributions that fully capture a continuous distribution by describing

their initial digits. These are rst studied graphically, then analytically, which also leads to a general

examination of the behavior of the distribution of trailing digits of continuous distributions. Finally,

some slightly novel, related results from the theory of computation are presented.

Orthogonal Abelian Cartan Subalgebra Decompositions Of Classical Lie Algebras Over Finite Commutative Rings, Songpon Sriwongsa

Theses and Dissertations

Orthogonal decompositions of classical Lie algebras over the complex numbers of types A, B, C and D were studied in the early 1980s and attracted further attention in the past decade, especially in the type A case, due to its application in quantum information theory. In this dissertation, we consider the orthogonal decomposition problem of Lie algebras of type A, B, C and D over a finite commutative ring with identity. We first establish the appropriate definition of orthogonal decomposition under our setting, and then derive some general properties that rely on the finite commutative rings theory. Our goal is …