Physical Sciences and Mathematics Commons^™

Right Focal Boundary Value Problems For Difference Equations, Johnny Henderson, Xueyan Liu, Jeffrey W. Lyons, Jeffrey T. Neugebauer

Mathematics Faculty Articles

An application is made of a new Avery et al. fixed point theorem of compression and expansion functional type in the spirit of the original fixed point work of Leggett and Williams, to obtain positive solutions of the second order right focal discrete boundary value problem. In the application of the fixed point theorem, neither the entire lower nor entire upper boundary is required to be mapped inward or outward. A nontrivial example is also Provided.

Symmetric Generators Of Order 3, Stewart Contreras

Theses Digitization Project

The main purpose of this project is to construct finite homomorphic images of infinite semi-direct products.

Symmetric Generation, Dung Hoang Tri

Theses Digitization Project

In this thesis we construct finite homorphic images of infinite semi-direct products, 2*n : N, where 2*n is a free product of n copies the cyclic group of permutations on n letter.

An Investigation Of Kurosh's Theorem, Keith Anthony Earl

Theses Digitization Project

The purpose of this project will be an exposition of the Kurosh Theorem and the necessary and suffcient condition that A must be algebraic and satisfy a P.I. to be locally finite.

Use Of Cognitive Constructs In Linear Algebra, Azucena Zamora

Open Access Theses & Dissertations

Thesis analyzed the presence of two cognitive entities-- modes of thinking and metonymies and metaphors- in the reasoning of three students enrolled in a first year matrix algebra course at a southwest university via the responses given to a set of eight questions asked during one-on-one interviews. The findings of our analysis shed light on the cognitive constructs that students employ to form their understanding of linear algebra concepts. Furthermore, our findings provide clues about the ways in which students move from one mode of thinking to another in the context of varying levels of exposure to graphical, algebraic, and …

Incidence Functions, Yiyu Liao

Open Access Theses & Dissertations

In the mid 1960's, the incidence algebra was introduced in the seminal paper of Gian-Carlo Rota. He addressed the importance of the Mobius function in combinatorics. In particular, the incidence algebra of a locally finite poset plays an essentially unifying role in the theory of the Mobius function. One of the significant generalizations is the incidence algebra of a Mobius category introduced by Pierre Leroux. With the help from Mobius category, it was exciting to be able to extend the combinatorial results more broadly than just on posets. Before attempting to study this generalization of the Mobius function, we have …

Signature Matrices: The Eigenvalue Problem, Valeria Aguirre Holguin

Open Access Theses & Dissertations

Dealing with matrices can give us a hard time, especially when their dimension is too big, but we also well know how valuable information a matrix may carry, and that is why we study them. When a matrix has a significant number of zeroes we realize how much easier all calculations are. For instance, the product will be simpler to calculate, the determinant, the inverse and even the eigenvalue problem. This thesis provides the description and behavior of a very special kind of matrices which we call signature matrices. A particular feature of these matrices lies in the fact that …

Begin The Adventure : How To Break The Light Barrier By A.D. 2079 (3rd Ed.), Florentin Smarandache, Homer B. Tilton

Branch Mathematics and Statistics Faculty and Staff Publications

This edition, the third, has undergone a subtle name change, going from "A.D. 2070" in the title to A.D. 2079 as the timeline is fine-tuned. Because of the almost universal failure to recognize the distinction between physical (reality-based, dynamical) and visual (appearance-based, kinematical) variables, a tremendous volume of mythology arose over the past 100 years centered around Einstein's reality view of the distortions of special relativity. To get a sense of it, we point the reader to Paul J. Nahin's heroic book, Time Machines, 2nd ed.,- to these Tech Notes in particular: TN#6. "A High-Speed Rocket Is a One-Way Time …

Social Network Gaming Trends, Michael Gathwright

Undergraduate Journal of Mathematical Modeling: One + Two

The purpose of this project was to determine how long the social network game Scratch-Offs, created by game development company Spice Rack Media, will remain financially viable. The game Scratch-Offs is a freeware game (users pay nothing for the actual software) and is funded through micro transactions (users must pay small amounts of money to play actual games). This implies a relationship between total games played and revenue earned. Using data provided by Spice Rack, we were able to develop an exponential equation that accurately depicts usage trends over time. This equation was used to determine the date Scratch-Offs will …

Population Dynamics Of Free-Roaming Cats In Florida's Lee County, Benjamin Taylor

Undergraduate Journal of Mathematical Modeling: One + Two

We investigate whether the Trap-Neuter-Return (TNR) program can be effectively used to control the population of free-roaming cats in Florida's Lee County. We do this by estimating the number of cats that must be spayed/neutered in order to keep the population from increasing.

Volume Of An Industrial Autoclave, Nicholas Madaffari

Undergraduate Journal of Mathematical Modeling: One + Two

We were able to determine the volume of an industrial autoclave sterilization tank using a technique learned in calculus. By measuring the dimensions of the tank and roughly estimating the equation of curvature at the ends of the tank, we were able to revolve half of the end of the tank around the x axis to get its fluid volume. Adding the two volumes of the ends and the volume of the cylindrical portion on the tank yielded the total volume.

Predator-Prey Modeling, Shaza Hussein

Undergraduate Journal of Mathematical Modeling: One + Two

Predator-prey models are useful and often used in the environmental science field because they allow researchers to both observe the dynamics of animal populations and make predictions as to how they will develop over time. The objective of this project was to create five projections of animal populations based on a simple predator-prey model and explore the trends visible. Each case began with a set of initial conditions that produced different outcomes for the function of the population of rabbits and foxes over an 80 year time span. Using Euler's method, an Excel spreadsheet was developed to produce the values …

The Fibonacci Sequence, Arik Avagyan

A with Honors Projects

A review was made of the Fibonacci sequence, its characteristics and applications.

On Hyperplanes And Semispaces In Max-Min Convex Geometry, Viorel Nitica, Sergeĭ Sergeev

Mathematics Faculty Publications

No abstract provided.

Continued Fraction Proofs Of M-Versions Of Some Identities Of Rogers-Ramanujan-Slater Type, Douglas Bowman, James Mclaughlin, Nancy Wyshinksi

Mathematics Faculty Publications

We derive two general transformations for certain basic hypergeometric series from the recurrence formulae for the partial numerators and denominators of two q-continued fractions previously investigated by the authors. By then specializing certain free parameters in these transformations, and employing various identities of Rogers-Ramanujan type, we derive m-versions of these identities. Some of the identities thus found are new, and some have been derived previously by other authors, using different methods. By applying certain transformations due to Watson, Heine and Ramanujan, we derive still more examples of such m-versions of Rogers Ramanujan-type identities.

General Wp-Bailey Chains, James Mclaughlin, Peter Zimmer

Mathematics Faculty Publications

Motivated by a recent paper of Liu and Ma, we describe a number of general WP-Bailey chains. We show that many of the existing WP-Bailey chains (or branches of the WP-Bailey tree), including chains found by Andrews, Warnaar and Liu and Ma, arise as special cases of these general WP-Bailey chains. We exhibit three new branches of the WP-Bailey tree, branches which also follow as special cases of these general WP-Bailey chains. Finally, we describe a number of new transformation formulae for basic hypergeometric series which arise as consequences of these new WP-Bailey chains.

An Identity Motivated By An Amazing Identity Of Ramanujan, James Mclaughlin

Mathematics Faculty Publications

Ramanujan stated an identity to the effect that if three sequences {an}, {bn} and {cn} are defined by r1(x) =: ∑∞ n=0 anx n , r2(x) =: ∑∞ n=0 bnx n and r3(x) =: ∑∞ n=0 cnx n (here each ri(x) is a certain rational function in x), then a 3 n + b 3 n − c 3 n = (−1)n , ∀ n ≥ 0. Motivated by this amazing identity, we state and prove a more general identity involving eleven sequences, the new identity being ”more general” in the sense that equality holds not just for the power …

Some Applications Of A Bailey-Type Transformation, James Mclaughlin, Peter Zimmer

Mathematics Faculty Publications

If k is set equal to aq in the definition of a WP Bailey pair, βn(a, k) = Xn j=0 (k/a)n−j (k)n+j (q)n−j (aq)n+j αj (a, k), this equation reduces to βn = Pn j=0 αj . This seemingly trivial relation connecting the αn’s with the βn’s has some interesting consequences, including several basic hypergeometric summation formulae, a connection to the Prouhet-Tarry-Escott problem, some new identities of the Rogers-Ramanujan-Slater type, some new expressions for false theta series as basic hypergeometric series, and new transformation formulae for poly-basic hypergeometric series.

Generalized Fourier-Feynman Transforms, Convolution Products, And First Variations On Function Space, Seung Jun Chang, Jae Gil Choi, David Skough

Department of Mathematics: Faculty Publications

In this paper we examine the various relationships that exist among the first variation, the convolution product and the Fourier-Feynman transform for functionals of the form F(x) = f((α₁, x), . . . , (α_n, x)) with x in a very general function space C_a,b[0,T].

A Comparison Of Prediction Methods Of Functional Autoregressive Time Series, Devin Didericksen

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

Functional data analysis (FDA) is a relatively new branch of statistics that has seen a lot of expansion recently. With the advent of computer processing power and more efficient software packages we have entered the beginning stages of applying FDA methodology and techniques to data. Part of this undertaking should include an empirical assessment of the effectiveness of some of the tools of FDA, which are sound on theoretical grounds. In a small way, this project helps advance this objective.

This work begins by introducing FDA, scalar prediction techniques, and the functional autoregressive model of order one - FAR(1). Two …

Simulating Power For One-Way Anova By Using Non-Normal Error Distributions, Caixia Xu

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

Usually we assume that the distribution of the additive errors in a one-way ANOVA linear model is normal. However, exceptions to this assumption about the error distribution may exist. In such cases, we might consider non-normal error distributions, but proceed with the "usual" ANOVA F-test analyses. This study focuses on simulating power for one-way ANOVA when using non-normal error distributions.

Early Intervention In College Mathematics Courses: A Component Of The Stem Rrg Program Funded By The Us Department Of Education, Rohitha Goonatilake, Eduardo Chappa

The Mathematics Enthusiast

Student preparedness in entry level college mathematics courses has decreased in the past. In order for students to be successful in these courses, early intervention is required. Texas A&M International University (TAMIU) has implemented an early intervention program, the Mathematics Enrichment Program (MEP), which will target freshman students entering College Algebra courses in Spring 2009. This project is part of the STEM Recruitment, Retention, and Graduation program, recently funded by the US Department of Education. This paper will highlight the components of the project, most importantly the extent of the intervention, how the project is planned, and preliminary results.

Randomness: Developing An Understanding Of Mathematical Order, Steve Humble

The Mathematics Enthusiast

Is randomness merely the human inability to recognise a pattern that may in fact exist?

The three activities described show how order can be found in seemly random activities. The author has found that by using these activities on randomness, his students have developed a greater understanding of mathematical pattern and sequence. The teaching mathematical concepts in this way, engages and reinforces learning. It puts the ideas learnt into a setting and allows time for those ideas to be developed without any of the maths hang-ups which can sometimes occur in the classroom. By taking the maths beyond the classroom, …

Proceedings Of The Fourth Annual Meeting Of The Georgia Association Of Mathematics Teacher Educators Introductory Texts

Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators

Contents of 1st Annual GAMTE Proceedings Front Matter:

• Proceedings Committee
• Officers of GAMTE
• Purposes and Goals of GAMTE
• Table of Contents

Towards An Automation Of The Circle Method, Andrew Sills

Department of Mathematical Sciences Faculty Publications

The derivation of the Hardy-Ramanujan-Rademacher formula for the number of partitions of n is reviewed. Next, the steps for finding analogous formulas for certain restricted classes of partitions or overpartitions is examined, bearing in mind how these calculations can be automated in a CAS. Finally, a number of new formulas of this type which were conjectured with the aid of Mathematica are presented along with results of a test for their numerical accuracy.

Some Implications Of Chu's 10Ψ10 Generalization Of Bailey's 6Ψ6 Summation Formula, James Mclaughlin, Andrew Sills, Peter Zimmer

Department of Mathematical Sciences Faculty Publications

Lucy Slater used Bailey's 6ψ6 summation formula to derive the Bailey pairs she used to construct her famous list of 130 identities of the Rogers-Ramanujan type.

In the present paper we apply the same techniques to Chu's 10ψ10 generalization of Bailey's formula to produce quite general Bailey pairs. Slater's Bailey pairs are then recovered as special limiting cases of these more general pairs.

In re-examining Slater's work, we find that her Bailey pairs are, for the most part, special cases of more general Bailey pairs containing one or more free parameters. Further, we also find new …

Conformal Classification Of (K, Μ)-Contact Manifolds, Ramesh Sharma, Luc Vrancken

Mathematics Faculty Publications

First we improve a result of Tanno that says "If a conformal vector field on a contact metric manifold M is a strictly infinitesimal contact transformation, then it is an infinitesimal automorphism of M" by waiving the "strictness" in the hypothesis. Next, we prove that a (k, μ)-contact manifold admitting a non-Killing conformal vector field is either Sasakian or has k = –n – 1, μ = 1 in dimension > 3; and Sasakian or flat in dimension 3. In particular, we show that (i) among all compact simply connected (k, μ)-contact manifolds of dimension > 3, only the unit sphere S2n+1 …

Packing Rates Of Measures And A Conjecture For The Packing Density Of 2413, C. B. Presutti, Walter Stromquist

Mathematics & Statistics Faculty Works

We give a new lower bound of 0.10472422757673209041 for the packing density of 2413, justify it by a construction, and conjecture that this value is actually equal to the packing density. Along the way we define the packing rate of a permutation with respect to a measure, and show that maximizing the packing rate of a pattern over all measures gives the packing density of the pattern.

The Principal Eigencurves For A Nonselfadjoint Elliptic Operator, Aomar Anane, Omar Chakrone, Abdellah Zerouali

Turkish Journal of Mathematics

In this paper we study the existence of the principal eigencurves for a nonselfadjoint elliptic operator. We obtain their variational formulation. We establish also the continuity and the differentiability of the principal eigencurves.

Weak Hardy Space And Endpoint Estimates For Singular Integrals On Space Of Homogeneous Type, Yong Ding, Xinfeng Wu

Turkish Journal of Mathematics

We develop the theory of weak Hardy spaces H^{1,\infty} on space of homogeneous type. As some applications, we show that certain singular integral operators and fractional integral operators are bounded from H^{1,\infty} to L^{1,\infty} and L^{\frac{1}{1-\alpha},\infty}, respectively. We give also the endpoint estimates for Nagel and Stein's singular integrals studied in [10].