Mathematics Commons^™

Uniform Stability In Nonlinear Infinite Delay Volterra Integro-Differential Equations Using Lyapunov Functionals, Youssef Raffoul, Habib Rai

Mathematics Faculty Publications

In [10] the first author used Lyapunov functionals and studied the exponential stability of the zero solution of nite delay Volterra Integro-dierential equation. In this paper, we use modified version of the Lyapunov functional that were used in [10] to obtain criterion for the stability of the zero solution of the infinite delay nonlinear Volterra integro-dierential equation

x′(t) = Px(t) + ^t∫ _−∞ C(t, s)g(x(s))ds.

Model Behavior: The Mathematics Behind Three-Dimensional Modeling And Animation, Kathryn Duff, Vivian Cyrus

Celebration of Student Scholarship Poster Sessions Archive

No abstract provided.

Mathematics And Origami; Unfolding Mathematical "Impossibilities", Dustin Tyler Adams

Celebration of Student Scholarship Poster Sessions Archive

No abstract provided.

Biological Aggregation Driven By Social And Environmental Factors: A Nonlocal Model And It Degenerate Cahn-Hilliard Approximation, Andrew J. Bernoff, Chad Topaz

Faculty Publications

No abstract provided.

Cosmological Models Through Spatial Ricci Flow, Ramesh Sharma

Mathematics Faculty Publications

We consider the synchronization of the Einstein’s flow with the Ricci-flow of the standard spatial slices of the Robertson–Walker space–time and show that associated perfect fluid solution has a quadratic equation of state and is either spherical and collapsing, or hyperbolic and expanding.
Read More: http://www.worldscientific.com/doi/abs/10.1142/S0219887816500699

Let's Nurture Science, Math Talent, Darren B. Glass

Math Faculty Publications

I recently saw the film The Man Who Knew Infinity, which was released in many American cities this weekend, and was struck by the beautiful telling of an inspirational story. The film, which stars Jeremy Irons and Dev Patel, is a biography of the mathematician Srinivasa Ramanujan, who was born in India at the end of the 19th century. [excerpt]

Finite Involution Semigroups With Infinite Irredundant Bases Of Identities, Edmond W. H. Lee

Mathematics Faculty Articles

A basis of identities for an algebra is irredundant if each of its proper subsets fails to be a basis for the algebra. The first known examples of finite involution semigroups with infinite irredundant bases are exhibited. These involution semigroups satisfy several counterintuitive properties: their semigroup reducts do not have irredundant bases, they share reducts with some other finitely based involution semigroups, and they are direct products of finitely based involution semigroups.

Identification Of Protein Palmitoylation Inhibitors From A Scaffold Ranking Library, Laura D. Hamel, Brian J. Lenhart, David A. Mitchell, Radleigh Santos, Marc A. Giulianotti, Robert J. Deschenes

Mathematics Faculty Articles

The addition of palmitoyl moieties to proteins regulates their membrane targeting, subcellular localization, and stability. Dysregulation of the enzymes which catalyzed the palmitoyl addition and/or the substrates of these enzymes have been linked to cancer, cardiovascular, and neurological disorders, implying these enzymes and substrates are valid targets for pharmaceutical intervention. However, current chemical modulators of zDHHC PAT enzymes lack specificity and affinity, underscoring the need for screening campaigns to identify new specific, high affinity modulators. This report describes a mixture based screening approach to identify inhibitors of Erf2 activity. Erf2 is the Saccharomyces cerevisiae PAT responsible for catalyzing the palmitoylation …

Undergraduate Research Fellowships: A Strategic Investment To Reduce Women Underrepresentation In The Mathematical Sciences, Janie L. Knell, Wilson Gonzalez-Espada

Celebration of Student Scholarship Poster Sessions Archive

No abstract provided.

Representations Of The Extended Poincare Superalgebras In Four Dimensions, John David Griffis

Mathematics Dissertations - Archive

Eugene Wigner used the Poincare group to induce representations from the fundamental internal space-time symmetries of (special) relativistic quantum particles. Wigner’s students spent considerable amount of time translating passages of this paper into more detailed and accessible papers and books. In 1975, R. Haag et al. investigated the possible extensions of the symmetries of relativistic quantum particles. They showed that the only consistent (super)symmetric extensions to the standard model of physics are obtained by using super charges to generate the odd part of a Lie superalgebra whos even part is generated by the Poincare group; this theory has become known …

A Bisection Method For The Banded Hyperbolic Quadratic Eigenvalue Problem, Ahmed T. Ali

Mathematics Dissertations - Archive

It is well-known that the eigenvalues of a Hermitian matrix in a given interval can be approximated within a predefined error tolerance using the bisection method as a direct application of the Sylvester's Law of Inertia. In this thesis, we will develop a bisection method for the hyperbolic quadratic eigenvalue problem (HQEP) which is guaranteed to have 2n real eigenvalues for a problem of size n. A number of numerical methods are available to solve HQEPs. Matlab's polyeig uses the QZ algorithm on the problem after linearizing it to a pencil of size 2n. Another approach is by finding a …

Stochastic Reliability Models For A General Server And Related Networks, Rachel Traylor

Mathematics Dissertations - Archive

There are many types of systems which can be dubbed servers, i.e. a retail checkout counter, a shipping company, a web server, or a customer service hotline. All of these systems have common general behavior: requests or customers arrive via a stochastic process, the service times vary randomly, and each request increases the stress on the server for some interval of time. A general stochastic model that describes the reliability of a server can provide the necessary informationfor optimal resource allocation and efficient task scheduling, leading to significant cost savings and improved performance metrics. In this work, we consider several …

The Eyes Have It: Eye Tracking Data Visualizations Of Viewing Patterns Of Statistical Graphics, Trent Fawcett

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

As statistical graphics continue to expand to manage an ever growing amount of diverse data, a need to evaluate the effectiveness of graphics, both basic and complex, has arisen. Technological advancements have given a means to evaluate the effectiveness of graphs and graphical components through eye tracking systems. Eye tracking systems are likewise in need of software that will enable easy evaluation and exploration of data. The focus of this Master's Report is to evaluate the dual solution. An exploration of an eye tracker setup is made, with extensive consideration of testing statistical graphics providing a basis for continued research …

On The Quantum Spaces Of Some Quadratic Regular Algebras Of Global Dimension Four, Richard Gene Chandler

Mathematics Dissertations - Archive

A quantum $\mathbb{P}^3$ is a noncommutative analogue of a polynomial ring on four variables, and, herein, it is taken to be a regular algebra of global dimension four. It is well known that if a generic quadratic quantum $\mathbb{P}^3$ exists, then it has a point scheme consisting of exactly twenty distinct points and a one-dimensional line scheme. In this thesis, we compute the line scheme of a family of algebras whose generic member is a candidate for a generic quadratic quantum $\mathbb{P}^3$. We find that, as a closed subscheme of $\mathbb{P}^5$, the line scheme of the generic member is the …

Sexual Assault And The Doctrine Of Chances, Ryan Wallentine

Undergraduate Honors Capstone Projects

Sexual assault is a crime whose offenders often commit multiple acts and its victims experience devastating effects. The doctrine of chances is a rule of evidence that may allow evidences of these past events or circumstances to be presented in a court case given they meet certain criteria. This research argues the probability of being innocently prosecuted for rape multiple times is sufficiently low to meet at least one of the criteria for the doctrine of chances to be used in a sexual assault case. Additional implications and related areas of research are included as well.

Tensor Products Of A Finite-Dimensional Representation And An Infinite-Dimensional Representation, Felicia Dewanaga

Mathematics Theses - Archive

In this project, we explicitly find the decomposition of the tensor product of a Verma module $Z(\lambda)$ and the standard module ${\mathbb C}^n$ of the Lie algebras $\mathfrak{sl}(n)$, $n=2,3$. The result provides an explicit description of the translation functor introduced by Bernstein and Gelfand.

Modeling Consequences Of Reduced Vaccination Levels On The Spread Of Measles, Guillermo Ortiz

Honors Program Theses and Projects

Introduction: In this thesis we propose a mathematical model for the spread of measles in a closed population. In section 1 we offer a motivation for the project, describe the measles virus as well as its history in the U.S., and provide a brief summary of three epidemiological models from the literature. In section 2.1 we introduce some probabilistic tools used in our model. Section 2.2.1 outlines our stochastic model used for the spread of measles in a population, which is refined in section 2.2.2 to include health interventions from the CDC. We conclude the thesis by presenting in section …

Present Value Calculations In Personal Injury, Nicholas J. Klinka

Honors Capstones

No abstract provided.

Resonance Varieties Of Pure Braid-Like Groups, Jared Able

Honors Capstones

No abstract provided.

Homological Properties Of Determinantal Arrangements, Arnold H. Yim

Open Access Dissertations

We study a certain family of hypersurface arrangements known as determinantal arrangements. Determinantal arrangements are a union of varieties defined by minors of a matrix of indeterminates. In particular, we investigate determinantal arrangements using the 2-minors of a 2 × n generic matrix (which can be thought of as natural extensions of braid arrangements), and prove certain statements about their freeness. We also study the topology of these objects. We construct a fibration for the complement of free determinantal arrangements, and use this fibration to prove statements about their homotopy groups. Furthermore, we show that the Poincaré polynomial of the …

Numerical Detection Of Wave Breaking In The Short-Pulse Equation, Jeffrey Slepoi

Theses, Dissertations and Culminating Projects

Numerical analysis is a powerful resource in all mathematical sciences especially in the study of partial differential equations (PDEs). It allows evaluating and demonstrating derived solutions for PDEs and whenever the solution can’t be derived analytically it provides us with ability to calculate the solution function numerically and predict its behavior over time. This work presents a numerical method to evaluate an analytically known solution, demonstrates the needed parameters to achieve the desired accuracy, extends the methodology into the sphere of the mathematical unknown to be able to predict the results by using the same numerical methodology. The equation in …

On God's Number(S) And The Rubik's Slide Extension, James F. Johnston Iii

Theses, Dissertations and Culminating Projects

In a recent article, Jones, Shelton and Weaverdyck and Aim, Gramelspacher, and Rice provided two analyses of the Rubik’s Slide game on a board of dimensions 3x3. This paper extends the work of Jones, Shelton, and Weaverdyck to a board of dimensions 4x4. Concepts from abstract algebra and graph theory are used to calculate the God’s number of many classes of puzzles, which is the least number of moves necessary to reach any end configuration from any starting configuration of game play. It turns out that God’s number is equivalent to the diameter of a graph of the group formed …

Application Of Nonequilibrium Thermodynamics To Pattern Selection In Fluid Solid Interaction, Blas J. Ortega

Theses, Dissertations and Culminating Projects

The terminal orientation of a rigid body is a classic example of a system out of thermodynamic equilibrium and a perfect testing ground for the validity of the maximum entropy production principle(MEPP). A freely falling body in a quiescent fluid generates fluid flow around the body resulting in dissipative losses. Thus far, dynamical equations have been employed in deriving the equilibrium states of such falling bodies, but they are far too complex and become analytically intractable when inertial effects come into play. At that stage, our only recourse is to rely on numerical techniques which can be computationally expensive. In …

New Flexible Regression Models Generated By Gamma Random Variables With Censored Data, Elizabeth M. Hashimoto, Gauss M. Cordeiro, Edwin M. M. Ortega, Gholamhossein G. Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

We propose and study a new log-gamma Weibull regression model. We obtain explicit expressions for the raw and incomplete moments, quantile and generating functions and mean deviations of the log-gamma Weibull distribution. We demonstrate that the new regression model can be applied to censored data since it represents a parametric family of models which includes as sub-models several widely-known regression models and therefore can be used more effectively in the analysis of survival data. We obtain the maximum likelihood estimates of the model parameters by considering censored data and evaluate local influence on the estimates of the parameters by taking …

Self-Monitoring Practices, Attitudes, And Needs Of Individuals With Bipolar Disorder: Implications For The Design Of Technologies To Manage Mental Health, Elizabeth L. Murnane, Dan Cosley, Pamara Chang, Shion Guha, Ellen Frank, Geri K. Gay, Mark Matthews

Mathematics, Statistics and Computer Science Faculty Research and Publications

Objective To understand self-monitoring strategies used independently of clinical treatment by individuals with bipolar disorder (BD), in order to recommend technology design principles to support mental health management.

Materials and Methods Participants with BD (N = 552) were recruited through the Depression and Bipolar Support Alliance, the International Bipolar Foundation, and WeSearchTogether.org to complete a survey of closed- and open-ended questions. In this study, we focus on descriptive results and qualitative analyses.

Results Individuals reported primarily self-monitoring items related to their bipolar disorder (mood, sleep, finances, exercise, and social interactions), with an increasing trend towards the use of digital …

A Geometric Approach To Ramanujan's Taxi Cab Problem And Other Diophantine Dilemmas, Zachary Kyle Easley

Graduate Theses/Dissertations

In 1917, the British mathematician G.H. Hardy visited the Indian mathematical genius Ramanujan in the hospital. The number of the taxicab Hardy arrived in was 1729. Ramanujan immediately recognized this as the smallest positive integer that can be expressed as the sum of two cubes in two essentially different ways. In this thesis, we use properties of conics and elliptic curves to investigate this problem, its generalization to fourth powers, and a Diophantine equation involving the distance of a point from the vertices of a regular tetrahedron (the latter extends work of Christina Bisges).

On The Conjugacy Problem For Automorphisms Of Trees, Kyle Douglas Beserra

Boise State University Theses and Dissertations

In this thesis we identify the complexity of the conjugacy problem of automorphisms of regular trees. We expand on the results of Kechris, Louveau, and Friedman on the complexities of the isomorphism problem of classes of countable trees. We see in nearly all cases that the complexity of isomorphism of subtrees of a given regular countable tree is the same as the complexity of conjugacy of automorphisms of the same tree, though we present an example for which this does not hold.

Number Sense In High School Mathematics Students, Vi Le Nguyen

Mathematics Theses - Archive

Understanding the real number system plays a very important role in each student’s mathematical achievement. The Texas Essential Knowledge and Skills (TEKS) for Mathematics Subchapter A. Elementary states, “For students to become fluent in mathematics, students must develop a robust sense of number” (TEKS Subchapter A Elementary, 2012). Knowledge of the real number system and number sense develops over several years. Once students get to high school, they are expected to have a large amount of knowledge about the real number system and number sense in order to effectively start and complete their high school math courses. However, many high …

A Model For Collective Dynamics In Ant Raids, Shawn D. Ryan

Mathematics and Statistics Faculty Publications

Ant raiding, the process of identifying and returning food to the nest or bivouac, is a fascinating example of collective motion in nature. During such raids ants lay pheromones to form trails for others to find a food source. In this work a coupled PDE/ODE model is introduced to study ant dynamics and pheromone concentration. The key idea is the introduction of two forms of ant dynamics: foraging and returning, each governed by different environmental and social cues. The model accounts for all aspects of the raiding cycle including local collisional interactions, the laying of pheromone along a trail, and …

A Physiologically-Based Pharmacokinetic Model For The Antibiotic Levofloxacin, Paezha M. Mccartt

Undergraduate Honors Theses

Levofloxacin is in a class of antibiotics known as fluoroquinolones, which treat infections by killing the bacteria that cause them. A physiologically-based pharmacokinetic (PBPK) model was developed to investigate the uptake, distribution, and elimination of Levofloxacin after a single dose. PBPK modeling uses parameters such as body weight, blood flow rates, partition coefficients, organ volumes, and several other parameters in order to model the distribution of a particular drug throughout the body. Levofloxacin is only moderately bound in human blood plasma, and, thus, for the purposes of this paper, linear bonding is incorporated into the model because the free or …