Mathematics Commons^™

Resonance Problems For Nonlinear Elliptic Equations With Nonlinear Boundary Conditions, Nsoki Mavinga, M. N. Nkashama

Mathematics & Statistics Faculty Works

We study the solvability of nonlinear second order elliptic partial differential equations with nonlinear boundary conditions where we impose asymptotic conditions on both nonlinearities in the differential equation and on the boundary in such a way that resonance occurs at a generalized eigenvalue; which is an eigenvalue of the linear problem in which the spectral parameter is both in the differential equation and on the boundary. The proofs are based on some variational techniques and topological degree arguments.

Prognostic Value Of Estimating Functional Capacity With The Use Of The Duke Activity Status Index In Stable Patients With Chronic Heart Failure, Justin L. Grodin, Muhammad Hammadah, Yiying Fan, Stanley L. Hazen, W.H. Wilson Tang

Mathematics and Statistics Faculty Publications

BACKGROUND: Over the years, several methods have been developed to reliably quantify functional capacity in patients with heart failure. Few studies have investigated the prognostic value of these assessment tools beyond cardiorenal prognostic biomarkers in stable patients with chronic heart failure. METHODS AND RESULTS: We administered the Duke Activity Status Index (DASI) questionnaire, a self-assessment tool comprising 12 questions for estimating functional capacity, to 1,700 stable nonacute coronary syndrome patients with history of heart failure who underwent elective diagnostic coronary angiography with 5-year follow-up of all-cause mortality. In a subset of patients (n = 800), B-type natriuretic peptide (BNP) was …

Rayleigh Approximation To Ground State Of The Bose And Coulomb Glasses, Shawn D. Ryan, V. Mityushev, V. M. Vinokur, L. Berlyand

Mathematics and Statistics Faculty Publications

Glasses are rigid systems in which competing interactions prevent simultaneous minimization of local energies. This leads to frustration and highly degenerate ground states the nature and properties of which are still far from being thoroughly understood. We report an analytical approach based on the method of functional equations that allows us to construct the Rayleigh approximation to the ground state of a two-dimensional (2D) random Coulomb system with logarithmic interactions. We realize a model for 2D Coulomb glass as a cylindrical type II superconductor containing randomly located columnar defects (CD) which trap superconducting vortices induced by applied magnetic field. Our …

Algebraic And Numerical Exploration Of Free Energies For Materials With Memory, John Murrough Golden, Giovambattista Amendola, Mauro Fabrizio

Articles

Abstract. We study the forms of a range of free energy functionals for materials with memory for two types of strain history, namely sinusoidal and ex- ponential behaviours. The work deals with discrete spectrum materials, which are those with relaxation functions given by sums of decaying exponentials.

On The Characterization Of Prime Sets Of Polynomials By Congruence Conditions, Arvind Suresh

CMC Senior Theses

This project is concerned with the set of primes modulo which some monic, irreducible polynomial over the integers has a root, called the Prime Set of the polynomial. We completely characterise these sets for degree 2 polynomials, and develop sufficient machinery from algebraic number theory to show that if the Galois group of a monic, irreducible polynomial over the integers is abelian, then its Prime Set can be written as the union of primes in some congruence classes modulo some integer.

Calculus For Everyone, Sandra Kingan, Brooklyn College Library And Academic It

Open Educational Resources

Professor Kingan’s motivation for writing her free Calculus I textbook was to help address the departments high failure rates in Calculus. Along with another CUNY initiative to offer Calculus workshops in advance of taking the course, Kingan’s concise textbook in Calculus I offers students inside and outside of CUNY an opportunity to prepare for Calculus I at their own pace. She also believes that by providing free access to this material she could help to overcome some of the inequity students experience when Calculus is not offered in their high school. The textbook was written specifically for this pilot project. …

The Wright Message, 2015-2016, University Of Northern Iowa. Department Of Mathematics.

The Wright Message

Inside this issue:

-- Dear Alumni and Friends
-- Dr. Edward Rathmell retires from UNI
-- 2015 Hari Shankar Lecture
-- Around Wright Hall
-- Congratulations to....
-- Faculty Highlights
-- Student News
-- 2015-2016 Tenure-Stream Faculty
-- Alumni Spotlight: Clayton Edwards & Mary Theilen
-- Department Interviews: Adrienne Stanley, Joel Haack, , Benjamin Castle & Suzanne Shontz
-- UNI Students Travel to Korea
-- Trijitzsky Scholarship Winner Emily Wardenburg
-- Student Spotlights: Amber Irlmeier, Britney Bockstahler, Derek Hofland & Julia Robinson
-- PAEMST Award Winner Allysen Lovstuen
-- Donor Spotlight: Alan and Barbara Hubbard
-- News fro KME
-- …

Chebyshev Polynomials And The Frohman-Gelca Formula, Heather M. Russell, Hoel Queffelec

Department of Math & Statistics Faculty Publications

Using Chebyshev polynomials, C. Frohman and R. Gelca introduced a basis of the Kauffman bracket skein module of the torus. This basis is especially useful because the Jones–Kauffman product can be described via a very simple Product-to-Sum formula. Presented in this work is a diagrammatic proof of this formula, which emphasizes and demystifies the role played by Chebyshev polynomials.

Mathematics In Contemporary Society Chapter 2, Patrick J. Wallach

Open Educational Resources

Mathematics in Contemporary Society is the textbook that corresponds to MA-321, the course of the same name. The course is designed to provide students with mathematical ideas and methods found in the social sciences, the arts, and in business. Topics will include fundamentals of statistics, scatterplots, graphics in the media, problem solving strategies, dimensional analysis, mathematics in music and art, and mathematical modeling. EXCEL is used to explore real world applications.

The textbook was posted in weekly installments:

• Chapter 1
• Chapter 2
• Chapter 3
• Chapter 4
• Chapter 5
• Chapter 6
• Chapter 7
• Chapter 8
• Chapter 9
• Chapter 10
• Chapter 11

Extensions Of Functors From Set To V-Cat, Adriana Balan, Alexander Kurz, Jirí Velebil

Engineering Faculty Articles and Research

We show that for a commutative quantale V every functor Set --> V-cat has an enriched left- Kan extension. As a consequence, coalgebras over Set are subsumed by coalgebras over V-cat. Moreover, one can build functors on V-cat by equipping Set-functors with a metric.

Coalgebraic Semantics Of Reflexive Economics (Dagstuhl Seminar 15042), Samson Abramsky, Alexander Kurz, Pierre Lescanne, Viktor Winschel

Engineering Faculty Articles and Research

This report documents the program and the outcomes of Dagstuhl Seminar 15042 “Coalgebraic Semantics of Reflexive Economics”.

Self-Mappings Of The Quaternionic Unit Ball: Multiplier Properties, Schwarz-Pick Inequality, And Nevanlinna-Pick Interpolation Problem, Daniel Alpay, Vladimir Bolotnikov, Fabrizio Colombo, Irene Sabadini, Fabrizio Colombo

Mathematics, Physics, and Computer Science Faculty Articles and Research

We study several aspects concerning slice regular functions mapping the quaternionic open unit ball B into itself. We characterize these functions in terms of their Taylor coefficients at the origin and identify them as contractive multipliers of the Hardy space H2(B). In addition, we formulate and solve the Nevanlinna-Pick interpolation problem in the class of such functions presenting necessary and sufficient conditions for the existence and for the uniqueness of a solution. Finally, we describe all solutions to the problem in the indeterminate case.

Quaternionic Hardy Spaces In The Open Unit Ball And Half Space And Blaschke Products, Daniel Alpay, Fabrizio Colombo, Irene Sabadini

Mathematics, Physics, and Computer Science Faculty Articles and Research

The Hardy spaces H2(B) and H2(H+), where B and H+ denote, respectively, the open unit ball of the quaternions and the half space of quaternions with positive real part, as well as Blaschke products, have been intensively studied in a series of papers where they are used as a tool to prove other results in Schur analysis. This paper gives an overview on the topic, collecting the various results available.

Tropical Linear Algebra: Notions Of Rank Over The Tropical Semiring, William D. Wise

Honors Papers

Three formulations of the rank of a matrix that are equivalent in classical linear algebra give rise to distinct notions of rank over the tropical semiring. This paper explores these three concepts of tropical rank and their relationships with one another, working up to a proof of the inequality that relates the three.

Unavoidable Minors Of Large 4-Connected Bicircular Matroids, Deborah Chun, Tyler Moss, Dan Slilaty, Xiangqian Zhou

Mathematics and Statistics Faculty Publications

It is known that any 3-connected matroid that is large enough is certain to contain a minor of a given size belonging to one of a few special classes of matroids. This paper proves a similar unavoidable minor result for large 4-connected bicircular matroids. The main result follows from establishing the list of unavoidable minors of large 4-biconnected graphs, which are the graphs representing the 4-connected bicircular matroids. This paper also gives similar results for internally 4-connected and vertically 4-connected bicircular matroids.

Price, Perceived Value And Customer Satisfaction: A Text-Based Econometric Analysis Of Yelp! Reviews, Eleanor A. Dwyer

Scripps Senior Theses

We examine the antecedents of customer satisfaction in the restaurant sector, paying particular attention to perceived value and price level. Using Latent Dirichlet Allocation, we extract latent topics from the text of Yelp! reviews, then analyze the relationship between these topics and satisfaction, measured as the difference between review rating and user average review rating.

Mathematics In Contemporary Society Chapter 5, Patrick J. Wallach

Open Educational Resources

Mathematics in Contemporary Society is the textbook that corresponds to MA-321, the course of the same name. The course is designed to provide students with mathematical ideas and methods found in the social sciences, the arts, and in business. Topics will include fundamentals of statistics, scatterplots, graphics in the media, problem solving strategies, dimensional analysis, mathematics in music and art, and mathematical modeling. EXCEL is used to explore real world applications.

The textbook was posted in weekly installments:

• Chapter 1
• Chapter 2
• Chapter 3
• Chapter 4
• Chapter 5
• Chapter 6
• Chapter 7
• Chapter 8
• Chapter 9
• Chapter 10
• Chapter 11

Mathematics In Contemporary Society Chapter 3, Patrick J. Wallach

Open Educational Resources

Mathematics in Contemporary Society is the textbook that corresponds to MA-321, the course of the same name. The course is designed to provide students with mathematical ideas and methods found in the social sciences, the arts, and in business. Topics will include fundamentals of statistics, scatterplots, graphics in the media, problem solving strategies, dimensional analysis, mathematics in music and art, and mathematical modeling. EXCEL is used to explore real world applications.

The textbook was posted in weekly installments:

• Chapter 1
• Chapter 2
• Chapter 3
• Chapter 4
• Chapter 5
• Chapter 6
• Chapter 7
• Chapter 8
• Chapter 9
• Chapter 10
• Chapter 11

Partial Orders On Partial Isometries, William T. Ross, Stephan Ramon Garcia, Robert T. W. Martin

Department of Math & Statistics Faculty Publications

This paper studies three natural pre-orders of increasing generality on the set of all completely non-unitary partial isometries with equal defect indices. We show that the problem of determining when one partial isometry is less than another with respect to these pre-orders is equivalent to the existence of a bounded (or isometric) multiplier between two natural reproducing kernel Hilbert spaces of analytic functions. For large classes of partial isometries these spaces can be realized as the well-known model subspaces and deBranges-Rovnyak spaces. This characterization is applied to investigate properties of these pre-orders and the equivalence classes they generate.

Mat 95: Problem Solving Process And Strategies, Salvatore Sommella

Open Educational Resources

Covers fundamentals and application of four steps of Problem Solving. Includes a problem solving strategy with a hands-on problems.

Characterizations Of Gamma Distribution Via Sub-Independent Random Variables, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

The concept of sub-independence is based on the convolution of the distributions of the random variables. It is much weaker than that of independence, but is shown to be sufficient to yield the conclusions of important theorems and results in probability and statistics. It also provides a measure of dissociation between two random variables which is much stronger than uncorrelatedness. Inspired by the excellent work of Jin and Lee (2014), we present certain characterizations of gamma distribution based on the concept of sub-independence.

Kumaraswamy-Half-Cauchy Distribution: Characterizations And Related Results, Gholamhossein Hamedani, I. Ghosh

Mathematics, Statistics and Computer Science Faculty Research and Publications

We present various characterizations of a recently introduced distribution (Ghosh 2014), called Kumaraswamy- Half- Cauchy distribution based on: (i) a simple relation between two truncated moments; (ii) truncated moment of certain function of the 1^st order statistic; (iii) truncated moment of certain function of the random variable; (iv) hazard function; (v) distribution of the 1^st order statistic; (vi) via record values. We also provide some remarks on bivariate Gumbel copula distribution whose marginal distributions are Kumaraswamy- Half-Cauchy distributions.

The Schwartz Space: Tools For Quantum Mechanics And Infinite Dimensional Analysis, Jeremy Becnel, Ambar Sengupta

Faculty Publications

An account of the Schwartz space of rapidly decreasing functions as a topological vector space with additional special structures is presented in a manner that provides all the essential background ideas for some areas of quantum mechanics along with infinite-dimensional distribution theory.

Math In The Modern World, Steven Cosares

Open Educational Resources

Students are asked to gather nutrition data regarding their favorite snacks and assess how well they contribute to their maintenance of a “healthy” diet, as defined through, articles, websites, and guidelines established by the US Department of Agriculture.

Elementary Algebra, Mangala Kothari

Open Educational Resources

Students use world population data to find the observed trend, the rate of population growth, build a model (linear equation) using the data, and predict the future world’s population size based on the model that they develop.

Nearest Neighbor Foreign Exchange Rate Forecasting With Mahalanobis Distance, Vindya Kumari Pathirana

USF Tampa Graduate Theses and Dissertations

Foreign exchange (FX) rate forecasting has been a challenging area of study in the past. Various linear and nonlinear methods have been used to forecast FX rates. As the currency data are nonlinear and highly correlated, forecasting through nonlinear dynamical systems is becoming more relevant. The nearest neighbor (NN) algorithm is one of the most commonly used nonlinear pattern recognition and forecasting methods that outperforms the available linear forecasting methods for the high frequency foreign exchange data. The basic idea behind the NN is to capture the local behavior of the data by selecting the instances having similar dynamic behavior. …

Statistical Learning With Artificial Neural Network Applied To Health And Environmental Data, Taysseer Sharaf

USF Tampa Graduate Theses and Dissertations

The current study illustrates the utilization of artificial neural network in statistical methodology. More specifically in survival analysis and time series analysis, where both holds an important and wide use in many applications in our real life. We start our discussion by utilizing artificial neural network in survival analysis. In literature there exist two important methodology of utilizing artificial neural network in survival analysis based on discrete survival time method. We illustrate the idea of discrete survival time method and show how one can estimate the discrete model using artificial neural network. We present a comparison between the two methodology …

Robust Fast Direct Integral Equation Solver For Quasi-Periodic Scattering Problems With A Large Number Of Layers, Min Hyung Cho, Alex H. Barnett

Dartmouth Scholarship

We present a new boundary integral formulation for time-harmonic wave diffraction from two-dimensional structures with many layers of arbitrary periodic shape, such as multilayer dielectric gratings in TM polarization. Our scheme is robust at all scattering parameters, unlike the conventional quasi-periodic Green’s function method which fails whenever any of the layers approaches a Wood anomaly. We achieve this by a decomposition into near- and far-field contributions. The former uses the free-space Green’s function in a second-kind integral equation on one period of the material interfaces and their immediate left and right neighbors; the latter uses proxy point sources and small …

Robust And Efficient Solution Of The Drum Problem Via Nyström Approximation Of The Fredholm Determinant, Lin Zhao, Alex Barnett

Dartmouth Scholarship

The “drum problem''---finding the eigenvalues and eigenfunctions of the Laplacian with Dirichlet boundary condition---has many applications, yet remains challenging for general domains when high accuracy or high frequency is needed. Boundary integral equations are appealing for large-scale problems, yet certain difficulties have limited their use. We introduce the following two ideas to remedy this: (1) We solve the resulting nonlinear eigenvalue problem using Boyd's method for analytic root-finding applied to the Fredholm determinant, and we show that this is many times faster than the usual iterative minimization of a singular value. (2) We fix the problem of spurious exterior resonances …

Professional Formation Of Engineers: Enhancing The First Year Student Experience, Eileen Goold

Conference Papers

This paper reports on a study investigating engineering students’ perceptions of engineering practice and whether engineering students’ cognitive engagement benefits from bridging the gap between the technical issues in their education and the practical realities of modern engineering practice.