Mathematics Commons^™

Results On N-Absorbing Ideals Of Commutative Rings, Alison Elaine Becker

Theses and Dissertations

Let R be a commutative ring with n≥0. In his paper On 2-absorbing Ideals of Commutative Rings, Ayman Badawi introduces a generalization of prime ideals called 2-absorbing ideals, and this idea is further generalized in a paper by Anderson and Badawi to a concept called n-absorbing ideals. A proper ideal I of R is said to be an n-absorbing ideal if whenever x_1…x_(n+1) ∈I for x_1,…,x_(n+1 )∈R then there are n of the x_i's whose product is in I. This paper will provide proofs of several properties in Badawi’s paper which are stated without proof, and will study how several …

On The Riesz Representation For Optimal Stopping Problems, Markus Schuster

Theses and Dissertations

In this thesis we summarize results about optimal stopping problems analyzed with

the Riesz representation theorem. Furthermore we consider two examples: Firstly

the optimal investment problem with an underlying d-dimensional geometric Brow-

nian motion. We derive formulas for the optimal stopping boundaries for the one-

and two-dimensional cases and we find a numerical approximation for the boundary

in the two-dimensional problem. After this we change the focus to a space-time

one-dimensional geometric Brownian motion with finite time horizon. We use the

Riesz representation theorem to approximate the optimal stopping boundaries for

three financial options: the American Put option, American Cash-or-Nothing …

Associated Hypotheses In Linear Models For Unbalanced Data, Carlos J. Soto

Theses and Dissertations

When looking at factorial experiments there are several natural hypotheses that can be tested. In a two-factor or a by b design, the three null hypotheses of greatest interest are the absence of each main effect and the absence of interaction. There are two ways to construct the numerator sum of squares for testing these, namely either adjusted or sequential sums of squares (also known as type I and type III in SAS). Searle has pointed out that, for unbalanced data, a sequential sum of squares for one of these hypotheses is equal (with probability 1) to an adjusted sum …

Counting Convex Sets On Products Of Totally Ordered Sets, Brandy Amanda Barnette

Masters Theses & Specialist Projects

The main purpose of this thesis is to find the number of convex sets on a product of two totally ordered spaces. We will give formulas to find this number for specific cases and describe a process to obtain this number for all such spaces. In the first chapter we briefly discuss the motivation behind the work presented in this thesis. Also, the definitions and notation used throughout the paper are introduced here The second chapter starts with examining the product spaces of the form {1; 2; : : : ;n} × {1; 2}. That is, we begin by analyzing …

Analysis Of Discrete Fractional Operators And Discrete Fractional Rheological Models, Meltem Uyanik

Masters Theses & Specialist Projects

This thesis is comprised of two main parts: Monotonicity results on discrete fractional operators and discrete fractional rheological constitutive equations. In the first part of the thesis, we introduce and prove new monotonicity concepts in discrete fractional calculus. In the remainder, we carry previous results about fractional rheological models to the discrete fractional case. The discrete method is expected to provide a better understanding of the concept than the continuous case as this has been the case in the past. In the first chapter, we give brief information about the main results. In the second chapter, we present some fundamental …

Boundary Problems For One And Two Dimensional Random Walks, Miky Wright

Masters Theses & Specialist Projects

This thesis provides a study of various boundary problems for one and two dimensional random walks. We first consider a one-dimensional random walk that starts at integer-valued height k > 0, with a lower boundary being the x-axis, and on each step moving downward with probability q being greater than or equal to the probability of going upward p. We derive the variance and the standard deviation of the number of steps T needed for the height to reach 0 from k, by first deriving the moment generating function of T. We then study two types of two-dimensional random walks with …

Numerical Study Of Body Shape And Wing Flexibility In Fluid Structure Interaction, Peter Nolan

Theses, Dissertations and Culminating Projects

We discuss the equilibrium configurations of fibers clamped to an ellipsoidal body and immersed in a flow ranging between 0-50 cm/s. Experimental and numerical results are presented and the effects of flow speed, body shape, and orientation of the fibers upon the equilibrium configuration are investigated. Our investigations reveal that the orientation of the fibers, the length of the length fibers, as well as, the shape of the body has a significant impact upon the bending and drag experienced by the ellipsoid-fiber system. We note that (i) less eccentric bodies experience greater drag forces and increased bending of the attached …

Efficient Estimation Of Cluster Population, Sanjeev K C

UNLV Theses, Dissertations, Professional Papers, and Capstones

Partitioning a given set of points into clusters is a well known problem in pattern recognition, data mining, and knowledge discovery. One of the well known methods for identifying clusters in Euclidean space is the K-mean algorithm. In using the K-mean clustering algorithm it is necessary to know the value of k (the number of clusters) in advance. We propose to develop algorithms for good estimation of k for points distributed in two dimensions. The techniques we pursue include a bucketing method, g-hop neighbors, and Voronoi diagrams. We also present experimental results for examining the performances of the bucketing method …

Generalized Markoff Equations, Euclid Trees, And Chebyshev Polynomials, Donald Joseph Mcginn

UNLV Theses, Dissertations, Professional Papers, and Capstones

The Markoff equation is x^2+y^2+z^2 = 3xyz, and all of the positive integer solutions

of this equation occur on one tree generated from (1, 1, 1), which is called the

Markoff tree. In this paper, we consider trees of solutions to equations of the form

x^2 + y^2 + z^2 = xyz + A. We say a tree of solutions satisfies the unicity condition

if the maximum element of an ordered triple in the tree uniquely determines the

other two. The unicity conjecture says that the Markoff tree satisifies the unicity

condition. In this paper, we show that there exists …

Book Review: How To Bake Pi: An Edible Exploration Of The Mathematics Of Mathematics, Darren B. Glass

Math Faculty Publications

If you think about it, mathematics is really just one big analogy. For one example, the very concept of the number three is an drawing an analogy between a pile with three rocks, a collection of three books, and a plate with three carrots on it. For another, the idea of a group is drawing an analogy between adding real numbers, multiplying matrices, and many other mathematical structures. So much of what we do as mathematicians involves abstracting concrete things, and what is abstraction other than a big analogy? [excerpt]

Revised Model For Antibiotic Resistance In A Hospital, Ruhang Pei

Electronic Theses and Dissertations

In this thesis we modify an existing model for the spread of resistant bacteria in a hospital. The existing model does not account for some of the trends seen in the data found in literature. The new model takes some of these trends into account. For the new model, we examine issues relating to identifiability, sensitivity analysis, parameter estimation, uncertainty analysis, and equilibrium stability.

Eigenvectors Of Interpoint Distance Matrices, Michelle F. Craft

Student Research Submissions

In this paper, the eigenvectors of interpoint distance matrices will be discussed. When plotted against each other, the eigenvectors of the distance matrix of evenly spaced points in one dimension produce some interesting patterns. An explanation and description of the patterns will be discussed. After examining many aspects of the general Euclidean interpoint distance matrix of order N, D, as well as characteristics of the eigenvectors themselves,some conclusions can be made. Furthermore, research revealed a similarity between our matrices, D, and the Discrete Cosine Transform Matrix, DCT-2. This research led to additional conclusion about our matrices D and allowed for …

The Markov-Dubins Problem With Free Terminal Direction In A Nonpositively Curved Cube Complex, Jason Thomson La Corte

Theses and Dissertations

State complexes are nonpositively curved cube complexes that model the state spaces of reconfigurable systems. The problem of determining a strategy for reconfiguring the system from a given initial state to a given goal state is equivalent to that of finding a path between two points in the state complex. The additional requirement that allowable paths must have a prescribed initial direction and minimal turning radius determines a Markov-Dubins problem with free terminal direction (MDPFTD).

Given a nonpositively curved, locally finite cube complex X, we consider the set of unit-speed paths which satisfy a certain smoothness condition in addition to …

Pricing European Option Under A Modified Cev Model, Wafaa Ibrahim Abuzarqa

Theses

A financial derivative is an instrument whose payoff is derived from the behavior of another underlying asset. One of the most commonly used derivatives is the option which gives the right to buy or to sell an underlying asset at a pre-specified price at (European) or at and before (American) an expiration date. Finding a fair price of the option is called the option pricing problem and it depends on the underlying asset prices during the period from the initial time to expiration date. Thus, a “good” model for the underlying asset price trajectory is needed. In this work, we …

The Groups Acting On The Riemann Sphere, Ruba Yousef Wadi

Theses

In this Master thesis we consider the group actions, with emphasis on the group of general Möbius transformations of one complex valuable acting on the Riemann sphere. We study some invariant subspaces of Riemann sphere under the actions of natural groups of transformations, including the invariant quantities in Hyperbolic Geometry that is a beautiful area of Mathematics. We use analytic and algebraic points of view to describe some group actions on Riemann sphere; in particular, we present the relationships between isometries of hyperbolic plane, Möbius transformations, and groups of matrices. Keywords: Group actions, Riemann sphere, general Möbius transformations, transitivity, hyperbolic

Quaternary Affine-Invariant Codes, Badria H Omar Salih

Theses

This thesis concerned with extended cyclic codes. The objective of this thesis is to give a full description of binary and quaternary affine-invariant codes of small dimensions. Extended cyclic codes are studied using group ring methods. Affine-invariant codes are described by their defining sets. Results are presented by enumeration of defining sets. Full description of affine-invariant codes is given for small dimensions

Manipulating The Mass Distribution Of A Golf Putter, Paul J. Hessler Jr.

Senior Honors Projects

Putting may appear to be the easiest but is actually the most technically challenging part of the game of golf. The ideal putting stroke will remain parallel to its desired trajectory both in the reverse and forward direction when the putter head is within six inches of the ball. Deviation from this concept will cause a cut or sidespin on the ball that will affect the path the ball will travel.

Club design plays a large part in how well a player will be able to achieve a straight back and straight through club head path near impact; specifically the …

Efficient Coupling For Random Walk With Redistribution, Elizabeth Tripp

Honors Scholar Theses

What can be said on the convergence to stationarity of a finite state Markov chain that behaves 'locally' like a nearest-neighbor random walk on the set of integers? In this work, we looked to obtain sharp bounds for the rate of convergence to stationarity for a particular non-symmetric Markov chain. Our Markov chain is a variant of the simple symmetric random walk on the state space {0, ..., N} obtained by allowing transitions from 0 to J₀ and from N to J_N. We first looked at the case where J₀ and J_N are fixed, deterministic …

Matrix Exponentiation Without Scaling And Squaring, Bruno Gabriel Beltran

Honors Theses

No abstract provided.

Modeling The Diffusion Of Heat Energy Within Composites Of Homogeneous Materials Using The Uncertainty Principle, Elyse M. Garon

Honors Theses

The purpose of this project is to model the diffusion of heat energy in one space dimension, such as within a rod, in the case where the heat flow is through a medium consisting of two or more homogeneous materials. The challenge of creating such a mathematical model is that the diffusivity will be represented using a piecewise constant function, because the diffusivity changes based on the material. The resulting model cannot be solved using analytical methods, and is impractical to solve using existing numerical methods, thus necessitating a novel approach.

The approach presented in this thesis is to represent …