Mathematics Commons^™

The Steiner Problem On Closed Surfaces Of Constant Curvature, Andrew Logan

Theses and Dissertations

The n-point Steiner problem in the Euclidean plane is to find a least length path network connecting n points. In this thesis we will demonstrate how to find a least length path network T connecting n points on a closed 2-dimensional Riemannian surface of constant curvature by determining a region in the covering space that is guaranteed to contain T. We will then provide an algorithm for solving the n-point Steiner problem on such a surface.

Symmetric Presentations And Related Topics, Mashael U. Alharbi

Electronic Theses, Projects, and Dissertations

In this thesis, we have presented our discovery of symmetric presentations of a number of non-abelian simple groups, including the Mathieu group M₁₂. We have given several progenitors, permutation and monomial, including 2*⁴:(2²:3), 2*⁵:D₁₀, 2*⁸:((4X2).D₄), 3*⁷:_m L₂(7), 2*⁶:(Z₃ wr Z₂), and 2*²⁴: (2^. A₅) and their homomorphic images which include 4.(M₁₂:2), the group of automorphisms of M₁₂ and several classical groups. We have given the isomorphism type of …

Existence Of Solutions For A Variable Exponent System Without Ps Conditions, Li Yin, Yuan Liang, Qihu Zhang, Chunshan Zhao

Mathematical Sciences: Faculty Publications

In this article, we study the existence of solution for the following elliptic system of variable exponents with perturbation terms − div |∇u| p(x)−2∇u) + |u| p(x)−2u = λa(x)|u| γ(x)−2u + Fu(x, u, v) in R N , − div |∇v| q(x)−2∇v) + |v| q(x)−2 v = λb(x)|v| δ(x)−2 v + Fv(x, u, v) in R N , u ∈ W1,p(·) (R N ), v ∈ W1,q(·) (R N ), where the corresponding functional does not satisfy PS conditions. We obtain a sufficient condition for the existence of solution and also present a result on asymptotic behavior of solutions at …

Cohen Factorizations: Weak Functoriality And Applications, Saeed Nasseh, Sean Sather-Wagstaff

Mathematical Sciences: Faculty Publications

We investigate Cohen factorizations of local ring homomorphisms from three perspectives. First, we prove a “weak functoriality” result for Cohen factorizations: certain morphisms of local ring homomorphisms induce morphisms of Cohen factorizations. Second, we use Cohen factorizations to study the properties of local ring homomorphisms (Gorenstein, Cohen–Macaulay, etc.) in certain commutative diagrams. Third, we use Cohen factorizations to investigate the structure of quasi-deformations of local rings, with an eye on the question of the behavior of CI-dimension in short exact sequences.

Subclinical Atherosclerosis And Obesity Phenotypes Among Mexican Americans, Susan T. Laing, Beverly Smulevitz, Kristina Vatcheva, Mohammad H. Rahbar, Belinda M. Reininger, David D. Mcpherson, Joseph B. Mccormick, Susan P. Fisher-Hoch

School of Mathematical & Statistical Sciences Faculty Publications

Background

Data on the influence of obesity on atherosclerosis in Hispanics are inconsistent, possibly related to varying cardiometabolic risk among obese individuals. We aimed to determine the association of obesity and cardiometabolic risk with subclinical atherosclerosis in Mexican‐Americans.

Methods and Results

Participants (n=503) were drawn from the Cameron County Hispanic Cohort. Metabolic health was defined as <2 of the following: blood pressure ≥130/85; triglyceride ≥150 mg/dL; high‐density lipoprotein cholesterol <40 mg/dL (men) or <50 mg/dL (women); fasting glucose ≥100 mg/dL; homeostasis model assessment of insulin resistance value >5.13; or high‐sensitivity C‐reactive protein >3 mg/L. Carotid intima media thickness (cIMT) was measured. A high proportion of participants (77.8%) were metabolically unhealthy; they were more likely to be male, older, with fewer years of education, and less likely to meet daily recommendations regarding …

Scattering Of Motion On A Half-Infinite Quantum Graph Tube, Jeremy Tillay

Honors Capstones

No abstract provided.

A Fundamental Unit Of O_K, Susana L. Munoz

Electronic Theses, Projects, and Dissertations

In the classical case we make use of Pells equation to compute units in the ring O_F. Consider the parallel to the classical case and the quadratic field extension that creates the ring O_K. We use the generalized Pell's equation to find the units in this ring since they are solutions. Through the use of continued fractions we may further characterize this ring and compute its units.

A Mathematical Model Of Amoeboid Cell Motion As A Continuous-Time Markov Process, Lynnae Despain

Theses and Dissertations

Understanding cell motion facilitates the understanding of many biological processes such as wound healing and cancer growth. Constructing mathematical models that replicate amoeboid cell motion can help us understand and make predictions about real-world cell movement. We review a force-based model of cell motion that considers a cell as a nucleus and several adhesion sites connected to the nucleus by springs. In this model, the cell moves as the adhesion sites attach to and detach from a substrate. This model is then reformulated as a random process that tracks the attachment characteristic (attached or detached) of each adhesion site, the …

Generic Constructions Of Different Cryptographic Primitives Over Various Public Key Paradigms., Sumit Kumar Pandey Dr.

Doctoral Theses

In this thesis, we study the generic construction of some cryptographic primitives over various public key paradigms like traditional Public Key Cryptosystems and Identity Based Cryptosystems. It can be broadly divided into two categories1. Generic construction of some highly secure cryptographic primitives from less secure cryptographic primitives, and2. Generic construction of some complex cryptographic primitives from basic cryptographic primitives. Mathematical tools provide a way to achieve cryptographic functionality like confidentiality, authentication, data-integrity, non-repudiation etc., but in the case of complex cryptographic functionality like achieving confidentiality and authentication at the same time or confidentiality, authentication and non-repudiation at the same time …

Three Essays On The Impact Of Global Warming In India., Eshita Gupta Dr.

Doctoral Theses

This dissertation consists of three chapters. The Örst chapter studies the impact of climate change on electricity demand in Delhi using daily data on electricity demand and apparent temperature for the period 2000-09. It estimates a semi-parametric variable coe¢ - cient model that allows for a non-linear relationship between temperature and electricity to shift over time, a feature that is necessary to incorporate given the rapid economic growth in India. As evident from previous studies, electricity demand is a U-shaped function of temperature. Three results from our analysis have important implications for electricityclimate policy: Firstly, the rising part of the …

Session B-1: Pipelines And Oil Spills!, Patrick Young

Professional Learning Day

Don’t miss this hands-on approach to middle school math. Participants will construct an actual pipeline from inexpensive materials and record evidence of leakage. They will then conduct an experiment and create a model relating liquid volume and spill area. They will apply their model to determine how much liquid leaked from their pipeline.

Session B-3: Mathematical Games, Puzzles, And Diversions, Steven M. Condie

Professional Learning Day

Delve into the exciting world of math through games, puzzles and other sources! Participants shall try their luck and test their skill at these diversions. Participants will leave this session with a wealth of mathematical activities appropriate for students of all ages.

Session B-2: The “Roll” Of Statistics In Modeling - It All Adds Up, Richard Stalmack, Janice Krouse

Professional Learning Day

The common core practice standards ask us to teach students to propose mathematical models and test their viability. Participants will do an experiment, collect data and use technological tools to combine modeling, analysis and basic statistics. Participants should bring a laptop, if possible; otherwise, bring a graphing calculator.

Session A-2: From Polynomial To Rational Functions: Flip!, Ruth Dover

Professional Learning Day

Ah HA! Making the connection between polynomial functions, rational functions and using reciprocals! Join us to flip, not flop, with trig for your classroom.

Session C-2: Problem-Based Mathematics: You Reap What You Sow, Nicole Ross, Lindsey Herlehy

Professional Learning Day

Approach problem-based mathematics through a historical perspective! Join us to learn a fun, hands-on approach to examining the science behind crop rotation systems originally implemented during the Medieval Period. This activity requires students to mathematically evaluate the efficiency of a crop rotation system, strategically complete an integers-based crop puzzle, and evaluate crop yield and profit through data analysis. This activity integrates a variety of middle school mathematics concepts.

Session A-1: Implementing Common Core In Middle School Math, Karen Togliatti

Professional Learning Day

This session will focus on implementing Common Core Middle-School Mathematics Standards using student-centered activities. Participants will receive three hands-on activities (one each at grades six, seven, and eight) to take back to their classrooms.

Taming The Unknown: A History Of Algebra From Antiquity To The Early Twentieth Century, Calvin Jongsma

Faculty Work Comprehensive List

Reviewed Title: Katz, Victor J. and Karen Hunger Parshall. Taming the Unknown: A History of Algebra from Antiquity to the Early Twentieth Century. Princeton, NJ: Princeton University Press, 2014. 485 pages. ISBN 9780691149059

Non-Isomorphic Real Simple Lie Algebras Of The Same Complex Type And Character, Ian M. Anderson

Tutorials on... in 1 hour or less

Complex simple Lie algebras are classified by their root types. The type of a real simple Lie algebra is the root type of the associated complex algebra. The character of a real simple Lie algebra is the signature of its Killing form.

For many root types, the character is sufficient to uniquely classify the corresponding real Lie algebras. However, one should not take this statement to be literally true – there are a few cases where the character does not suffice to distinguish all possible real forms.

In this worksheet we will show that the 2 real non-isomorphic Lie algebras …

Some Conjugacy Problems In Algebraic Groups., Anirban Bose Dr.

Doctoral Theses

In this thesis we address two problems related to the study of algebraic groups and Lie groups. The first one deals with computation of an invariant called the genus number of a connected reductive algebraic group over an algebraically closed field and that of a compact connected Lie group. The second problem is about characterisation of real elements in exceptional groups of type F4 defined over an arbitrary field. Let G be a connected reductive algebraic group over an algebraically closed field or a compact connected Lie group. Let ZG(x) denote the centralizer of x ∈ G. Define the genus …

Tropical Determinant On Transportation Polytopes, Sailaja Gajula, Ivan Soprunov, Jenya Soprunova

Mathematics and Statistics Faculty Publications

Let D^k,l(m, n)be the set of all the integer points in the transportation polytope of kn × ln matrices with row sums lm and column sums km. In this paper we find the sharp lower bound on the tropical determinant over the set D^k,l(m, n). This integer piecewise linear programming problem in arbitrary dimension turns out to be equivalent to an integer non-linear (in fact, quadratic) optimization problem in dimension two. We also compute the sharp upper bound on a modification of the tropical determinant, where the maximum over all the transversals in a matrix is …