Mathematics Commons^™

Improved Full-Newton-Step Infeasible Interior-Point Method For Linear Complementarity Problems, Mustafa Ozen

College of Graduate Studies: Theses & Dissertations

In this thesis, we present an improved version of Infeasible Interior-Point Method (IIPM) for monotone Linear Complementarity Problem (LCP). One of the most important advantages of this version in compare to old version is that it only requires feasibility steps. In the earlier version, each iteration consisted of one feasibility step and some centering steps (at most three in practice). The improved version guarantees that after one feasibility step, the new iterated point is feasible and close enough to central path. Thus, the centering steps are eliminated. This improvement is based on the Lemma(Roos, 2015). Thanks to this lemma, proximity …

Labeled Trees And Spanning Trees: Computational Discrete Mathematics And Applications, Demet Yalman

College of Graduate Studies: Theses & Dissertations

In this thesis, we examine two topics. In the first part, we consider Leech tree which is a tree of order n with positive integer edge weights such that the weighted distances between pairs of vertices are exactly from 1 to n choose 2. Only five Leech trees are known and some non-existence results have been presented through the years. Variations of Leech trees such as the minimal distinct distance trees and modular Leech trees have been considered in recent years. In this thesis, such Leech-type questions on distances between leaves are studied as well as some other labeling questions …

Modeling Network Worm Outbreaks, Evan Foley

Electronic Theses and Dissertations

Due to their convenience, computers have become a standard in society and therefore, need the utmost care. It is convenient and useful to model the behavior of digital virus outbreaks that occur, globally or locally. Compartmental models will be used to analyze the mannerisms and behaviors of computer malware. This paper will focus on a computer worm, a type of malware, spread within a business network. A mathematical model is proposed consisting of four compartments labeled as Susceptible, Infectious, Treatment, and Antidotal. We shall show that allocating resources into treating infectious computers leads to a reduced peak of infections across …

Aspects Of Fourier Analysis On Euclidean Space, Joseph William Roberts

Graduate Theses/Dissertations

The field of Fourier analysis encompasses a vast spectrum of mathematics and has far reaching applications in all STEM fields. Here we introduce and study the Fourier transform and Fourier series on Euclidean space. After defining the Fourier transform, establishing its basic properties, and presenting some classical results we looked into what impact the smoothness of a function has on the growth and integrability of its Fourier transform. This endeavor also involved a brief study of Bessel functions and interpolation of operators. Having established several results indicating that the behavior of a function's Fourier transform is largely dictated by the …

The Simulation & Evaluation Of Surge Hazard Using A Response Surface Method In The New York Bight, Michael H. Bredesen

UNF Graduate Theses and Dissertations

Atmospheric features, such as tropical cyclones, act as a driving mechanism for many of the major hazards affecting coastal areas around the world. Accurate and efficient quantification of tropical cyclone surge hazard is essential to the development of resilient coastal communities, particularly given continued sea level trend concerns. Recent major tropical cyclones that have impacted the northeastern portion of the United States have resulted in devastating flooding in New York City, the most densely populated city in the US. As a part of national effort to re-evaluate coastal inundation hazards, the Federal Emergency Management Agency used the Joint Probability Method …

Vitis Gene Expression Profiling Using Mixed Models, Yin Yin

Graduate Theses/Dissertations

The purpose of this thesis is to analyze gene expression in grapevine under different treatments using a mixed linear statistical model. The experiment involves two Vitis species (V. vinifera Cabernet sauvignon and V. aestivalis Norton) and applies two different treatments to them (inoculation with Erysiphe necator conidiospores and mock inoculation). There are three biological replicates measured at each of the following six assigned time points: 0, 4, 8, 12, 24, and 48 hours. By setting up split-plot model for the data, statistical hypotheses concerning gene expressions, especially gene expressions in terms of treatment effect, are tested. The result of the …

Connections Of Zero Curvature And Bäcklund Transformations, Paul Bracken

School of Mathematical & Statistical Sciences Faculty Publications

Zero curvature connections in a principal bundle are introduced. It is shown that such connections are very useful in formulating the Bäcklund problem and in constructing transformations. A general technique can be proposed for producing such transformations by defining the relevant connection coefficients appropriately. Finally, several applications of this work to various types of nonlinear partial differential equations will be presented.

Customizing Course Redesign And Flipped Classroom Models To Improve Learning Environment, Taeil Yi, Jerzy Mogilski

School of Mathematical & Statistical Sciences Faculty Publications

This article is about a successful adoption of course redesign model of mathematics courses at the Department of Mathematics in the University of Texas at Brownsville (UTB), a Hispanic serve university in the south Texas. Around 2007 National Center for Academic Transformation (NCAT) recommended six models for using of information technology to redesign courses in mathematics: the supplemental model, the replacement model, the emporium model, the fully online model, the buffet model, and the linked workshop model. Because of the local educational environment and resources none of the six models could be implemented exactly like it was described by NCAT. …

The Central Hankel Transform, Matthew J. Levine

Honors Theses

This honors thesis presents the Hankel transform on an integer sequence, a function with colorful mathematical history and rich theoretical background. We then introduce a matricial Toeplitz transform that parallels some of most famous qualities of the Hankel transform, especially when in consideration of popular sequences like the Fibonacci numbers. The result is a characterization of the injectivity of this new function, a description of some of its interesting behaviors, and a discussion of a few new Fibonacci identities.

Calibration Of Option Pricing In Reproducing Kernel Hilbert Space, Lei Ge

Electronic Theses and Dissertations

A parameter used in the Black-Scholes equation, volatility, is a measure for variation of the price of a financial instrument over time. Determining volatility is a fundamental issue in the valuation of financial instruments. This gives rise to an inverse problem known as the calibration problem for option pricing. This problem is shown to be ill-posed. We propose a regularization method and reformulate our calibration problem as a problem of finding the local volatility in a reproducing kernel Hilbert space. We defined a new volatility function which allows us to embrace both the financial and time factors of the options. …

Critical Controlled Branching Processes And Their Relatives, George Yanev

School of Mathematical & Statistical Sciences Faculty Publications

This survey aims at collecting and presenting results for one-type, discrete time branching processes with random control functions. In particular, the subclass of critical migration processes with different regimes of immigration and emigration is reviewed in detail. Critical controlled branching processes with continuous state space are also discussed.

Symmetries Of Monocoronal Tilings, Dirk Frettlöh, Alexey Garber

School of Mathematical & Statistical Sciences Faculty Publications

The vertex corona of a vertex of some tiling is the vertex together with the adjacent tiles. A tiling where all vertex coronae are congruent is called monocoronal. We provide a classification of monocoronal tilings in the Euclidean plane and derive a list of all possible symmetry groups of monocoronal tilings. In particular, any monocoronal tiling with respect to direct congruence is crystallographic, whereas any monocoronal tiling with respect to congruence (reflections allowed) is either crystallographic or it has a one-dimensional translation group. Furthermore, bounds on the number of the dimensions of the translation group of monocoronal tilings in higher …

Propagation Failure In Discrete Inhomogeneous Medium Using A Caricature Of The Cubic, Elizabeth Lydon

Electronic Theses and Dissertations

Spatially discrete Nagumo equations have widespread physical applications, including modeling electrical impulses traveling through a demyelinated axon, an environment typical in multiple scle- rosis. We construct steady-state, single front solutions by employing a piecewise linear reaction term. Using a combination of Jacobi-Operator theory and the Sherman-Morrison formula we de- rive exact solutions in the cases of homogeneous and inhomogeneous diffusion. Solutions exist only under certain conditions outlined in their construction. The range of parameter values that satisfy these conditions constitutes the interval of propagation failure, determining under what circumstances a front becomes pinned in the media. Our exact solutions represent …

Tiling With Polyominoes, Polycubes, And Rectangles, Michael Saxton

Electronic Theses and Dissertations

In this paper we study the hierarchical structure of the 2-d polyominoes. We introduce a new infinite family of polyominoes which we prove tiles a strip. We discuss applications of algebra to tiling. We discuss the algorithmic decidability of tiling the infinite plane Z x Z given a finite set of polyominoes. We will then discuss tiling with rectangles. We will then get some new, and some analogous results concerning the possible hierarchical structure for the 3-d polycubes.

Quaternionic Hardy Spaces In The Open Unit Ball And Half Space And Blaschke Products, Daniel Alpay, Fabrizio Colombo, Irene Sabadini

Mathematics, Physics, and Computer Science Faculty Articles and Research

The Hardy spaces H2(B) and H2(H+), where B and H+ denote, respectively, the open unit ball of the quaternions and the half space of quaternions with positive real part, as well as Blaschke products, have been intensively studied in a series of papers where they are used as a tool to prove other results in Schur analysis. This paper gives an overview on the topic, collecting the various results available.

Self-Mappings Of The Quaternionic Unit Ball: Multiplier Properties, Schwarz-Pick Inequality, And Nevanlinna-Pick Interpolation Problem, Daniel Alpay, Vladimir Bolotnikov, Fabrizio Colombo, Irene Sabadini, Fabrizio Colombo

Mathematics, Physics, and Computer Science Faculty Articles and Research

We study several aspects concerning slice regular functions mapping the quaternionic open unit ball B into itself. We characterize these functions in terms of their Taylor coefficients at the origin and identify them as contractive multipliers of the Hardy space H2(B). In addition, we formulate and solve the Nevanlinna-Pick interpolation problem in the class of such functions presenting necessary and sufficient conditions for the existence and for the uniqueness of a solution. Finally, we describe all solutions to the problem in the indeterminate case.

Infinite Product Representations For Kernels And Iteration Of Functions, Daniel Alpay, Palle Jorgensen, Izchak Lewkowicz, Itzik Marziano

Mathematics, Physics, and Computer Science Faculty Articles and Research

We study infinite products of reproducing kernels with view to their use in dynamics (of iterated function systems), in harmonic analysis, and in stochastic processes. On the way, we construct a new family of representations of the Cuntz relations. Then, using these representations we associate a fixed filled Julia set with a Hilbert space. This is based on analysis and conformal geometry of a fixed rational mapping R in one complex variable, and its iterations.

Realizations Of Infinite Products, Ruelle Operators And Wavelet Filters, Daniel Alpay, Palle Jorgensen, Izchak Lewkowicz

Mathematics, Physics, and Computer Science Faculty Articles and Research

Using the system theory notion of state-space realization of matrix-valued rational functions, we describe the Ruelle operator associated with wavelet filters. The resulting realization of infinite products of rational functions have the following four features: 1) It is defined in an infinite-dimensional complex domain. 2) Starting with a realization of a single rational matrix-function M, we show that a resulting infinite product realization obtained from M takes the form of an (infinitedimensional) Toeplitz operator with the symbol that is a reflection of the initial realization for M. 3) Starting with a subclass of rational matrix functions, including scalar-valued ones corresponding …

Wiener-Chaos Approach To Optimal Prediction, Daniel Alpay, Alon Kipnis

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this work we combine Wiener chaos expansion approach to study the dynamics of a stochastic system with the classical problem of the prediction of a Gaussian process based on part of its sample path. This is done by considering special bases for the Gaussian space G generated by the process, which allows us to obtain an orthogonal basis for the Fock space of G such that each basis element is either measurable or independent with respect to the given samples. This allows us to easily derive the chaos expansion of a random variable conditioned on part of the sample …

Spectral Theory For Gaussian Processes: Reproducing Kernels, Random Functions, Boundaries, And L2-Wavelet Generators With Fractional Scales, Daniel Alpay

Mathematics, Physics, and Computer Science Faculty Articles and Research

A recurrent theme in functional analysis is the interplay between the theory of positive definite functions, and their reproducing kernels, on the one hand, and Gaussian stochastic processes, on the other. This central theme is motivated by a host of applications, e.g., in mathematical physics, and in stochastic differential equations, and their use in financial models. In this paper, we show that, for three classes of cases in the correspondence, it is possible to obtain explicit formulas which are amenable to computations of the respective Gaussian stochastic processes. For achieving this, we first develop two functional analytic tools. They are: …

Teac 451p: Learning And Teaching Principles And Practices (Secondary Mathematics)—A Peer Review Of Teaching Project Benchmark Portfolio, Lorraine Males

UNL Faculty Course Portfolios

The goal of my peer review portfolio was to better understand how to improve students' learning of how to teach secondary mathematics in reform-oriented ways. Most students that pursue admission into the Secondary Mathematics Teacher Education Program have little to no experience learning mathematics in reform-oriented ways. These preservice teachers (PSTs) were “successful” in mathematics courses in middle and high school, most of them taking honors or accelerated courses. However, many of these PSTs did not have opportunities to engage as active participants in their own learning and develop complex cognitive skills and processes, the focus of reform-oriented instruction. This …

Question 1: Shaving Time; Question 2: Half-Filling The Gas Tank, Larry Weinstein

Physics Faculty Publications

How much total time does a typical American spend shaving during his or her life? How much total time per year do Americans spend shaving?

How much money can you save by only half-filling your car's gas tank to reduce weight?

Question 1: Kill The K-Cup; Question 2: Water Cooling, Larry Weinstein

Physics Faculty Publications

According to KillTheKCup.org, single-use non-recyclable Keurig K-cups “are killing our planet.” How large is the environmental impact of K-Cups?

How much more cooling do you get from drinking cold rather than room-temperature water on a hot day? How much do you sweat per day when the ambient temperature is about 35 °C (95 °F)?