Physical Sciences and Mathematics Commons^™

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.

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 …

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 …

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 …

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 …