Mathematics Commons^™

Possible Bias In Asset Valuations: An Application Of The Fraud Risk Triangle To Divorce Cases, Jennifer Tomasetti

Honors Projects in Accounting

No abstract provided.

Applications Of Microlocal Analysis To Some Hyperbolic Inverse Problems, Andrew J Homan

Open Access Dissertations

This thesis compiles my work on three inverse problems: ultrasound recovery in thermoacoustic tomography, cancellation of singularities in synthetic aperture radar, and the injectivity and stability of some generalized Radon transforms. Each problem is approached using microlocal methods. In the context of thermoacoustic tomography under the damped wave equation, I show uniqueness and stability of the problem with complete data, provide a reconstruction algorithm for small attenuation with complete data, and obtain stability estimates for visible singularities with partial data. The chapter on synthetic aperture radar constructs microlocally several infinite-dimensional families of ground reflectivity functions which appear microlocally regular when …

Math Quiz On The Radio, Darren B. Glass

Math Faculty Publications

What word, often spelled with an umlaut, is used to identify a point on a two-dimensional graph?

Many of you probably already figured out the answer is "coordinate." But that's because you are sitting comfortably in your dorm room rather than being on a stage with bright lights in front of a few hundred people being recorded for national broadcast on public radio. [excerpt]

Why Some Families Of Probability Distributions Are Practically Efficient: A Symmetry-Based Explanation, Vladik Kreinovich, Olga Kosheleva, Hung T. Nguyen, Songsak Sriboonchitta

Departmental Technical Reports (CS)

Out of many possible families of probability distributions, some families turned out to be most efficient in practical situations. Why these particular families and not others? To explain this empirical success, we formulate the general problem of selecting a distribution with the largest possible utility under appropriate constraints. We then show that if we select the utility functional and the constraints which are invariant under natural symmetries -- shift and scaling corresponding to changing the starting point and the measuring unit for describing the corresponding quantity $x$. then the resulting optimal families of probability distributions indeed include most of the …

Transforming Precalculus Instruction: Evidence-Based Course Design, Wendy M. Smith

Discipline-Based Education Research Group Speaker Series

The UNL Mathematics Department has been focused on transforming precalculus instruction since 2012, with a goal of greater levels of student success. A short-term measure of student success is the passing rate (C or better), which has jumped from an average of 62% (2007-2011) to 80% for the past two falls. A longer-term measure of student success is recruiting and retaining undergraduates to STEM disciplines and careers. In this talk I will share specifics of the reform efforts (the who-what-when-where-why-and-how), and also share preliminary results from the research we have simultaneously been conducting into the reform efforts.

Parallel Preconditioners For Finite Element Computations, Emily Furst

Honors Theses, 1963-2015

This thesis sought to explore numerical methods for solving partial differential equations and to determine the best method of updating the deal.II software to utilize new Trilinos software packages. The one dimensional heat equation with Dirichlet boundary conditions and nonzero initial conditions was solved analytically, using the Forward in Time, Central in Space scheme of the finite difference method, and the Crank-Nicolson scheme of the finite element method. The solutions from using the finite difference method and the finite element method were then compared to the analytic solution to determine accuracy. An example using the same Trilinos packages that are …

Once We Know That A Polynomial Mapping Is Rectifiable, We Can Algorithmically Find A Rectification, Julio Urenda, David Finston, Vladik Kreinovich

Departmental Technical Reports (CS)

It is known that some polynomial mappings φ: C^k --> Cⁿ are rectifiable in the sense that there exists a polynomial mapping α: Cⁿ --> Cⁿ whose inverse is also polynomial and for which α(φ(z₁, ...,z_k)) = (z₁, ...,z_k, 0, ..., 0) for all z₁, ...,z_k. In many cases, the existence of such a rectification is proven indirectly, without an explicit construction of the mapping α.

In this paper, we use Tarski-Seidenberg algorithm (for deciding the first order theory of real numbers) to design …

When Can We Simplify Data Processing: An Algorithmic Answer, Julio Urenda, Olga Kosheleva, Vladik Kreinovich, Berlin Wu

Departmental Technical Reports (CS)

In many real-life situations, we are interested in the values of physical quantities x₁, ..., x_n which are difficult (or even impossible) to measure directly. To estimate these values, we measure easier-to-measure quantities y₁, ..., y_m which are related to the desired quantities by a known relation, and use these measurement results to estimate x_i. The corresponding data processing algorithms are sometimes very complex and time-consuming, so a natural question is: are simpler (and, thus, faster) algorithms possible for solving this data processing problem? In this paper, we show that by using …

Sensitivity Of Mixed Models To Computational Algorithms Of Time Series Data, Gunaime Nevine

Doctoral Dissertations

Statistical analysis is influenced by implementation of the algorithms used to execute the computations associated with various statistical techniques. Over many years; very important criteria for model comparison has been studied and examined, and two algorithms on a single dataset have been performed numerous times. The goal of this research is not comparing two or more models on one dataset, but comparing models with numerical algorithms that have been used to solve them on the same dataset.

In this research, different models have been broadly applied in modeling and their contrasting which are affected by the numerical algorithms in different …

Root Cover Pebbling On Graphs, Claire A. Sonneborn

Honors Theses

Consider a graph, G, with pebbles on its vertices. A pebbling move is defined to be the removal of two pebbles from one vertex and the addition of one pebble to an adjacent vertex. The cover pebbling number of a graph, γ(G), is the minimum number of pebbles such that, given any configuration of γ(G) pebbles on the vertices of G, pebbling moves can be used to place one pebble on each vertex of G. We define the root vertex of a graph and fix an initial configuration of pebbles on G where we place all pebbles on the root …

A Comparison Of Mathematics Content In The 2002 And 2014 Ged Test, Genice Cox

All Capstone Projects

As society changes and competition grows, the skilled worker becomes hard to find. For these reasons, secondary education is the starting point for pursuing college, a trade, and a career. For more than 60 years individuals have been given a second chance to complete their high school education by taking the General Education Development (GED) exam. This exam has been updated to correspond to changes in society and the workforce. As of 2014, the GED test was changed dramatically. This research project traced from past to present the intent of the assessment, teaching methods, curriculum, statistics, and overall preparation of …

Mathematical Modeling Of The Imported Malaria In The United Arab Emirates, Fatima Hassan Ali Alawadhi

Theses

Although the UAE was certified to be free of local malaria transmission cases in 2007, the increased number of imported malaria cases in recent years required the attention of the public health professionals. The aim of this work is to study, via mathematical modeling, the impact of imported malaria cases on the population of the UAE. The nature of the health policies in the UAE imposes on us a model that classifies the living population of the UAE in two categories. The local population, who represent the permanent residents that do not have any health requirement for their residency, and …

Development Of Analytical Sensitivity Analysis For Ahp Applications, Marie L. Ivanco

Mechanical & Aerospace Engineering Theses & Dissertations

Decision makers often face complex problems, which can seldom be addressed without the use of structured analytical models. Mathematical models have been developed over the last 50 years to streamline and facilitate decision making activities. The Analytic Hierarchy Process constitutes one of the most utilized Multi-Criteria Decision Analysis Methods. While AHP has been thoroughly researched and applied, the method still shows limitations in terms of integrating profile disparities of Subject Matter Experts (SMEs). This thesis develops an analytical sensitivity analysis method for AHP based on local partial derivatives to address these limitations. Four examples are presented to demonstrate and validate …

Uncertainty Quantification And Calibration Of Physical Models, Xian He

Open Access Dissertations

An ecosystem model is a representation of a real complex ecological system, and is usually described by sophisticated mathematical models. Terrestrial Ecosystem Model (TEM) is one of the ecosystem models, that describes the dynamics of car- bon, nitrogen, water and other vegetation related variables. There are uncertainties in the TEM which are attributed to inaccurate input data, insufficient knowledge of the parameters, inherent randomness and simplification of the physical model. Quantification of uncertainty of such an ecosystem model is computationally very heavy. Bayesian calibration method has been used as an efficient way to calibrate and quantify uncertainties of the computer …

Functional Inequalities And The Curvature Dimension Inequality On Totally Geodesic Foliations, Bumsik Kim

Open Access Dissertations

We discover following analytic / geometric properties on Riemannian foliations with bundle-like metric and totally geodesic leaves, or shortly, totally geodesic foliations. Under a certain curvature condition, we obtain (1) Sobolev-isoperimetric inequalities, global Poincar\'e inqualities, and a lower bound for Cheeger's isoperimetric constant, (2) Poincar\'e inequalities on balls and uniqueness of positive(or $L^p,p\geq 1$) solutions for the subelliptic heat equation, (3) A lower bound for the first non-zero eigenvalue of sub-Laplacians (Lichnerowicz theorem), and Obata's sphere theorem. In this context, the curvature condition is a sub-Riemannian analogue of lower bounds for Ricci curvature tensor. Earlier, it is given by Baudoin-Garofalo's …

A Pure-Jump Market-Making Model For High-Frequency Trading, Chi Wai Law

Open Access Dissertations

We propose a new market-making model which incorporates a number of realistic features relevant for high-frequency trading. In particular, we model the dependency structure of prices and order arrivals with novel self- and cross-exciting point processes. Furthermore, instead of assuming the bid and ask prices can be adjusted continuously by the market maker, we formulate the market maker's decisions as an optimal switching problem. Moreover, the risk of overtrading has been taken into consideration by allowing each order to have different size, and the market maker can make use of market orders, which are treated as impulse control, to get …

G-Frobenius Manifolds, Byeongho Lee

Open Access Dissertations

The goal of this dissertation is to introduce the notion of G-Frobenius manifolds for any finite group G. This work is motivated by the fact that any G-Frobenius algebra yields an ordinary Frobenius algebra by taking its G-invariants. We generalize this on the level of Frobenius manifolds. To define a G-Frobenius manifold as a braided-commutative generalization of the ordinary commutative Frobenius manifold, we develop the theory of G-braided spaces. These are defined as G-graded G-modules with certain braided-commutative "rings of functions", generalizing the commutative rings of power series on ordinary vector spaces. As the genus zero part of any ordinary …

Ergodic Properties Of Countable Extensions, Samuel Joshua Roth

Open Access Dissertations

First, we study countably piecewise continuous, piecewise monotone interval maps. We establish a necessary and sufficient criterion for the existence of a non-decreasing semiconjugacy to an interval map of constant slope in terms of the existence of an eigenvector of an operator acting on a space of measures. Then we give examples, both Markov and non-Markov, for which the criterion is violated. ^ Next, we establish a criterion for the existence of a constant slope map on the extended real line conjugate to a given countably piecewise monotone interval map. We require the given interval map to be continuous, Markov, …

Heat Trace And Heat Content Asymptotics For Schrodinger Operators Of Stable Processes/Fractional Laplacians, Luis Guillermo Acuna Valverde

Open Access Dissertations

Let V be a bounded and integrable potential over R^d and 0 < α ≤ 2. We show the existence of an asymptotic expansion by means of Fourier Transform techniques and probabilistic methods for the following quantities [special characters omitted] and [special characters omitted] as t ↓ 0. These quantities are called the heat trace and heat content in R^d with respect to V, respectively. Here, p((α)/ t)(x, y) and p( ^H_V/t)(x, y) denote, respectively, the heat kernels of the heat semigroups with infinitesimal generators given by (-Δ)(α/2) and H_V = (-Δ)(α/2) + V. The former operator is known as the fractional Laplacian whereas the latter one is known as the fractional Schrödinger Operator. ^ The study …

Orderability And Rigidity In Contact Geometry, Peter Weigel

Open Access Dissertations

We study the existence of positive loops of contactomorphisms on a Liouville-fillable contact manifold (&Sgr;, ξ = ker(α)). Previous results (see [1]) show that a large class of Liouville-fillable contact manifolds admit contractible positive loops. In contrast, we show that for any Liouville-fillable (&Sgr;, α) with dim(&Sgr;) ≥ 7, there exists a Liouville-fillable contact structure ξ' on &Sgr; which admits no positive loop at all. Further, ξ' can be chosen to agree with ξ' on the complement of a Darboux ball. We then define a relative version of orderability for a Legendrian submanifold, and discuss the relationship between the two …