Mathematics Commons^™

One-Dimensional Weakly Nonlinear Model Equations For Rossby Waves, David Henry, Rossen Ivanov

Articles

In this study we explore several possibilities for modelling weakly nonlinear Rossby waves in fluid of constant depth, which propagate predominantly in one direction. The model equations obtained include the BBM equation, as well as the integrable KdV and Degasperis-Procesi equations.

Fejér And Suffridge Polynomials In The Delayed Feedback Control Theory, Dmitriy Dmitrishin, Anna Khamitova, Anatolii Korenovskyi, Alexander M. Stokolos

Mathematical Sciences: Faculty Publications

A remarkable connection between optimal delayed feedback control (DFC) and complex polynomial mappings of the unit disc is established. The explicit form of extremal polynomials turns out to be related with the Fejer polynomials. The constructed DFC can be used to stabilize cycles of one-dimensional non-linear discrete systems.

An Empirical Study Of Some Branching Processes With Upper Barrier, Alejandro Aguilar

Theses and Dissertations - UTB/UTPA

We consider discrete time branching processes with a reflecting upper barrier. The processes differ in their offspring distributions being either binary splitting or binomial one. Two important factors for the behavior of the processes characteristics are studied as follows: time to extinction and total progeny up to the n th generation. More specifically, we investigate the distribution and expected value of the time to extinction as well as the probability mass functions of the total progeny. The tools used are basic results for a finite state Markov chain.

Algebraic Properties Of Ext-Modules Over Complete Intersections, Jason Hardin

Department of Mathematics: Dissertations, Theses, and Student Research

We investigate two algebraic properties of Ext-modules over a complete intersection R of codimension c. Given an R-module M, Ext(M,k) can be viewed as a graded module over a polynomial ring in c variables with an action given by the Eisenbud operators. We provide an upper bound on the degrees of the generators of this graded module in terms of the regularities of two associated coherent sheaves. In the codimension two case, our bound recovers a bound of Avramov and Buchweitz in terms of the Betti numbers of M. We also provide a description of the differential graded (DG) R-module …

Approaches For Generating 2d Shapes, Pratik Shankar Hada

UNLV Theses, Dissertations, Professional Papers, and Capstones

Constructing a two dimensional shape from given a set of point sites is a well known problem in computation geometry. We present a critical review of the existing algorithms for constructing polygonal shapes. We present a new approach calledinward dentingfor constructing simple polygons. We then extend the proposed approach for modeling polygons with holes. This is the

first known algorithm for modeling holes in the interior of 2d shapes. We also present experimental investigations of the quality of the solutions generated by the proposed algorithms.

For this we implemented the proposed algorithms in Java programming language. The prototype program can …

Numerical Simulations Of Traffic Flow Models, Puneet Lakhanpal

UNLV Theses, Dissertations, Professional Papers, and Capstones

Traffic flow has been considered to be a continuum flow of a compressible liquid having a certain density profile and an associated velocity, depending upon density, position and time. Several one-equation and two-equation macroscopic continuum flow models have been developed which utilize the fluid dynamics continuity equation and help us find analytical solutions with simplified initial and boundary conditions. In this thesis, the one-equation Lighthill Witham and Richards (LWR) model combined with the Greenshield's model, is used for finding analytical and numerical solutions for four problems: Linear Advection, Red Traffic Light turning into Green, Stationary Shock and Shock Moving towards …

Anxiety, Depression And Smoking Status Among Adults Of Mexican Heritage On The Texas-Mexico Border, Anna V. Wilkinson, Kristina Vatcheva, Adriana Pérez, Belinda M. Reininger, Joseph B. Mccormick, Susan P. Fisher-Hoch

School of Mathematical & Statistical Sciences Faculty Publications

The goal of the current analysis is to examine relationships between smoking status and anxiety and depression among adults of Mexican heritage to inform the development of culturally relevant smoking cessations efforts. Mexican heritage residents (N=1,791) of the city of Brownsville, TX, aged 18 years or older, enrolled in the Cameron County Hispanic Cohort, were selected through two stage cluster sampling of randomly selected census tracts from the first and third quartile of SES using Census 2000. Among current smokers, anxiety and depression scores were highest among women who had not completed high school (p<0.05). Former smoking women, but not men, with at least a high school education and former smoking women born in the United States reported higher levels of anxiety and depression than never smoking women. Negative affective states may represent a greater barrier to smoking cessation among women than men.

Living At The Friendship House: Findings From Thetransition Planning Inventory, Jane E. Finn, Vicky-Lynn Holmes, Rebecca Johnson

Faculty Publications

A residential initiative, named the Friendship House, was created through advocates focused on helping people with intellectual disabilities live independently in affordable and safe housing on a university campus. The Friendship House is a small residence hall where individuals with intellectual disabilities live side-by-side with similarly aged and same gendered university students. Qualitative finding as in resident reports and observational data provides support that the Friendship House experience has been successful. However, to better equip these residents with intellectual disabilities, it is important to assess the program in terms of post school transition acquisition skills. This study focuses on whether …

Antimagic-Type Labelings, Sogol Jahanbekam

Faculty Publications

No abstract provided.

Deconstructing The Welch Equation Using P-Adic Methods, Abigail Mann, Adelyn Yeoh

Mathematical Sciences Technical Reports (MSTR)

The Welch map x -> g^x-1+c is similar to the discrete exponential map x -> g^x, which is used in many cryptographic applications including the ElGamal signature scheme. This paper analyzes the number of solutions to the Welch equation: g^x-1+c = x (mod p^e) where p is a prime, and looks at other patterns of the equation that could possibly exploited in a similar cryptographic system. Since the equation is modulo p^e, where p is a prime number, p-adic methods of analysis are used in counting the number of solutions modulo p …

Deconstructing The Welch Equation Using P-Adic Methods, Abigail Mann, Adelyn Yeoh

Rose-Hulman Undergraduate Research Publications

The Welch map x -> g^x-1+c is similar to the discrete exponential map x -> g^x, which is used in many cryptographic applications including the ElGamal signature scheme. This paper analyzes the number of solutions to the Welch equation: g^x-1+c = x (mod p^e) where p is a prime, and looks at other patterns of the equation that could possibly exploited in a similar cryptographic system. Since the equation is modulo p^e, where p is a prime number, p-adic methods of analysis are used in counting the number of solutions modulo p …

Hoijer '15 Studies Correlations Between Mathematics And Music, Danielle Kamp

News and Events (Discontinued Series)

No abstract provided.

Simmons' Research Aims To Improve Function For Online Security, Danielle Kamp

News and Events (Discontinued Series)

No abstract provided.

Near Oracle Performance And Block Analysis Of Signal Space Greedy Methods, Raja Giryes, Deanna Needell

CMC Faculty Publications and Research

Compressive sampling (CoSa) is a new methodology which demonstrates that sparse signals can be recovered from a small number of linear measurements. Greedy algorithms like CoSaMP have been designed for this recovery, and variants of these methods have been adapted to the case where sparsity is with respect to some arbitrary dictionary rather than an orthonormal basis. In this work we present an analysis of the so-called Signal Space CoSaMP method when the measurements are corrupted with mean-zero white Gaussian noise. We establish near-oracle performance for recovery of signals sparse in some arbitrary dictionary. In addition, we analyze the block …

Modelling Stock Returns In 'Volatility-In-Mean' Framework Under Up And Down Market Movements, Srikanta Kundu Dr.

Doctoral Theses

The first chapter of this thesis begins with a brief review of the existing literature on empirical studies on stock returns, especially those in the context of the relationship between risk and return, at both univariate and multivariate levels. In the next section, studies on the relationship between stock return and monetary policy are reviewed. The motivation of this work is discussed in Section 1.4. Finally, the format of the thesis is given in Section 1.5.A Brief Review of the Literature on Risk-Return Relationship-Both Univariate and Multivariate Cases. In this section, we first present a brief review of this literature …

Transposing Noninvertible Polynomials, Nathan Cordner

Library Research Grants

In the class of invertible polynomials, the notion of dual polynomials W and W^T, as well as dual groups G and G^T is well-understood. In this paper we investigate finding dual pairs W and W^T for noninvertible polynomials. We find that in many instances, our intuition that stems from invertible polynomials does not extend to the noninvertible case.

The Physicist's Basement, Nora Culik

Journal of Humanistic Mathematics

No abstract provided.

The Discipline Of History And The “Modern Consensus In The Historiography Of Mathematics”, Michael N. Fried

Journal of Humanistic Mathematics

Teachers and students of mathematics often view history of mathematics as just mathematics as they know it, but in another form. This view is based on a misunderstanding of the nature of history of mathematics and the kind of knowledge it attempts to acquire. Unfortunately, it can also lead to a deep sense of disappointment with the history of mathematics itself, and, ultimately, a misunderstanding of the historical nature of mathematics. This kind of misunderstanding and the disappointment following from it--both raised to the level of resentment--run through the paper "A Critique of the Modern Consensus in the Historiography of …

A Critique Of The Modern Consensus In The Historiography Of Mathematics, Viktor Blåsjö

Journal of Humanistic Mathematics

The history of mathematics is nowadays practiced primarily by professional historians rather than mathematicians, as was the norm a few decades ago. There is a strong consensus among these historians that the old-fashioned style of history is “obsolete,” and that “the gains in historical understanding are incomparably greater” in the more “historically sensitive” works of today. I maintain that this self-congratulatory attitude is ill-founded, and that the alleged superiority of modern historiographical standards ultimately rests on a dubious redefinition of the purpose of history rather than intrinsic merit.

How Do I Love Thee? Let Me Count The Ways For Syllabic Variation In Certain Poetic Forms, Mike Pinter

Journal of Humanistic Mathematics

The Dekaaz poetic form, similar to haiku with its constrained syllable counts per line, invites a connection between poetry and mathematics. Determining the number of possible Dekaaz variations leads to some interesting counting observations. We discuss two different ways to count the number of possible Dekaaz variations, one using a binary framework and the other approaching the count as an occupancy problem. The counting methods described are generalized to also count variations of other poetic forms with syllable counts specified, including haiku. We include Dekaaz examples and suggest a method that can be used to randomly generate a Dekaaz variation.

Fields In Math And Farming, Susan D'Agostino

Journal of Humanistic Mathematics

A young woman’s search for a a contemplative, insightful experience leads her from farming to mathematics.

Being Reasonable: Using Brainteasers To Develop Reasoning Ability In Humanistic Mathematics Courses, Gary Stogsdill

Journal of Humanistic Mathematics

Developing reasoning ability is often cited as one of the principal justifications of a mathematics requirement for liberal arts undergraduates. Humanistic math courses have become recognized as a paradigm for liberal arts mathematics, but such courses may not provide the opportunity to develop reasoning ability. The author describes his procedure for using brainteasers to promote reasoning in a humanistic math course for liberal arts undergraduates.

Joining ``The Mathematician's Delirium To The Poet's Logic'': Mathematical Literature And Literary Mathematics, Rita Capezzi, Christine Kinsey

Journal of Humanistic Mathematics

This paper describes our team-taught interdisciplinary mathematics and literature course, Mathematical Literature and Literary Mathematics, which invites students to consider Raymond Queneau's challenge: "Why shouldn't one demand a certain effort on the reader's part? Everything is always explained to him. He must eventually tire of being treated with such contempt.'' We study works by Berge, Borges, Calvino, Perec, Queneau, Robbe-Grillet and Stoppard, among others. From a literary critical perspective, the course highlights the play of language rather than the primacy of meaning. We choose texts where mathematical concepts are subjects or structuring elements of the literature, and ideally both. …

Some Effects Of The Human Genome Project On The Erdős Collaboration Graph, Chris Fields

Journal of Humanistic Mathematics

The Human Genome Project introduced large-scale collaborations involving dozens to hundreds of scientists into biology. It also created a pressing need to solve discrete mathematics problems involving tens of thousands of elements. In this paper, we use minimal path lengths in the Erdős Collaboration Graph between prominent individual researchers as a measure of the distance between disciplines, and we show that the Human Genome Project brought laboratory biology as a whole closer to mathematics. We also define a novel graph reduction method and a metric that emphasizes the robustness of collaborative connections between researchers; these can facilitate the analysis of …

Thin Sequences And The Gram Matrix, Pamela Gorkin, John E. Mccarthy, Sandra Pott, Brett D. Wick

Mathematics Faculty Research

We provide a new proof of Volberg’s Theorem characterizing thin interpolating sequences as those for which the Gram matrix associated to the normalized reproducing kernels is a compact perturbation of the identity. In the same paper, Volberg characterized sequences for which the Gram matrix is a compact perturbation of a unitary as well as those for which the Gram matrix is a Schatten-2 class perturbation of a unitary operator. We extend this characterization from 2 to p, where 2 p ≤∞.

How Do They Know It Is A Parallelogram? Analysing Geometric Discourse At Van Hiele Level 3, Sasha Wang, Margaret Kinzel

Mathematics Faculty Publications and Presentations

In this article, we introduce Sfard's discursive framework and use it to investigate prospective teachers' geometric discourse in the context of quadrilaterals. In particular, we focus on describing and analysing two participants' use of mathematical words and substantiation routines related to parallelograms and their properties at van Hiele level 3 thinking. Our findings suggest that a single van Hiele level of thinking encompasses a range of complexity of reasoning and differences in discourse and thus a deeper investigation of students' mathematical thinking within assigned van Hiele levels is warranted.

Agriculture Trade And Protectionism., Debasmita Basu Dr.

Doctoral Theses

Ever since the inception of the World Trade Organization free trade in agricultural goods has been difficult to implement. The developed countries, who are otherwise active proponents of free trade, seem reluctant to remove the subsidies from the agricultural sector, making way for unfair competition against the poor developing nations. The Common Agricultural Program (CAP) spending of around ¿58 bn each year in the European countries as agricultural subsidy has always been subject to controversy.The U.S. Department of Agriculture (USDA) has also devised a variety of programs to supplement the farmers’ income, support commodity market price and manage supply. The …

Reconstruction Of Structured Quadratic Pencils From Eigenvalues On Ellipses And Parabolas, R. Ibragimov, Vesselin Vatchev

School of Mathematical & Statistical Sciences Faculty Publications

In the present paper we study the reconstruction of a structured quadratic pencil from eigenvalues distributed on ellipses or parabolas. A quadratic pencil is a square matrix polynomial

QP(λ) = M λ²+Cλ +K,

where M, C, and K are real square matrices. The approach developed in the paper is based on the theory of orthogonal polynomials on the real line. The results can be applied to more general distribution of eigenvalues. The problem with added single eigenvector is also briefly discussed. As an illustration of the reconstruction method, the eigenvalue problem …

Review Of The Joy Of X: A Guided Tour Of Math, From One To Infinity By Steven Strogatz, Michael T. Catalano

Numeracy

Strogatz, Steven. The Joy of x: A Guided Tour of Math, from One to Infinity, (New York, NY, Houghton Mifflin Harcourt, 2012). 316 pp. ISBN 978-0-547-51765-0

The Joy of x: A Guided Tour of Math, from One to Infinity, by Steven Strogatz, is an engaging and example-filled argument for mathematics as a valuable and enjoyable activity. The thirty chapters are divided into six parts, entitled Numbers, Relationships, Shapes, Change, Data, and Frontiers. The discussion ranges from intuitive explanations of basic concepts such as place value, the four arithmetic operations, percentage increase and decrease, and solving equations, to “higher” levels …

How Does One Design Or Evaluate A Course In Quantitative Reasoning?, Bernard L. Madison

Numeracy

In the absence of generally accepted content standards and with little evidence on the learning for long-term retrieval and transfer, how does one design or evaluate a course in quantitative reasoning (QR)? This is a report on one way to do so. The subject QR course, which has college algebra as a prerequisite and has been taught for 8 years, is being modified slightly to be offered as an alternative to college algebra. One modification is adding a significant formal writing component. As the modification occurs, the current course and the modified one are judged according to six sets of …