Digital Commons Network^™

Pm2.5 Data Reliability And Air Quality Improvement Trends In Beijing, Huimin Li

Theses and Dissertations

PM2.5 has been a main environmental concern due to its adverse effects on human health and society. We used data from two sources: monitoring station of the U.S. Embassy in Beijing, and several nearby monitoring stations of the Chinese Ministry of Environmental Protection. This study includes investigating (1) PM2.5 historical data reliability, (2) PM2.5 real-time data reliability, and (3) air quality improvement trends in Beijing over the past decade. We used graphical methods, descriptive statistics, correlation analysis, and inferential analyses including paired samples t-test, ANOVA, and Kruskal-Wallis test. We reported effect sizes to aid study on practical significance. Inferential procedures' …

Existence And Classification Of Solutions To Nonlinear Elliptic Equations, Haseeb E. Ansari

Theses and Dissertations

The so-called Lane-Emden equation is a model in astrophysics, useful to problems in analysis and conformal geometry, and is closely related to the Yamabe Problem and the Uniformization Theorem. We discuss several important results for the equation, which include proving that the equation admits a distribution solution if and only if p is greater than the Serrin exponent, that classical solutions admit the form of a "bubble function" if p is equal to the Sobolev exponent, and no classical solutions exist for p less than the Sobolev exponent. A new proof of an extended result is also included.

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 …

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 …

Hankel Partial Contraction, Contractive Completion, Moore-Penrose Inverse, Extremal Case, Manuel A. Villarreal Jr.

Theses and Dissertations

In this article we find concrete necessary and sufficient conditions for the existence of contractive completions of Hankel partial contractions of size 3x3 non-extremal case.

Multi-Type Branching Processes Model Of Nosocomial Epidemic, Zeinab Nageh Mohamed

Theses and Dissertations

The potency of an infectious disease to spread between different types of susceptible individuals in a hospital determines the fate of controlling nosocomial epidemics. I use a multi-type branching process with a joint negative binomial offspring distribution to study nosocomial epidemics. In particular, I estimate the basic reproduction number R0 and study its relationship with the offspring distribution’s parameters at different and fixed number of generations. Also, I study the effect of contact tracing on estimates of R0.

Disease Modeling Using Fractional Differential Equations And Estimation, Daniel P. Medina

Theses and Dissertations

Ordinary differential equations has been the most conventional approach when modeling spread of infectious diseases. Effective research has shown that using fractional-order differentiation can be a very useful and efficient extension for some mathematical models. In this thesis, fractional calculus is used to depict an SEIR model with a system of fractional-order differential equations. I also simulate the fractional-order SEIR using integer-order numerical methods. I also establish the estimation framework and show that it is accurately working.

Mathematical Modeling Of Mers-Cov Nosocomial Epidemic, Adriana Quiroz

Theses and Dissertations

This thesis concerns about the analysis and modeling of spread of an infectious disease inside a hospital. We begin from the basic knowledge of the simple models: SIR and SEIR, to show an appropriate understanding of the epidemic dynamic process. We consider the Middle East Respiratory Syndrome Corona Virus (MERS-CoV), in Saudi Arabia, to introduce MERS-CoV SEIR ward model by developing different systems of equations in each ward (unit). We use the Next Generation Matrix method to calculate the basic reproduction number R0. Simulations of different scenarios are done using different combination of parameters.

To model MERS-CoV we established …

Problem Book On Higher Algebra And Number Theory, Ryanto Putra

Theses and Dissertations

This book is an attempt to provide relevant end-of-section exercises, together with their step-by-step solutions, to Dr. Zieschang's classic class notes Higher Algebra and Number Theory. It's written under the notion that active hands-on working on exercises is an important part of learning, whereby students would see the nuance and intricacies of a math concepts which they may miss from passive reading. The problems are selected here to provide background on the text, examples that illuminate the underlying theorems, as well as to fill in the gaps in the notes.

Coupled Telegraph And Sir Model Of Information And Diseases, Jose De Jesus Galarza

Theses and Dissertations

In this work, the effect of information propagation on disease spread and vaccination uptake through networks is studied. In this model the information reaches different people at different distances from the center of information containing the health data. We use a pair of Telegraph equations to depict the vaccine and disease information propagation on a network embedded into a straight line. The Telegraph equation is coupled with an SIR (Susceptible-Infected-Recovered) model to examine the anticipated mutual influence. Numerical simulations and stability analysis were made to study the model. We show how the propagation of information about the disease impacts the …

A New Approach To Ramanujan's Partition Congruences, Mayra C. Huerta

Theses and Dissertations

MacMahon provided Ramanujan and Hardy a table of values for p(n) with the partitions of the first 200 integers. In order to make the table readable, MacMahon grouped the entries in blocks of five. Ramanujan noticed that the last entry in each block was a multiple of 5. This motivated Ramanujan to make the following conjectures, p(5n+4) ≡ 0 (mod 5); p(7 n+5) ≡ 0 (mod 7); p(11n+6) ≡ 0 (mod 11) which he eventually proved.

The purpose of this thesis is to give new proofs for Ramanujan's partition …

Numerical Simulations Of Shock Waves Reflection And Interaction, Ligang Sun

Theses and Dissertations

The main objective of this dissertation is to detect and study the phenomena of reflection of one shock wave and interaction of two shock waves using numerical methods. In theory, solutions of non-linear Euler equations of compressive inviscid gas dynamics in two dimensions can display various features including shock waves and rarefaction waves. To capture the shock waves properly, highly accurate numerical schemes are designed according to second order Lax-Wendroff method. In this thesis, three numerical experiments were designed to show the reflection and interaction phenomena. Firstly, one shock was formed due to the encounter of two high speed gas …

Sparse Representation For The Isar Image Reconstruction, Mengqi Hu

Theses and Dissertations

In this paper, a sparse representation for the data form a multi-input multi-output based inverse synthetic aperture radar (ISAR) system is derived for two dimensions. The proposed sparse representation motivates the use a of a Convex Optimization directly that recovers the image without the loss information of the image with far less samples that that is required by Nyquist–Shannon sampling theorem, which increases the efficiency and decrease the cost of calculation in radar imaging.

Lie Symmetry To Second-Order Nonlinear Differential Equations And Its First Integrals, Pengfei Gu

Theses and Dissertations

There are many well-known techniques for obtaining exact solutions of differential equations, but most of them are merely special cases of a few powerful symmetry methods. In this paper, we focus our attention on a second-order nonlinear ordinary differential equation of special forms with arbitrary parameters, which is a combination of Liénard-type equation and equation with quadratic friction. With the help of Lie Symmetry methods, we identify several integrable cases of this equation. And for each case, we use the Lie Symmetry method to derive the associated determining system, and apply it further to find infinitesimal generators under …

A Comparative Study And Data Analysis For The Ultimate Fighting Championship, Victor Villalpando

Theses and Dissertations

Mixed Martial Arts is the fastest growing sport with many organizations worldwide. The biggest stage or biggest organization for Mixed Martial Arts is the Ultimate Fighting Championship (UFC). There are eight weight classes for men. The website: http://www.foxsports.com/ufc/stats provides data on fighters in all these categories. This data measures Striking Accuracy, Take downs, Reversals, Knockdowns, etc. in each category. It is interesting to understand and interpret all these numbers and study their relationships. Statistical tools like both parametric and nonparametric inference may give rise to such interpretations and provide explanations how the weight classes differ from one another. In this …

Compressive Sensing And Radar Imaging, John Montalbo

Theses and Dissertations

The field of remote sensing contains many unique and practical problems. Radar imaging, in all of its many forms, lies within this field of study. One problem is the need to acquire high-resolution images and store them on-board the system acquisition vessel . For some systems this could mean storing very high amounts of data, depending on the scene in question [3]. So a very natural goal is to store only what is absolutely necessary and nothing more. We investigate methods to compress signals into their most important components so that other parties can recover the original data completely or …

Lie Symmetry To Nonlinear Oscillator Systems And Applications, Xiaoyan Li

Theses and Dissertations

In this paper, we apply the theory of Lie symmetry to study a generalized second-order nonlinear differential equation, which includes several physical nonlinear oscillators such as force-free Helmholtz oscillator, force-free Duffing and Duffing-van der Pol oscillators, modified Emden-type equation and its hierarchy etc, and investigate the dynamical properties of this rather general equation. We identify and classify several new integrable cases for arbitrary values of exponents, which determine the tangent vector as well as the infinitesimal generator. Using the Lie point symmetry, we find the useful infinitesimal generators and canonical coordinates, and obtain the first integrals of the second-order nonlinear …

On Hypergroups Of Order At Most 6, Jordy C. Lopez

Theses and Dissertations

This thesis surveys recent results on hypergroups as defined by Frédéric Marty in [3] and [4] and their relation to association schemes as presented in [5]. We show that every association scheme is a hypergroup. Then, we compile a few general results on hypergroups needed for our investigation of hypergroups with three, four and six elements. From [1] and [7], we give examples of hypergroups that do not come from finite schemes and from no scheme at all. Our main result occurs when considering hypergroups S with six elements that have a non-normal closed subset T of order 2 with …

Opinion Formation About Childhood Immunization And Disease Spread On Networks, Shan Shan Zhao

Theses and Dissertations

People are physically and socially connected with each other. Those connections between people represent two, probably overlapping, networks: biological networks, through which physical contacts occur, or social network, through which information diffuse. In my thesis research, I am trying to answer that question in the context of pediatric disease spread on the biological network between households as well as within them and its relationship with information sharing on the social network of households (parents in that case) via "Information Cascades." I mainly focus on the Erdos-Renyi network model. In particular, I use two different but overlapping Erdos-Renyi networks for the …

The Bourbaki-Jacobson Correspondence, Jose R. Vera

Theses and Dissertations

A general ring theoretic correspondence between subrings of the endomorphism ring of the additive group of a commutative field will be established. This correspondence (called Bourbaki-Jacobson Correspondence) provides the ordinary Galois correspondence when applied to specific group rings. Throughout this thesis, we will work with finite dimensional field extensions.