Applied Mathematics Commons^™

A Heterogeneous Multiscale Method For Poroelasticity, Paul M. Delgado

Open Access Theses & Dissertations

In this Thesis, we develop and analyze a heterogeneous multiscale model for coupled fluid flow and solid deformation in porous media based on operator splitting and finite volume method. The splitting method results in two elliptic multiscale PDE's in the form of a reaction diffusion equation and a linear elasticity equation. We extend our previous multiscale method from 1D to higher dimensions and develop new approaches for the inclusion of mixed boundary conditions and source terms. We derive an error estimate for our multiscale method and analyze the stability of our splitting method. We also test the effectiveness of our …

Some Combinatorial Applications Of Sage, An Open Source Program, Jessica Ruth Chowning

Masters Theses

"In this thesis, we consider the usefulness of Sage, an online and open-source program, in analyzing permutation puzzles such as the Rubik's cube and a specific combinatorial structure called the projective plane. Many programs exist to expedite calculations in research and provide previously-unavailable solutions; some require purchase, while others, such as Sage, are available for free online. Sage is asked to handle a small permutation puzzle called Swap, and then we explore how it calculates solutions for a Rubik's cube. We then discuss projective planes, Sage's library of functions for dealing with projective planes, and how they relate to the …

Periodic State Revivals In Commensurate Waveguide Arrays, Jovan Petrovic, J. J. P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

Emerging optical and quantum computers require hardware capable of coherent transport of and operations on quantum states. Here, we investigate finite optical waveguide arrays with linear coupling as means of efficient and compact coherent state transfer. Coherent transfer with periodic state revivals is enabled by engineering coupling coefficients between neighbouring waveguides to yield commensurate eigenvalue spectrum. Particular cases of finite arrays have been actively studied to achieve the perfect state transfer by mirroring the input into the output state.

We explore a much wider scope of coherent propagation and revivals of both the state amplitude and phase. We analytically solve …

Singular Value Computation And Subspace Clustering, Qiao Liang

Theses and Dissertations--Mathematics

In this dissertation we discuss two problems. In the first part, we consider the problem of computing a few extreme eigenvalues of a symmetric definite generalized eigenvalue problem or a few extreme singular values of a large and sparse matrix. The standard method of choice of computing a few extreme eigenvalues of a large symmetric matrix is the Lanczos or the implicitly restarted Lanczos method. These methods usually employ a shift-and-invert transformation to accelerate the speed of convergence, which is not practical for truly large problems. With this in mind, Golub and Ye proposes an inverse-free preconditioned Krylov subspace method, …

To Play Or Not To Play? That’S A Resource Abundance Question, Jeremy David Auerbach, Andrew R. Kanarek, Gordon M. Burghardt

Faculty Publications and Other Works -- Ecology and Evolutionary Biology

Although play occurs in a wide variety of animals, models of the origins of play behavior are lacking. We propose a novel computational model exploring the evolution of non-social frivolous play. Asexually reproducing semelparous animals can either rest or forage. Foraging occurs when an organism is below an energy threshold. Success is determined by the combination of skill and availability of resources, which declines over time but replenishes for each generation. Play was introduced as a mutant strategy: a frivolous activity that uses energy and increases the probability of dying over resting with no direct fitness benefit. Simulations show that …

Lexical Mechanics: Partitions, Mixtures, And Context, Jake Ryland Williams

Graduate College Dissertations and Theses

Highly structured for efficient communication, natural languages are complex systems. Unlike in their computational cousins, functions and meanings in natural languages are relative, frequently prescribed to symbols through unexpected social processes. Despite grammar and definition, the presence of metaphor can leave unwitting language users "in the dark," so to speak. This is not problematic, but rather an important operational feature of languages, since the lifting of meaning onto higher-order structures allows individuals to compress descriptions of regularly-conveyed information. This compressed terminology, often only appropriate when taken locally (in context), is beneficial in an enormous world of novel experience. However, what …

Using Empirical Mode Decomposition To Study Periodicity And Trends In Extreme Precipitation, Noah Pfister

Graduate College Dissertations and Theses

Classically, we look at annual maximum precipitation series from the perspective of extreme value statistics, which provides a useful statistical distribution, but does not allow much flexibility in the context of climate change. Such distributions are usually assumed to be static, or else require some assumed information about possible trends within the data. For this study, we treat the maximum rainfall series as sums of underlying signals, upon which we perform a decomposition technique, Empirical Mode Decomposition. This not only allows the study of non-linear trends in the data, but could give us some idea of the periodic forces that …

Exploring The Google Books Corpus: An Information-Theoretic Approach To Linguistic Evolution, Eitan Pechenick

Graduate College Dissertations and Theses

The Google Books corpus contains millions of books in a variety of languages. Due to this incredible volume and its free availability, it is a treasure trove that has inspired a plethora of linguistic research.

It is tempting to treat frequency trends from Google Books data sets as indicators for the true popularity of various words and phrases. Doing so allows us to draw novel conclusions about the evolution of public perception of a given topic. However, sampling published works by availability and ease of digitization leads to several important effects, which have typically been overlooked in previous studies. One …

The Pascal Matrix Function And Its Applications To Bernoulli Numbers And Bernoulli Polynomials And Euler Numbers And Euler Polynomials, Tian-Xiao He, Jeff Liao, Peter Shiue

Tian-Xiao He

Wavelet Analysis And Applications In Economics And Finance, Tian-Xiao He, Tung Nguyen, '15

Tian-Xiao He

Multistrain Infections In Metapopulations, Sydney Garmer, Rachel Lynn, Dan Rossi, Alex Capaldi

Alex Capaldi

Investigating Anthropogenic Mammoth Extinction With Mathematical Models, Michael Frank, Anneliese Slaton, Teresa Tinta, Alex Capaldi

Alex Capaldi

Convexity Of Spherical Bernstein-B´Ezier Patches And Circular Bernstein-B´Ezier Curves, Tian-Xiao He, Ram Mohapatray

Tian-Xiao He

Studying The Effects Of Non Oil Exports On Targeted Economic Growth In Iranian 5th Development Plan: A Computable General Equilibrium Approach, Rasoul Bakhsi Dastjerdi Dr., Reza Moosavi Mohseni Dr., Somayye Jafari

Reza Moosavi Mohseni

we investigate the effects of non oil export on Iran’s economic growth using a computable general equilibrium (CGE) and study which tradable sectors has a larger share in reaching to targeted growth rate 8% in 5th socio economic development plan. We calibrate the model by GAMS (with emphasis on foreign trade sector). Numerical solution to the model is based on Iran’s social accounting matrix (SAM). Results show that 2.03% of targeted economic growth rate is achieved by encouraging a 6% growth in export. It also be mentioned that industry and mine sector in Iran, has more influence on growth than …

Riemann Hypothesis Disproved Using Infinity, Elements, Solution Operator Defined To Solve Riemann But Not Have Solutions 1/2 And Other Solutions With Real Solutions Not 1/2, James T. Struck

James T Struck

Riemann Hypothesis Disproved Using Infinity, Elements, solution operator defined to solve Riemann but not have solutions 1/2 and other Solutions with Real Solutions Not 1/2 The Riemann hypothesis is that all [[Triviality (mathematics)|nontrivial]] zeros of the analytical continuation of the [[Riemann zeta function]] have a real part of 1/2. A proof or disproof of this would have far-reaching implications in [[number theory]], especially for the distribution of [[prime number]]s. This was [[Hilbert's problems|Hilbert's eighth problem]], and is still considered an important open problem a century later. One of James T. Struck's Disproofs of the Riemann Hypothesis is that zeros can …

Zespół Energii Odnawialnej I Zrównoważonego Rozwoju (Eozr), Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.

Elementary Differential Equations With Boundary Value Problems, William F. Trench

William F. Trench

Elementary Differential Equations with Boundary Value Problems is written for students in science, engineering, and mathematics who have completed calculus through partial differentiation. If your syllabus includes Chapter 10 (Linear Systems of Differential Equations), your students should have some prepa- ration in linear algebra. In writing this book I have been guided by the these principles: An elementary text should be written so the student can read it with comprehension without too much pain. I have tried to put myself in the student’s place, and have chosen to err on the side of too much detail rather than not enough. …

Elementary Differential Equations, William F. Trench

William F. Trench

Elementary Differential Equations with Boundary Value Problems is written for students in science, engineering, and mathematics who have completed calculus through partial differentiation. If your syllabus includes Chapter 10 (Linear Systems of Differential Equations), your students should have some preparation in linear algebra. In writing this book I have been guided by the these principles: An elementary text should be written so the student can read it with comprehension without too much pain. I have tried to put myself in the student’s place, and have chosen to err on the side of too much detail rather than not enough. An …

Student Solutions Manual For Elementary Differential Equations And Elementary Differential Equations With Boundary Value Problems, William F. Trench

William F. Trench

No abstract provided.

Introduction To Real Analysis, William F. Trench

William F. Trench

This is a text for a two-term course in introductory real analysis for junior or senior math- ematics majors and science students with a serious interest in mathematics. Prospective educators or mathematically gifted high school students can also benefit from the mathe- matical maturity that can be gained from an introductory real analysis course. The book is designed to fill the gaps left in the development of calculus as it is usually presented in an elementary course, and to provide the background required for insight into more advanced courses in pure and applied mathematics. The standard elementary calcu- lus sequence …