Mathematics Commons^™

On The Geometry Of Virtual Knots, Rachel Elizabeth Byrd

Boise State University Theses and Dissertations

The Dehn complex of prime, alternating virtual links has been shown to be non-positively curved in the paper "Generalized knot complements and some aspherical ribbon disc complements" by J. Harlander and S. Rosebrock (2003) [7]. This thesis investigates the geometry of an arbitrary alternating virtual link. A method is constructed for which the Dehn complex of any alternating virtual link may be decomposed into Dehn complexes with non-positive curvature. We further study the relationship between the Dehn space and Wirtinger space, and we relate their fundamental groups using generating curves on surfaces. We conclude with interesting examples of Dehn complexes …

Assessing Changes In The Abundance Of The Continental Population Of Scaup Using A Hierarchical Spatio-Temporal Model, Beth E. Ross

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

In ecological studies, the goal is often to describe and gain further insight into ecological processes underlying the data collected during observational studies. Because of the nature of observational data, it can often be difficult to separate the variation in the data from the underlying process or 'state dynamics.' In order to better address this issue, it is becoming increasingly common for researchers to use hierarchical models. Hierarchical spatial, temporal, and spatio-temporal models allow for the simultaneous modeling of both first and second order processes, thus accounting for underlying autocorrelation in the system while still providing insight into overall spatial …

Validation Study: A Case Study Of Calculus 1 (Math 1210), Abibat Adebisi Lasisi

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

This report discusses the process of assessing the validity of a test. We provide an analysis of the validation study of a test administered to the first semester calculus students at Utah State University in the Fall 2011 semester. The results of our analysis suggest that the test has some measurement relevance. This implies that the subject contents of the test correlate with the syllabus of the course. Thus, the measurement has some learning level relevance. Our analysis also revealed that the measurement has a high reliability coefficient which signifies some internal consistency of the mea- surement. The relevancy and …

Ignoring The Spatial Context In Intro Statistics Classes - And Some Simple Graphical Remedies, Nathan Voge

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Statistical data often have a spatial (geographic) context, be it countries of the world, states in the US, counties within a state, cities across the globe, or locations where measurements have been taken. However, most introductory statistics books do not even suggest that such data often are not independent from location, but rather are eected by some spatial association. Remedies are simple: Display data via various map views and brie y discuss which additional information can be extracted from such a graphical representation. In this report, we will visit a variety of popular introductory statistics textbooks and show how some …

Enumeration Of Independent Sets In Graphs, James Alexander

Theses, Dissertations and Culminating Projects

An independent set is one of the most natural structures in a graph to focus on, from both a pure and applied perspective. In the realm of graph theory, and any concept it can represent, an independent set is the mathematical way of capturing a set of objects, none of which are related to each other. As graph theory grows, many questions about independent sets are being asked and answered, many of which are concerned with the enumeration of independent sets in graphs. We provide a detailed introduction to general graph theory for those who are not familiar with the …

Challenging Disciplinary Boundaries In The First Year: A New Introductory Integrated Science Course For Stem Majors, Lisa Gentile, Lester Caudill, Mirela Fetea, April L. Hill, Kathy Hoke, Barry Lawson, Ovidiu Z. Lipan, Michael Kerckhove, Carol A. Parish, Krista J. Stenger, Doug Szajda

Biology Faculty Publications

To help undergraduates make connections among disciplines so they are able to approach, evaluate, and contribute to the solutions of important global problems, our campus has been focused on interdisciplinary research and education opportunities across the science, technology, engineering, and mathematics (STEM) disciplines. This paper describes the mobilization, planning, and implementation of a first-year interdisciplinary course for STEM majors that integrates key concepts found in traditional first-semester biology, chemistry, computer science, mathematics, and physics courses. This team-taught course, Integrated Quantitative Science (IQS), is half of a first-year student’s schedule in both semesters and is composed of a double lecture and …

Qualitative Analysis Of The Burgers-Huxley Equation, Jing Tian

Theses and Dissertations - UTB/UTPA

There are many well-known techniques for obtaining exact solutions of differential equations, but some of them only work for a very limited class of problems and are merely special cases of a few power symmetry methods. These approaches can be applied to nonlinear differential of unfamiliar type; they do not rely on special “tricks." Instead, a given differential equation can be made to reveal its symmetries, which are then used to construct exact solutions. In this thesis, we briefly present the theory of the Lie symmetry method for finding exact solutions of nonlinear differential equations, then apply it to the …

Valuation Of Financial Derivatives Subject To Liquidity Risk, Yanan Jiang

UNLV Theses, Dissertations, Professional Papers, and Capstones

Valuation of financial derivatives subject to liquidity risk remains an open problem in finance. This dissertation focuses on the valuation of European-style call option under limited market liquidity through the dynamic management of a portfolio of assets. We investigate liquidity from three perspectives: market breadth, depth, and immediacy. We present a general framework of valuation based on the optimal realization of a performance index relative to the set of all feasible portfolio trajectories. Numerical examples are then presented and analyzed that show option price increases as the market transitions from liquid to less liquid state. Furthermore, buying and selling activities, …

Periodic Solutions And Positive Solutions Of First And Second Order Logistic Type Odes With Harvesting, Cody Alan Palmer

UNLV Theses, Dissertations, Professional Papers, and Capstones

It was recently shown that the nonlinear logistic type ODE with periodic harvesting has a bifurcation on the periodic solutions with respect to the parameter ε:

u' = f (u) - ε h (t).

Namely, there exists an ε0 such that for 0 < ε < ε0 there are two periodic solutions, for ε = ε0 there is one periodic solution, and for ε >ε0 there are no periodic solutions, provided that....

In this paper we look at some numerical evidence regarding the behavior of this threshold for various types of harvesting terms, in particular we find evidence in the negative or a conjecture regarding the behavior of this threshold value.

Additionally, we look at analagous steady states for the reaction-diusion …

Homogenization Of Large-Scale Movement Models In Ecology With Application To The Spread Of Chronic Wasting Disease In Mule Deer, Martha J. Garlick

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Chronic wasting disease (CWD) is a transmissible spongiform encephalopathy (TSE) that affects deer, elk, and moose. TSEs are prion diseases which include mad cow disease and scrapie in sheep and goats. The disease agent is a misshapen protein called a prion, which causes lesions in the brain, and to date, there is no cure. CWD is a slow-developing, fatal disease, which is rare in the free-ranging mule deer population of Utah. Infected deer shed prions into the environment through saliva, feces, and decaying carcasses. These prions remain infective in soils for many years and healthy deer may contract CWD by …

Elliptic Curves Of High Rank, Cecylia Bocovich

Mathematics, Statistics, and Computer Science Honors Projects

The study of elliptic curves grows out of the study of elliptic functions which dates back to work done by mathematicians such as Weierstrass, Abel, and Jacobi. Elliptic curves continue to play a prominent role in mathematics today. An elliptic curve E is defined by the equation, y^₂ = x³ + ax + b, where a and b are coefficients that satisfy the property 4a³ + 27b² = 0. The rational solutions of this curve form a group. This group, denoted E(Q), is known as the Mordell-Weil group and was proved by Mordell to be isomorphic …

Essays On Regular Variations In Classical And Free Setup: Randomaly Weighted Sums, Products In Cevm And Free Subexponentiality., Rajat Subhra Hazra Dr.

Doctoral Theses

In this thesis, we shall be focusing on some problems in probability theory involving regularly varying functions. The theory of regular variations has played an important role in probability theory, harmonic analysis, number theory, complex analysis and many more areas of mathematics. For an encyclopedic treatment of the subject, we refer to Bingham et al. (1987). In probability theory, the limiting behavior of the sums of independent and identically distributed (i.i.d.) random variables is closely related to regular variation. The books by Feller (1971) and Gnedenko and Kolmogorov (1968) give characterizations of random variables in the domains of attraction of …

Spectrum Estimation With Uniformly And Stochastically Sampled Data: Some Challenges And Strategies., Radhendushka Srivastava Dr.

Doctoral Theses

No abstract provided.

2012 Sonia Kovalevsky Math For Girls Day Report, Association For Women In Mathematics, Lincoln University Of Missouri, Donna L. Stallings

Math for Girls Day Documents

Report for the 7th Annual Lincoln University Sonia Kovalevsky Math for Girls Day that was held on April 27th, 2012 from 8:00am to 2:00pm on the campus of Lincoln University in Jefferson City, MO.

Hadamard Renormalization Of The Stress Energy Tensor In A Spherically Symmetric Black Hole Space-Time With An Application To Lukewarm Black Holes, Cormac Breen, Adrian Ottewill

Articles

We consider a quantum field which is in a Hartle-Hawking state propagating in a spherically symmetric black hole space-time. We calculate the components of the stress tensor, renormalized using the Hadamard form of the Green's function, in the exterior region of this space-time. We then specialize these results to the case of the `lukewarm' Riessner-Nordstrom-de Sitter black hole.

Generic Special Objects, Sławomir Solecki

Dalrymple Lecture Series

I will talk about mathematical objects that have two seemingly contradictory attributes. On the one hand, they are generic within a given class, in the sense that if most objects within the class have a property, then our object has it as well. So generic objects are common. On the other hand, they are very special if they exist, for example, there is always, in essence, at most one such object within a given class. Generic objects show up in various areas of mathematics, for example, in topology, geometry, and analysis. They tend to have astonishing mathematical features. Can you …

Stiefel And Grassmann Manifolds In Quantum Chemistry, Eduardo Chiumiento, Michael Melgaard

Articles

We establish geometric properties of Stiefel and Grassmann manifolds which arise in relation to Slatertype variational spaces in many-particle Hartree-Fock theory and beyond. In particular, we prove thatthey are analytic homogeneous spaces and submanifolds of the space of bounded operators on the single-particle Hilbert space. As a by-product we obtain that they are complete Finsler manifolds. These geometric properties underpin state-of-the-art results on existence of solutions to Hartree-Fock type equations.

K-8 Preservice Teachers’ Inductive Reasoning In The Problem-Solving Contexts, Marta Magiera

Mathematics, Statistics and Computer Science Faculty Research and Publications

This paper reports the results from an exploratory study of K-8 pre-service teachers’ inductive reasoning. The analysis of 130 written solutions to seven tasks and 77 reflective journals completed by 20 pre-service teachers lead to descriptions of inductive reasoning processes, i.e. specializing, conjecturing, generalizing, and justifying, in the problem-solving contexts. The uncovered characterizations of the four inductive reasoning processes were further used to describe pathways of successful generalizations. The results highlight the importance of specializing and justifying in constructing powerful generalizations. Implications for teacher education are discussed.

Matrix Product Application To Fibonacci Sequence, Abigail Damaris Muniz^, Jesus Loya^, Hamide Dogan*

COURI Symposium Abstracts, Spring 2012

No abstract provided.

Using Bioinformatics To Efficiently Organize And Analyze Significant Immunogenic Epitope Sequences In Various Stages Of Trypanosoma Cruzi, Karla Singh^, Andrea Wurm, Clemente Aguilar, Alexandre Marques, M-Y Leung*, Igor Almeida*

COURI Symposium Abstracts, Spring 2012

No abstract provided.