Locally Convex Words And Permutations,
2016
Dartmouth College
Locally Convex Words And Permutations, Christopher Coscia, Jonathan Dewitt
Dartmouth Scholarship
We introduce some new classes of words and permutations characterized by the second difference condition pi(i - 1) + pi(i + 1) - 2 pi(i)
Rigidity Of The Frobenius, Matlis Reflexivity, And Minimal Flat Resolutions,
2016
University of Nebraska-Lincoln
Rigidity Of The Frobenius, Matlis Reflexivity, And Minimal Flat Resolutions, Douglas J. Dailey
Department of Mathematics: Dissertations, Theses, and Student Research
Let R be a commutative, Noetherian ring of characteristic p >0. Denote by f the Frobenius endomorphism, and let R^(e) denote the ring R viewed as an R-module via f^e. Following on classical results of Peskine, Szpiro, and Herzog, Marley and Webb use flat, cotorsion module theory to show that if R has finite Krull dimension, then an R-module M has finite flat dimension if and only if Tor_i^R(R^(e),M) = 0 for all i >0 and infinitely many e >0. Using methods involving the derived category, we show that one only needs vanishing for dim R +1 consecutive values of …
Harmonic Maps Surfaces And Relativistic Strings,
2016
The University of Texas Rio Grande Valley
Harmonic Maps Surfaces And Relativistic Strings, Paul Bracken
School of Mathematical & Statistical Sciences Faculty Publications
The harmonic map is introduced and several physical applications are presented. The classical nonlinear σ model can be looked at as the embedding of a two-dimensional surface in a threedimensional sphere, which is itself embedded in a four-dimensional space. A system of nonlinear evolution equations are obtained by working out the zero curvature condition for the Gauss equations relevant to this geometric formulation.
Geometric Flows,
2016
University of Miami
Geometric Flows, Ming-Liang Cai
Mathematics Colloquium Series
A geometric flow is a process which is defined by a differential equation and is used to evolve a geometric object from a general shape to a one with more symmetries. For example, the curve-shortening flow deforms a simple closed curve to a round one ; the Ricci flow deforms a simply connected surface (say, a football shaped one) to a round sphere. In this talk, we will give an overview of some of these geometric flows, in particular, some discussions on singularities that these flows often run into.
Solving The Ko Labyrinth,
2016
Loyola Marymount University
The Role Of Mathematical Modeling In Designing And Evaluating Antimicrobial Stewardship Programs,
2016
University of Richmond
The Role Of Mathematical Modeling In Designing And Evaluating Antimicrobial Stewardship Programs, Lester Caudill, Joanna R. Wares
Department of Math & Statistics Faculty Publications
Antimicrobial agent effectiveness continues to be threatened by the rise and spread of pathogen strains that exhibit drug resistance. This challenge is most acute in healthcare facilities where the well-established connection between resistance and suboptimal antimicrobial use has prompted the creation of antimicrobial stewardship programs (ASPs). Mathematical models offer tremendous potential for serving as an alternative to controlled human experimentation for assessing the effectiveness of ASPs. Models can simulate controlled randomized experiments between groups of virtual patients, some treated with the ASP measure under investigation, and some without. By removing the limitations inherent in human experimentation, including health risks, study …
Aspects Of Non-Commutative Function Theory,
2016
Washington University in St Louis
Aspects Of Non-Commutative Function Theory, Jim Agler, John E. Mccarthy
Mathematics Faculty Research
We discuss non commutative functions, which naturally arise when dealing with functions of more than one matrix variable.
A High-Order Radial Basis Function (Rbf) Leray Projection Method For The Solution Of The Incompressible Unsteady Stokes Equations,
2016
High Point University
A High-Order Radial Basis Function (Rbf) Leray Projection Method For The Solution Of The Incompressible Unsteady Stokes Equations, Edward J. Fuselier, Varun Shankar, Grady B. Wright
Mathematics Faculty Publications and Presentations
A new projection method based on radial basis functions (RBFs) is presented for discretizing the incompressible unsteady Stokes equations in irregular geometries. The novelty of the method comes from the application of a new technique for computing the Leray-Helmholtz projection of a vector field using generalized interpolation with divergence-free and curl-free RBFs. Unlike traditional projection methods, this new method enables matching both tangential and normal components of divergence-free vector fields on the domain boundary. This allows incompressibility of the velocity field to be enforced without any time-splitting or pressure boundary conditions. Spatial derivatives are approximated using collocation with global RBFs …
Combating Human Trafficking Using Mathematics,
2016
Duquesne University
Combating Human Trafficking Using Mathematics, Alfred (Aj) Vogt
Undergraduate Research and Scholarship Symposium
Human trafficking is the modern-day form of slavery. Human trafficking occurs on a daily basis throughout the United States with the majority of victims being women and children. Existing programs to reduce human trafficking are primarily focused on either the prevention of first-time victims or the aid of previously victimized individuals. In this study, we propose a mathematical model describing human trafficking of underage females and the use of prevention and short and long-term aid programs to reduce victimization. The model is a system of differential equations describing the movement of underage females between susceptible, victimized, and aided classes within …
Yeast For Mathematicians - A Ferment Of Discovery,
2016
Utah State University
Yeast For Mathematicians - A Ferment Of Discovery, Matthew Lewis, James A. Powell
Mathematics and Statistics Faculty Publications
In addition to the memorization, algorithmic skills and vocabulary which are the default focus in many mathematics classrooms, professional mathematicians are expected to creatively apply known techniques, construct new mathematical approaches and communicate with and about mathematics. We propose that students can learn these professional, higher-level skills through Laboratory Experiences in Mathematical Biology which put students in the role of mathematics researcher creating mathematics to describe and understand biological data. Here we introduce a laboratory experience centered on yeast (Saccharomyces cerevisiae) growing in a small capped flask with a jar to collect carbon dioxide created during yeast growth …
A Statistical Analysis Of Hurricanes In The Atlantic Basin And Sinkholes In Florida,
2016
University of South Florida
A Statistical Analysis Of Hurricanes In The Atlantic Basin And Sinkholes In Florida, Joy Marie D'Andrea
USF Tampa Graduate Theses and Dissertations
Beaches can provide a natural barrier between the ocean and inland communities, ecosystems, and resources. These environments can move and change in response to winds, waves, and currents. When a hurricane occurs, these changes can be rather large and possibly catastrophic. The high waves and storm surge act together to erode beaches and inundate low-lying lands, putting inland communities at risk. There are thousands of buoys in the Atlantic Basin that record and update data to help predict climate conditions in the state of Florida. The data that was compiled and used into a larger data set came from two …
The Cantor Set Before Cantor,
2016
Ursinus College
The Cantor Set Before Cantor, Nicholas A. Scoville
Topology
A special construction used in both analysis and topology today is known as the Cantor set. Cantor used this set in a paper in the 1880s. Yet it appeared as early as 1875 in a paper by the Irish mathematician Henry John Stephen Smith (1826 - 1883). Smith, who is best known for the Smith normal form of a matrix, was a professor at Oxford who made great contributions in matrix theory and number theory. In this project, we will explore parts of a paper he wrote titled On the Integration of Discontinuous Functions.
Topology From Analysis,
2016
Ursinus College
Topology From Analysis, Nicholas A. Scoville
Topology
Topology is often described as having no notion of distance, but a notion of nearness. How can such a thing be possible? Isn't this just a distinction without a difference? In this project, we will discover the notion of nearness without distance by studying the work of Georg Cantor and a problem he was investigating involving Fourier series. We will see that it is the relationship of points to each other, and not their distances per se, that is a proper view. We will see the roots of topology organically springing from analysis.
Variance Of Clusterings On Graphs,
2016
Rose-Hulman Institute of Technology
Variance Of Clusterings On Graphs, Thomas Vlado Mulc
Mathematical Sciences Technical Reports (MSTR)
Graphs that represent data often have structures or characteristics that can represent some relationships in the data. One of these structures is clusters or community structures. Most clustering algorithms for graphs are deterministic, which means they will output the same clustering each time. We investigated a few stochastic algorithms, and look into the consistency of their clusterings.
The Effect Of Tommy John (Ucl) Reconstructive Surgery On A Pitcher’S Arm And Career Progression,
2016
Bryant University
The Effect Of Tommy John (Ucl) Reconstructive Surgery On A Pitcher’S Arm And Career Progression, Jack Grant
Honors Projects in Mathematics
Injuries have plagued professional athletes since their sports have been in existence. The examination of how teams can diminish the side effects of the injuries en route to a speedy recovery remains an evolving process and a topic of concern for all. Injury preventative tactics have been implemented by coaching staffs and various training personnel. Major League Baseball (MLB) pitchers are noticing an increase in the number of surgeries performed each year. The tearing of the ulnar collateral ligament (UCL) in the elbow has become a predominant injury among pitchers in the MLB. Reconstructive surgery, also known as Tommy John …
Predictions Of Success In The Actuarial Major,
2016
Bryant University
Predictions Of Success In The Actuarial Major, Jessica Soojian
Honors Projects in Mathematics
This study finds predictive factors that have a significant effect on the ending Mathematics/Actuarial GPA of Actuarial majors at Bryant University. This was done to add clarity to incoming students for what it takes to do well in the actuarial major. There were 266 subjects consisting of Bryant students that graduated between the years 2009 and 2015. The data was received in the form of final transcripts upon graduation for these students. Through manipulation of these transcripts, GPAs were calculated for Mathematics/Actuarial, English/Literary Cultural Studies, History/Politics, Economics, Science, Social Sciences, Computer Information Systems, Finance, Accounting, Management, and Marketing. These GPAs …
How To Predict Nesting Sites And How To Measure Shoreline Erosion: Fuzzy And Probabilistic Techniques For Environment-Related Spatial Data Processing,
2016
The University of Texas at El Paso
How To Predict Nesting Sites And How To Measure Shoreline Erosion: Fuzzy And Probabilistic Techniques For Environment-Related Spatial Data Processing, Stephen Escarzaga, Craig Tweedie, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In this paper, we show how fuzzy and probabilistic techniques can be used in environment-related data processing. Specifically, we will show that these methods help in solving two environment-related problems: how to predict the birds' nesting sites and how to measure shoreline erosion.
Polyhedral Painting With Group Averaging,
2016
Santa Clara University
Polyhedral Painting With Group Averaging, Frank A. Farris, Ryan Tsao
Mathematics and Computer Science
The technique of group-averaging produces colorings of a sphere that have the symmetries of various polyhedra. The concepts are accessible at the undergraduate level, without being well-known in typical courses on algebra or geometry. The material makes an excellent discovery project, especially for students with some background in computer science; indeed, this is where the authors first worked through the material, as teacher and student, producing a previously unseen type of artistic image. The process uses a photograph as a palette, whose colors and textures appear in kaleidoscopic form on the surface of a sphere. We depict tetrahedral, octahedral, and …
Bytes Of Π, Spring 2016,
2016
Bridgewater State University
Bytes Of Π, Spring 2016, Department Of Mathematics, Bridgewater State University
Department of Mathematics Newsletter
No abstract provided.
Connecting Connectedness,
2016
Ursinus College
