Mathematics Commons^™

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 …

Teaching Algebra: A Comparison Of Scottish And American Perspectives, Brittany Munro

Undergraduate Honors Theses

A variety of factors influence what teaching strategies an educator uses. I analyze survey responses from algebra teachers in Scotland and Appalachia America to discover how a teacher's perception of these factors, particularly their view of mathematics itself, determines the pedagogical strategies employed in the classroom.

Counting On R-Fibonacci Numbers, Arthur Benjamin, Curtis Heberle

All HMC Faculty Publications and Research

We prove the r-Fibonacci identities of Howard and Cooper using a combinatorial tiling approach.

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

Mathematical Modeling Of Communicable Imported Diseases Screening In The United Arab Emirates, Lahbib Ben Ahmadi

Theses

The United Arab Emirates (UAE), as one of the countries with high numbers of expatriates in the world, is expected to face public health challenges. The reason for this situation is that the majority of those expatriates belong to regions where health issues are usually left behind. This may create the possibility of having imported communicable diseases. However, screening policy should be tested and adapted to protect the population from any imported communicable disease. This study aims at identifying an approach and method to deal with these imported diseases via a set of differential equations. The spread of a communicable …

On The Geometry Of Fuchsian Groups, Hala Alaqad

Theses

In this Master thesis we consider the discrete groups with emphasis on the geometry of discrete groups, which lie at the intersection between Hyperbolic Geometry, Topology, Abstract Algebra, and Complex Analysis. Fuchsian groups are discrete subgroups of the group PSL(2,ℝ) of linear fractional transformations of one complex variable, which is isomorphic to a quotient topological group: PSL(2,ℝ)≅SL(2,ℝ)/{±I}. Here SL (2,ℝ) is special linear group and I is the identity. We study discrete groups, in particular, Fuchsian groups. We present the geometric properties of Fuchsian groups such as fundamental domains, compactness, and Dilichlet tessellations. In addition, we also present some algebraic …

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 …

Encoding Knots, Rachael Keller

Honors Capstones

No abstract provided.

Nonlinear Gravitational-Wave Memory From Merging Binary Black Holes, Goran Dojcinoski

Theses, Dissertations and Culminating Projects

Gravitational waves are oscillations in spacetime that propagate throughout the universe at the speed of light. They are a prediction of Einstein’s theory of General Relativity. Detectable sources of gravitational waves are typically collisions of black holes or other compact objects (neutron stars, white dwarfs). While most gravitational-wave signals are expected to be oscillatory in nature, some will exhibit a phenomenon called gravitational-wave memory. This refers to a non-oscillatory component of the gravitational wave signal that can leave a permanent distortion (or “memory” ) in a gravitational-wave detector. The nonlinear memory effect is a type of memory signal that arises …

Interlace Polynomial Of A Special Eulerian Graph, Christian A. Hyra

Theses, Dissertations and Culminating Projects

In a recent paper, Arratia, Bollobas and Sorkin discussed a graph polynomial defined recursively, which they call the interlace polynomial. There have been previous results on the interlace polynomials for special graphs, such as paths, cycles, and trees. Applications have been found in biology and other areas. In this research, I focus on the interlace polynomial of a special type of Eulerian graph, built from one cycle of size n and n cycle three graphs. I developed explicit formulas by implementing the toggling process to the graph. I further investigate the coefficients and special values of the interlace polynomial. Some …

Geometry Of Hilbert Space Frames, Stephen Sorokanich Iii

Renée Crown University Honors Thesis Projects - All

In applied linear algebra, the term frame is used to refer to a redundant or linearly dependent coordinate system. The concept was introduced in the study of Fourier series and is pertinent in signal processing, where the reconstruction property for finite frames allows for redundant transmission of data to guard against losses due to noise. We give a brief introduction to the theory of finite frames in Section 1, including the major results that allow for the easy construction and description of frames. The subsequent sections relate to the theoretical importance of frames. As a natural extension of the definition …

The Minimal Zn-Symmetric Graphs That Are Not Zn-Spherical, Lowell Abrams, Dan Slilaty

Mathematics and Statistics Faculty Publications

Given a graph G equipped with faithful and fixed-point-free Γ-action (Γ a finite group) we define an orbit minor H of G to be a minor of G for which the deletion and contraction sets are closed under the Γ-action. The orbit minor H inherits a Γ-symmetry from G, and when the contraction set is acyclic the action inherited by H remains faithful and fixed-point free. When G embeds in the sphere and the Γ-action on G extends to a Γ-action on the entire sphere, we say that G is Γ-spherical. In this paper we determine for every odd value …

Development Of A Tridimensional Measuring Application For Ipads, Michael Casebolt, Nicolas Kouatli, Jack Mullen

Computer Science and Software Engineering

In today’s fast-paced distribution centers workers and management alike are constantly searching for the quickest and most efficient way to package items for distribution. Even with the advancement of app-oriented solutions to a variety of problems across many industries there is a distinct unmet need in distribution environments for an application capable of increasing the efficiency and accuracy of packaging items. This senior project focused on the development and testing of an application utilizing the Structure Three Dimensional Sensor and a 4th generation iPad to scan an object or group of objects to be packaged and determine the overall dimensions …

Student Understanding Of Function And Success In Calculus, Daniel I. Drlik

Boise State University Theses and Dissertations

The purpose of this study was to determine if there is a relationship between student success in calculus and student understanding of function. Student understanding of function was measured using two questionnaires, one of which is a modification of an existing measure based on APOS theory. The other I developed with items from the concept image literature. The participants of this study were 116 high school students who were enrolled in a first-year calculus course. The results of the questionnaires were aligned to course exam scores to determine connections between function understanding and rate of success in calculus.

A major …

Eigenvectors Of Interpoint Distance Matrices, Michelle F. Craft

Departmental Honors & Graduate Capstone Projects

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 …

2-Domination And Annihilation Numbers, Sean C. Patterson

Honors Theses

Using information provided by Ryan Pepper and Ermelinda DeLaVina in their paper On the 2-Domination number and Annihilation Number, I developed a new bound on the 2- domination number of trees. An original bound, γ₂(G) ≤ (n+n₁)/ 2 , had been shown by many other authors. Our goal was to generate a tighter bound in some cases and work towards generating a more general bound on the 2-domination number for all graphs. Throughout the span of this project I generated and proved the bound γ₂(T ) ≤ …

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 …

Averaged Instrumental Variables Estimators, Yoonseok Lee, Yu Zhou

Center for Policy Research

We develop averaged instrumental variables estimators as a way to deal with many weak instruments. We propose a weighted average of the preliminary k-class estimators, where each estimator is obtained using different subsets of the available instrumental variables. The averaged estimators are shown to be consistent and to satisfy asymptotic normality. Furthermore, its approximate mean squared error reveals that using a small number of instruments for each preliminary k-class estimator reduces the finite sample bias, while averaging prevents the variance from inflating. Monte Carlo simulations find that the averaged estimators compare favorably with alternative instrumental-variable-selection approaches when the strength levels …

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 …