Mathematics Commons^™

Solution Of Nonlinear Time-Dependent Pde Through Componentwise Approximation Of Matrix Functions, Alexandru Cibotarica

Dissertations

Exponential propagation iterative (EPI) methods provide an efficient approach to the solution of large stiff systems of ODE, compared to standard integrators. However, the bulk of the computational effort in these methods is due to products of matrix functions and vectors, which can become very costly at high resolution due to an increase in the number of Krylov projection steps needed to maintain accuracy. In this dissertation, it is proposed to modify EPI methods by using Krylov subspace spectral (KSS) methods, instead of standard Krylov projection methods, to compute products of matrix functions and vectors. This improvement allowed the benefits …

Zeros Of Cubic Eisenstein Series, Sahak D. Sandragorsian

Theses and Dissertations - UTB/UTPA

This thesis provides a detailed exposition and extension of the work of F. K. C. Rankin and Swinnerton-Dyer on the location of the zeros of Eisenstein series for SL(2,Z). Exact values of the zeros in special cases will be given in terms of modular functions. Analogous new results on zeros of cubic Eisenstein series will be presented.

On A Convex Set With Nondifferentiable Metric Projection, Shyan S. Akmal, Nguyen Mau Nam, J. J. P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

A remarkable example of a nonempty closed convex set in the Euclidean plane for which the directional derivative of the metric projection mapping fails to exist was constructed by A. Shapiro. In this paper, we revisit and modify that construction to obtain a convex set with smooth boundary which possesses the same property.

On Supervised And Unsupervised Methodologies For Mining Of Text Data., Tanmay Basu Dr.

Doctoral Theses

The supervised and unsupervised methodologies of text mining using the plain text data of English language have been discussed. Some new supervised and unsupervised methodologies have been developed for effective mining of the text data after successfully overcoming some limitations of the existing techniques.The problems of unsupervised techniques of text mining, i.e., document clustering methods are addressed. A new similarity measure between documents has been designed to improve the accuracy of measuring the content similarity between documents. Further, a hierarchical document clustering technique is designed using this similarity measure. The main significance of the clustering algorithm is that the number …

Properties Of Multilayered Zno/Al/Zno Transparent Film Electrodes: Models And Experiments, E. R. Rwenyagila, M. E. Samiji

Tanzania Journal of Science

ZnO/Metal/ZnO multilayers have been recognized as good candidates for transparent conductive thin films for applications in solar cells and optoelectronic devices. One of the important challenges in the experimental designs of such structures is the lack of optimum metal thickness range such as Al in ZnO/Al/ZnO multilayers. The present work overcomes this limitation by investigating how Al thickness affects the optical properties of such multilayered films. In this paper, optical simulations are used to explore the possibility of ultrathin, high transparent ZnO/Al/ZnO multilayer films. Multilayered ZnO/Al/ZnO film with mid-Al layer thicknesses between 1 and 10 nm are shown to have …

Meander Graphs And Frobenius Seaweed Lie Algebras Ii, Vincent Coll, Matthew Hyatt, Colton Magnant, Hua Wang

Mathematical Sciences: Faculty Publications

We provide a recursive classification of meander graphs, showing that each meander is identified by a unique sequence of fundamental graph theoretic moves. This sequence is called the meander’s signature and can be used to construct arbitrarily large sets of meanders, Frobenius or otherwise, of any size and configuration. In certain special cases, the signature is used to produce an explicit formula for the index of seaweed Lie subalgebra of sl(n) in terms of elementary functions.

The Topology Of Absence, Nora E. Culik

Journal of Humanistic Mathematics

“The Topology of Absence” literalizes triangulations, hyperbeloids, and the concept of the limit in the story of “locating” a lost mother. This story, like “The Physicist’s Basement” in the July 2014 issue, is part of a series that worries about competing notions of mathematics, i.e., mathematics as some sort of disembodied configuration or as emergent in the material reality of human life.

Geometry Of Life, Janice Dykacz

Journal of Humanistic Mathematics

Relationships in life can be expressed through geometric curves

Mathematical Double Dactyls, Tristan Miller

Journal of Humanistic Mathematics

No abstract provided.

On Mathematicians' Eccentricity, Robert Haas

Journal of Humanistic Mathematics

Eccentricity, though not inevitable, happens. Lightheartedly classifying examples, the author traces it back to factors, like creativity and absorption, essential to mathematical success, and recommends an attitude of amused tolerance towards others as well as to ourselves.

A System Of Equations: Mathematics Lessons In Classical Literature, Valery F. Ochkov, Andreas Look

Journal of Humanistic Mathematics

The aim of this paper is to showcase a handful of mathematical challenges found in classical literature and to offer possible ways of integrating classical literature in mathematics lessons. We analyze works from a range of authors such as Jules Verne, Anton Chekhov, and others. We also propose ideas for further tasks. Most of the problems can be restated in terms of simple mathematical equations, and they can often be solved without a computer. Nevertheless, we use the computer program Mathcad to solve the problems and to illustrate the solutions to enhance the reader’s mathematical experience.

Mathematics: What Has It To Do With Me?, Man Keung Siu

Journal of Humanistic Mathematics

Mathematics teachers must have encountered the following question raised by students: “What is the use of mathematics?” Although the value of mathematics is not to be determined solely by its applications, to the general public this is a more important and more convincing facet of the subject. Nevertheless, this also brings up the corresponding query: is this subject being properly used? Does mathematics play a role in moral education?

On Similarities And Differences Between Proving And Problem Solving, Milos Savic

Journal of Humanistic Mathematics

A link between proving and problem solving has been established in the literature [5, 21]. In this paper, I discuss similarities and differences between proving and problem solving using the Multidimensional Problem-Solving Framework created by Carlson and Bloom [2] with Livescribepen data from a previous study [13]. I focus on two participants’ proving processes: Dr. G, a topologist, and L, a mathematics graduate student. Many similarities between the framework and the proving processes of Dr. G and L were revealed, but there were also some differences. In addition, there were some distinct differences between the proving actions of the …

Counting The Angels And Devils In Escher's Circle Limit Iv, John Choi, Nicholas Pippenger

Journal of Humanistic Mathematics

We derive the rational generating function that enumerates the angels and devils in M. C. Escher's Circle Limit IV according to their combinatorial distance from the six creatures whose feet meet at the center of the disk. This result shows that the base of the exponential rate of growth is 1.582... (the largest root of the polynomial 1 - z^2 - 2z^3 - z^4 + z^6).

Long-Time Dynamics Of 2d Double-Diffusive Convection: Analysis And/Of Numerics, Florentina Tone, Xiaoming Wang, Djoko Wirosoetisno

Mathematics and Statistics Faculty Research & Creative Works

We consider a two-dimensional model of double-diffusive convection and its time discretisation using a second-order scheme (based on backward differentiation formula for the time derivative) which treats the non-linear term explicitly. Uniform bounds on the solutions of both the continuous and discrete models are derived (under a timestep restriction for the discrete model), proving the existence of attractors and invariant measures supported on them. as a consequence, the convergence of the attractors and longtime statistical properties of the discrete model to those of the continuous one in the limit of vanishing timestep can be obtained following established methods.

Complete And Partial Ordering Approaches In The Context Of Poverty Ordering And On The Impacts Of Growth And Inequality On Poverty., Sandip Sarkar Dr.

Doctoral Theses

No abstract provided.

Wavelet Analysis On Local Fields Of Positive Characteristic., Quiser Jahan Dr.

Doctoral Theses

In this chapter, we will give a brief history of wavelet analysis on R. We will also list some bask results on local felds which will be used in subvequent chapters.1.1 Wavelets on RWe fiest start with a brief history of wavelets und some basic defnitions and results conceming the orthonormal wavekts on R.1.1.1 A brief historyIn the last few decades vaveler theory has growa extensively and has drawn great atlention sot only in mathematies bu also in engineering, pitysics, computer science and many other fields. In signal and image processing, wavelets play a very important role.In 1910, A. Haar …

Euler Class Groups Of Polynomial And Sub Integral Extensions Of A Noetherian Ring., Md. Ali Zinna Dr.

Doctoral Theses

ObjectiveThe main objectives of this thesis are the following:(i) To investigate the behaviour of the Euler class groups under integral and subintegral extensions. More precisely, given a subintegral (or integral) extension R+ S of Noetherian rings, we are interested in finding out the relationship between the Euler class group of R and the Euler class group of S.(ii) To develop a theory (namely, an extension of the theory of Euler class group to the Euler class group of R[T) relative to a projective R[T|-module L of rank 1) in order to detect the precise obstruction for a projective R[T]-module P …

Modular Classes Of Lie Groupoid Representations Up To Homotopy, Rajan Amit Mehta

Mathematics Sciences: Faculty Publications

We describe a construction of the modular class associated to a representation up to homotopy of a Lie groupoid. In the case of the adjoint representation up to homotopy, this class is the obstruction to the existence of a volume form, in the sense of Weinstein’s “The volume of a differentiable stack”.

Discrete Morse Functions, Vector Fields, And Homological Sequences On Trees, Ian B. Rand

Mathematics Summer Fellows

The goal of this project is to construct a discrete Morse function which induces both a unique gradient vector field and homological sequence on a given tree. After reviewing the basics of discrete Morse theory, we will show that the two standard notions of equivalence of discrete Morse functions, Forman and homological equivalence, are independent of one another. We then show through a constructive algorithm the existence of a discrete Morse function on a tree inducing a desired gradient vector field and homological sequence. After proving that our algorithm is correct, we give an example to illustrate its use.

How Does “Collaboration” Occur At All? Remarks On Epistemological Issues Related To Understanding / Working With ‘The Other’, Don Faust, Judith Puncochar

Conference Presentations

Collaboration, if to occur successfully at all, needs to be based on careful representation and communication of each stakeholder’s knowledge. In this paper, we investigate, from a foundational logical and epistemological point of view, how such representation and communication can be accomplished. What we tentatively conclude, based on a careful delineation of the logical technicalities necessarily involved in such representation and communication, is that a complete representation is not possible. This inference, if correct, is of course rather discouraging with regard to what we can hope to achieve in the knowledge representations that we bring to our collaborations. We suggest …

Rows Vs. Columns: Randomized Kaczmarz Or Gauss-Seidel For Ridge Regression, Ahmed Hefny, Deanna Needell, Aaditya Ramdas

CMC Faculty Publications and Research

The Kaczmarz and Gauss-Seidel methods aim to solve a linear m × n system Xβ = y by iteratively refining the solution estimate; the former uses random rows of X to update β given the corresponding equations and the latter uses random columns of X to update corresponding coordinates in β. Interest in these methods was recently revitalized by a proof of Strohmer and Vershynin showing linear convergence in expectation for a randomized Kaczmarz method variant (RK), and a similar result for the randomized Gauss-Seidel algorithm (RGS) was later proved by Lewis and Leventhal. Recent work unified the analysis of …

Modelling The Links Between Inflation, Output Growth, Inflation Uncertainty And Output Growth Uncertainty In The Frameworks Of Regime-Switching And Multiple Structural Breaks: Evidence From The G7 Countries., Kushal Banik Chowdhury Dr.

Doctoral Theses

One of the long-standing and most investigated issues in macroeconomics is the nature of the relationship between inflation and output growth. Given this relationship as a central point of intense interest, one strand of studies has focused on the levels of the two series, while, more recently, an overgrowing body of research has highlighted the importance of the effects which are due to both the levels and the uncertainties associated with these two variables. These studies raise a number of interesting issues regarding the relationship between inflation and output growth. First, is there any direct effect of inflation on output …

What You Gotta Know To Play Good In The Iterated Prisoner’S Dilemma, Ethan Akin

Mathematics and Statistics Faculty Research & Creative Works

For the iterated Prisoner's Dilemma there exist good strategies which solve the problem when we restrict attention to the long-term average payoff. When used by both players, these assure the cooperative payoff for each of them. Neither player can benefit by moving unilaterally to any other strategy, i.e., these provide Nash equilibria. In addition, if a player uses instead an alternative which decreases the opponent's payoff below the cooperative level, then his own payoff is decreased as well. Thus, if we limit attention to the long-term payoff, these strategies effectively stabilize cooperative behavior. The existence of such strategies follows from …

Prevalence And Prediction Of Obstructive Coronary Artery Disease In Patients Referred For Valvular Heart Surgery, Jason M. Lappe, Justin L. Grodin, Yuping Wu, Corinne Bott Silverman, Leslie Cho

Mathematics and Statistics Faculty Publications

Current guidelines recommend a coronary evaluation before valvular heart surgery (VHS). Diagnostic coronary angiography is recommended in patients with known coronary artery disease (CAD) and those with high pretest probability of CAD. In patients with low or intermediate pretest probability of CAD, the guidelines recommend coronary computed tomographic angiography. However, there are no tools available to objectively assess a patient’s risk for obstructive CAD before VHS. To address this deficit, 5,360 patients without histories of CAD who underwent diagnostic coronary angiography as part of preoperative evaluation for VHS were identified. Obstructive CAD was defined as ≥50% stenosis in ≥1 artery. …

Undiagnosed Diabetes And Pre-Diabetes In Health Disparities, Susan P. Fisher-Hoch, Kristina Vatcheva, Mohammad H. Rahbar, Joseph B. Mccormick

School of Mathematical & Statistical Sciences Faculty Publications

Globally half of all diabetes mellitus is undiagnosed. We sought to determine the extent and characteristics of undiagnosed type 2 diabetes mellitus and pre-diabetes in Mexican Americans residing in the United States. This disadvantaged population with 50% lifetime risk of diabetes is a microcosm of the current pandemic. We accessed baseline data between 2004 and 2014 from 2,838 adults recruited to our Cameron County Hispanic Cohort (CCHC); a two-stage randomly selected 'Framingham-like' cohort of Mexican Americans on the US Mexico border with severe health disparities. We examined prevalence, risk factors and metabolic health in diagnosed and undiagnosed diabetes and pre-diabetes. …

Characterizing The Properties Of Specific Binomial Coefficients In Congruence Relations, Tyler Robert Russ

Master's Theses and Doctoral Dissertations

The number theoretic conjecture we examine in this paper originates when trying to construct a characterizable generating set for the complex cobordism polynomial ring. To date there is no efficient, universal method for characterizing such a generating set. Wilfong conjectures that smooth projective toric varieties can act as these generators [7]. Toric varieties are related to polytopes by a bijective correspondence. Studying the combinatorial structure of these polytopes is much more manageable than studying properties of toric varieties directly. This gives rise to the number theoretic conjecture considered here. A proof of this number theoretic conjecture would in turn prove …

Review: Nevanlinna-Pick Spaces With Hyponormal Multiplication Operators, Stephan Ramon Garcia

Pomona Faculty Publications and Research

No abstract provided.

Mathematician's Apology, Tom Clark

Faculty Work Comprehensive List

"Better standards may help all math teachers to shape our classes to better reflect the creativity and play at the heart of mathematics."

Posting about ways to improve math's negative image­­­­­­­­ from In All Things - an online hub committed to the claim that the life, death, and resurrection of Jesus Christ has implications for the entire world.

http://inallthings.org/a-mathematicians-apology/

Tame Filling Functions And Closure Properties, Anisah Nu'man

Department of Mathematics: Dissertations, Theses, and Student Research

Let G be a group with a finite presentation P = such that A is inverse- closed. Let f : N[1/4] → N[1/4] be a nondecreasing function. Loosely, f is an intrinsic tame filling function for (G;P) if for every word w over A* that represents the identity element in G, there exists a van Kampen diagram Δ for w over P and a continuous choice of paths from the basepoint * of Δ to points on the boundary of Δ such that the paths are steadily moving outward as measured by f. The isodiametric function (or intrinsic diameter function) …