Physical Sciences and Mathematics Commons^™

On Logconcavity Of Multivariate Discrete Distributions, Majed Ghazi Alharbi

Theses and Dissertations

The contribution of this dissertation to the literature is twofold. First, we use a geometric perspective to present all possible subdivisions of R³ into tetrahedra with disjoint interiors and adopt a combinatorial approach to obtain a special subdivision of Rⁿ into simplices with disjoint interiors, where two simplices are called neighbors if they share a common facet. We then use the neighborhood relationship of the simplices in each subdivision to fully describe the sufficient conditions for the strong unimodality/logconcavity of the trivariate discrete distributions and further extend these results to present a new sufcient condition for the strong unimodality/logconcavity of …

Parametric And Non-Parametric Regression Models With Applications To Climate Change, Osita Eluemuno Onyejekwe

Theses and Dissertations

In this dissertation we have studied the climate factors that contribute to climate change using univariate and multivariate parametric methods as well as nonparametric models. In this study, we have three major contributions. First, the extent of mountain glaciers around the globe and their responses to climate factors are investigated using multivariate methods and we have proposed a predictive model to estimate the mountain glacier response to climate factors. Second, we have addressed the important problem of bandwidth selection in presence of correlated noise in nonparametric regression analysis. We have proposed a denoising method based on an ensemble bandwidth optimization …

Nonlocal Electrostatics In Spherical Geometries, Andrew Bolanowski

Theses and Dissertations

Nonlocal continuum electrostatic models have been used numerically in protein simulations, but analytic solutions have been absent. In this paper, two modified nonlocal continuum electrostatic models, the Lorentzian Model and a Linear Poisson-Boltzmann Model, are presented for a monatomic ion treated as a dielectric continuum ball. These models are then solved analytically using a system of differential equations for the charge distributed within the ion ball. This is done in more detail for a point charge and a charge distributed within a smaller ball. As the solutions are a series, their convergence is verified and criteria for improved convergence is …

Splittings Of Relatively Hyperbolic Groups And Classifications Of 1-Dimensional Boundaries, Matthew Haulmark

Theses and Dissertations

In the first part of this dissertation, we show that the existence of non-parabolic local cut point in the relative (or Bowditch) boundary, $\relbndry$, of a relatively hyperbolic group $(\Gamma,\bbp)$ implies that $\Gamma$ splits over a $2$-ended subgroup. As a consequence we classify the homeomorphism type of the Bowditch boundary for the special case when the Bowditch boundary $\relbndry$ is one-dimensional and has no global cut points.

In the second part of this dissertation, We study local cut points in the boundary of CAT(0) groups with isolated flats. In particular the relationship between local cut points in $\bndry X$ and …

Extensions Of Enveloping Algebras Via Anti-Cocommutative Elements, Daniel Owen Yee

Theses and Dissertations

We know that given a connected Hopf algebra H, the universal enveloping algebra

U(P(H)) embeds in H as a Hopf subalgebra. Depending on P(H), we show that

there may be another enveloping algebra (not as a Hopf subalgebra) within H by

using anti-cocommutative elements. Thus, this is an extension of enveloping

algebras with regards to the Hopf structure. We also use these discoveries to apply

to global dimension, and finish with antipode behavior and future research projects.

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.

Modeling The Influence Of El Niño On Parasite Transmission In Sand Crab Populations And Seabird Abundance Along The Californian Coast, Aboubacar Dio Seck

Theses and Dissertations

Pacific mole crabs (Emerita analoga) are one of the most important and abundant

invertebrates in sandy beach environments. Consequently, they are a common food source

for seabirds and sea otters. Since the mole crab serves as the primary intermediate host for

acanthocephalan parasites, they have been linked to a number of mortality events. It is

currently estimated that 13-16% of deaths in the threatened California sea otter population

have been caused by infection. In addition, unusually high loads of acanthocephalan

parasites have been linked to episodic deaths of thousands of surf scoters. Studies suggest

that acanthocephalan development and transmission may …

Weakly Holomorphic Modular Forms In Level 64, Christopher William Vander Wilt

Theses and Dissertations

Let M^#_k(64) be the space of weakly holomorphic modular forms in level 64 and weight k which can have poles only at infinity, and let S^#_k(64) be the subspace of M^#_k(64) consisting of forms which vanish at all cusps other than infinity. We explicitly construct canonical bases for these spaces and show that the coefficients of these basis elements satisfy Zagier duality. We also compute the generating function for the canonical basis.

Busemann G-Spaces, Cat(K) Curvature, And The Disjoint (0, N)-Cells Property, Clarke Alexander Safsten

Theses and Dissertations

A review of geodesics and Busemann G-spaces is given. Aleksandrov curvature and the disjoint (0, n)-cells property are defined. We show how these properties are applied to and strengthened in Busemann G-spaces. We examine the relationship between manifolds and Busemann G-spaces and prove that all Riemannian manifolds are Busemann G-spaces, though not all metric manifolds are Busemann G-spaces. We show how Busemann G-spaces that also have bounded Aleksandrov curvature admit local closest-point projections to geodesic segments. Finally, we expound local properties of Busemann G-spaces and define a new property which we call the symmetric property. We show that Busemann …

Spaces Of Weakly Holomorphic Modular Forms In Level 52, Daniel Meade Adams

Theses and Dissertations

Let M^#_k(52) be the space of weight k level 52 weakly holomorphic modular forms with poles only at infinity, and S^#_k(52) the subspace of forms which vanish at all cusps other than infinity. For these spaces we construct canonical bases, indexed by the order of vanishing at infinity. We prove that the coefficients of the canonical basis elements satisfy a duality property. Further, we give closed forms for the generating functions of these basis elements.

Stability Of Planar Detonations In The Reactive Navier-Stokes Equations, Joshua W. Lytle

Theses and Dissertations

This dissertation focuses on the study of spectral stability in traveling waves, with a special interest in planar detonations in the multidimensional reactive Navier-Stokes equations. The chief tool is the Evans function, combined with STABLAB, a numerical library devoted to calculating the Evans function. Properly constructed, the Evans function is an analytic function in the right half-plane whose zeros correspond in multiplicity and location to the spectrum of the traveling wave. Thus the Evans function can be used to verify stability, or to locate precisely any unstable eigenvalues. We introduce a new method that uses numerical continuation to follow unstable …

Infinite-Dimensional Traits: Estimation Of Mean, Covariance, And Selection Gradient Of Tribolium Castaneum Growth Curves, Ly Viet Hoang

Theses and Dissertations

In evolutionary biology, traits like growth curves, reaction norms or morphological shapes cannot be described by a finite vector of components alone. Instead, continuous functions represent a more useful structure. Such traits are called function-valued or infinite-dimensional traits. Kirkpatrick and Heckmann outlined the first quantitative genetic model for these traits. Beder and Gomulkiewicz extended the theory on the selection gradient and the evolutionary response from finite- to infinite-dimensional traits.

Rigorous methods for the estimation of these quantities were developed throughout the years. In his dissertation, Baur defines estimators for the mean and covariance function, as well as for the selection …

Robust And Computationally Efficient Methods For Fitting Loss Models And Pricing Insurance Risks, Qian Zhao

Theses and Dissertations

Continuous parametric distributions are useful tools for modeling and pricing insurance risks, measuring income inequality in economics, investigating reliability of engineering systems, and in many other areas of application. In this dissertation, we propose and develop a new method for estimation of their parameters—the method of Winsorized moments (MWM)—which is conceptually similar to the method of trimmed moments (MTM) and thus is robust and computationally efficient. Both approaches yield explicit formulas of parameter estimators for location-scale and log-location-scale families, which are commonly used to model claim severity. Large-sample properties of the new estimators are provided and corroborated through simulations. Their …

Performance Optimization Of Onboard Lithium Ion Batteries For Electric Vehicles, Rohit Anil Ugle

Theses and Dissertations

Next generation of transportation in the form of electric vehicles relies on better operation and control of large battery packs. The individual modules in large battery packs generally do not have identical characteristics and may degrade differently due to manufacturing variability and other factors. Degraded battery modules waste more power, affecting the performance and economy for the whole battery pack. Also, such impact varies with different trip patterns. It will be cost effective if we evaluate the performance of the battery modules prior to replacing the complete battery pack. The knowledge of the driving cycle and battery internal resistance will …

Adaptive Monte Carlo Sampling For Cloud And Microphysics Calculations, Thomas Franz-Peter Roessler

Theses and Dissertations

An important problem in large-scale modeling of the atmosphere is the parametrization of clouds and microphysics on subgrid scales. The framework Cloud Layers Unified By Binormals (CLUBB) was developed to improve the parametrization of subgrid variability. Monte Carlo sampling is used to couple the different physical processes, which improves the grid average of subgrid tendencies.

In this Thesis we develop an adaptive Monte Carlo sampling algorithm that re-uses sample points of the previous time step by re-weighting them according to the change of the underlying distribution. This process is called 'what-if sampling' and is an application of importance sampling. An …

Goodness-Of-Fit Testing For Copula-Based Models With Application In Atmospheric Science, Albert Rapp

Theses and Dissertations

Every elementary probability course discusses how to construct joint distribution functions of independent random variables but joint distribution functions of dependent random variables are usually omitted. Obviously, the reason is that things are not as simple as in the independent case. In this matter, so-called copulas can be an elegant tool to investigate dependency structures other than independence.

A copula is a convenient function which links the marginal distributions of random variables to their joint distribution. The beauty here is that one can use suitable copulas to model any desired dependence structure between any set of random variables without even …

Associated Hypothesis In Linear Models With Unbalanced Data, Rica Katharina Wedowski

Theses and Dissertations

In a two-way linear model one can test six different hypotheses regarding the effects in this model. Those hypotheses can be ranked from less specific to more specific. Therefore the more specific hypotheses are nested in the less specific ones. To test those nested hypotheses sequential sums of squares are used. Searle sees a problem with these since they test an associated hypothesis that has the same sums of squares but involve the sample sizes. Hypotheses should be generic and not dependent on the data. The proof he uses in his book Linear Models for Unbalanced Data is not easy …

A Study Of The Effect Of Using Simulations On Students' Learning Of Inferential Statistics In The Elementary Statistics Classes In The Mathematics Department Of The University Of Wisconsin Milwaukee, Alexa Schut

Theses and Dissertations

This thesis reports the results of a studying into the use of simulation-based teaching in Introductory Statistics Class to analyze the effectiveness of this teaching strategy. We give a brief overview of the more recent research into the impact of using computer simulations in an introductory statistics course in order to deepen student understanding of inferential statistics along with the a look at a similar study recently conducted at another university. We then give a review of our study conducted in Math Stat 215 classes at UW-Milwaukee to evaluate whether or not the use of simulations in this introductory statistics …

On Some One-Complex Dimensional Slices Of The Boundedness Locus Of A Multi-Parameter Rational Family, Matthew Hoeppner

Theses and Dissertations

Complex dynamics involves the study of the behavior of complex-valued functions when they are composed with themselves repeatedly. We observe the orbits of a function by passing starting values through the function iteratively. Of particular interest are the orbits of any critical points of the function, called critical orbits. The behavior of a family of functions can be determined by examining the change in the critical orbit(s) of the functions as the values of the associated parameters vary. These behaviors are often separated into two categories: parameter values where one or more critical orbits remain bounded, and parameter values where …

Modeling Of Anticancer Drug Delivery By Temperature-Sensitive Liposomes, Vera Franziska Loeser

Theses and Dissertations

Cytotoxic anticancer drugs are used to treat cancer, particularly tumors. These drugs themselves do not distinguish between healthy and tumor cells and attack all of them. Consequently physicians and chemists investigate safer ways of delivery that minimize damage to healthy cells. One of these ways are liposomal formulations of the anticancer drugs. Liposomes are vesicles that encapsulate the drug to shield the healthy parts of the body from the toxicity of the drugs. Due to the abnormal structure of tumors, especially their leaky vasculature, these macromolecules are able to diffuse into the tumor tissue whereas the normal vasculature prevents them …

Numerical Methods For Hamilton-Jacobi-Bellman Equations, Constantin Greif

Theses and Dissertations

In this work we considered HJB equations, that arise from stochastic optimal control problems

with a finite time interval. If the diffusion is allowed to become degenerate, the solution cannot be

understood in the classical sense. Therefore one needs the notion of viscosity solutions. With some

stability and consistency assumptions, monotone methods provide the convergence to the viscosity

solution. In this thesis we looked at monotone finite difference methods, semi lagragian methods and

finite element methods for isotropic diffusion. In the last chapter we introduce the vanishing moment

method, a method not based on monotonicity.

Optimal Trading Under The American Perpetual Put Option For Geometric Brownian Motion And Mean-Reverting Processes, Ines Larissa Siebigteroth

Theses and Dissertations

This thesis is focused on the perpetual American put option under the geometric Brownian motion and mean-reverting models. Two approaches, which have been applied before to the call option of a mean-reverting process, will be studied in details for the two models. The first approach amounts to solving the associated quasi-variational inequality for the optimal stopping problem. A verification theorem is proved to demonstrate that the solution to the quasi-variational inequality agrees with the value function. The second approach is based on detailed analyses of an auxiliary two-point stopping problem, which leads to an explicit expression for the value function. …

Cocompact Cubulations Of Mixed 3-Manifolds, Joseph Dixon Tidmore

Theses and Dissertations

In this dissertation, we complete the classification of which compact 3-manifolds have a virtually compact special fundamental group by addressing the case of mixed 3-manifolds. A compact aspherical 3-manifold M is mixed if its JSJ decomposition has at least one JSJ torus and at least one hyperbolic block. We show the fundamental group of M is virtually compact special iff M is chargeless, i.e. each interior Seifert fibered block has a trivial Euler number relative to the fibers of adjacent blocks.

Asymptotic Expansion Of The L^2-Norm Of A Solution Of The Strongly Damped Wave Equation, Joseph Silvio Barrera

Theses and Dissertations

The Fourier transform, F, on R^N (N≥1) transforms the Cauchy problem for the strongly damped wave equation u_tt(t,x) - Δu_t(t,x) - Δu(t,x) = 0 to an ordinary differential equation in time t. We let u(t,x) be the solution of the problem given by the Fourier transform, and v(t,ƺ) be the asymptotic profile of F(u)(t,ƺ) = û(t,ƺ) found by Ikehata in [4].

In this thesis we study the asymptotic expansions of the squared L^2-norms of u(t,x), û(t,ƺ) - v(t,ƺ), and v(t,ƺ) as t → ∞. With suitable initial data u(0,x) and u_t(0,x), we establish the rate of growth or decay of …

Black-Scholes Model: An Analysis Of The Influence Of Volatility, Cornelia Krome

Theses and Dissertations

In this thesis the influence of volatility in the Black-Scholes model is analyzed. The deduced Black-Scholes formula estimates the price of European options. Contrary to the other parameters of the formula, the future volatility of the underlying asset cannot be observed in the market. The parameter needs to be assumed in order to calculate the option price. An inaccurate assumption may lead to an erroneous volatility. It is studied how a falsely assumed volatility impacts on the option price. Empirical simulations will be carried out to get an impression of possible errors in the computations. Afterwards, those results will be …

Investigating The Mathematical Dispositions And Self-Efficacy For Teaching Mathematics Of Preservice Teachers, Jasmine M. Cruz

Theses and Dissertations

The study of the individual's beliefs and the role and influence they have on the individual's actions and behaviors, have long been examined and investigated by educators and psychologists. Moreover, researchers have overwhelmingly claimed and demonstrated that the beliefs held by teachers significantly influences their behavior and educational practices in the classroom. This thesis study investigates the mathematical disposition and self-efficacy for teaching mathematics of preservice teachers. The study's primary goals are to discover if there is a relationship or association between a teacher's mathematical disposition(MD) and his/her self-efficacy for teaching mathematics (SEFTM), and if there are significant differences between …

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.