Mathematics Commons^™

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, 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, 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, Alissa S. Crans

Faculty Pub Night

No abstract provided.

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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, Department Of Mathematics, Bridgewater State University

Department of Mathematics Newsletter

No abstract provided.

Connecting Connectedness, Nicholas A. Scoville

Topology

No abstract provided.

The Exigency Of The Euclidean Parallel Postulate And The Pythagorean Theorem, Jerry Lodder

Geometry

No abstract provided.

How To Estimate Resilient Modulus For Unbound Aggregate Materials: A Theoretical Explanation Of An Empirical Formula, Pedro Barragan Olague, Soheil Nazarian, Vladik Kreinovich, Afshin Gholamy

Departmental Technical Reports (CS)

To ensure the quality of pavement, it is important to make sure that the resilient moduli -- that describe the stiffness of all the pavement layers -- exceed a certain threshold. From the mechanical viewpoint, pavement is a non-linear medium. Several empirical formulas have been proposed to describe this non-linearity. In this paper, we describe a theoretical explanation for the most accurate of these empirical formulas.

How To Make A Solution To A Territorial Dispute More Realistic: Taking Into Account Uncertainty, Emotions, And Step-By-Step Approach, Mahdokhat Afravi, Vladik Kreinovich

Departmental Technical Reports (CS)

In many real-life situations, it is necessary to divide a disputed territory between several interested parties. The usual way to perform this division is by using Nash's bargaining solution, i.e., by finding a partition that maximizes the product of the participants' utilities. However, this solution is based on several idealized assumptions: that we know the exact values of all the utilities, that division is performed on a purely rational basis, with no emotions involved, and that the entire decision is made once. In practice, we only know the utilities with some uncertainty, emotions are often involved, and the solution is …

On Phase Ii Monitoring Of The Probability Distributions Of Univariate Continuous Processes, Partha Sarathi Mukherjee

Mathematics Faculty Publications and Presentations

Statistical process control (SPC) charts are widely used in industry for monitoring the stability of certain sequential processes like manufacturing, health care systems etc. Most SPC charts assume that the parametric form of the “in-control” process distribution F₁ is available. However, it has been demonstrated in the literature that their performances are unreliable when the pre-specified process distribution is incorrect. Moreover, most SPC charts are designed to detect any shift in mean and/or variance. In real world problems, shifts in higher moments can happen without much change in mean or variance. If we fail to detect those and let …

Prefrontal White Matter Pathology In Air Pollution Exposed Mexico City Young Urbanites And Their Potential Impact On Neurovascular Unit Dysfunction And The Development Of Alzheimer’S Disease, Partha S. Mukherjee

Mathematics Faculty Publications and Presentations

Millions of urban children are chronically exposed to high concentrations of air pollutants, i.e., fine particulate matter (PM_2.5) and ozone, associated with increased risk for Alzheimer’s disease. Compared with children living with clear air those in Mexico City (MC) exhibit systemic, brain and intrathecal inflammation, low CSF Aβ ₄₂, breakdown of the BBB, attention and short-term memory deficits, prefrontal white matter hyperintensities, damage to epithelial and endothelial barriers, tight junction and neural autoantibodies, and Alzheimer and Parkinson's hallmarks. The prefrontal white matter is a target of air pollution. We examined by light and electron microscopy the prefrontal …

What Is The True Cost To Stay In The Hospital?, Samantha Alicandro

Honors Projects in Mathematics

Currently, the unfortunate reality that receiving diverse health procedures can be extremely expensive is widely acknowledged and woefully accepted. However, have you inquired or been curious about the specific factors that influence the cost per day expensed by a hospital? Through examination, investigation, and evaluation operating SAS Enterprise Guide, SAS Enterprise Miner and Tableau I have attempted to arrive at a conclusion for this very question. Utilizing a 1.5 million row data set provided by Rhode Island, for the years 2003-2013, I analyzed the assorted elements conceivably bearing impact on the cost per day at a hospital. Regressions, decision trees, …

Collaboration And Creativity In Southern Califonia: An Offering, Gizem Karaali, Ami Radunskaya

Pomona Faculty Publications and Research

WiMSoCal (Women in Math in Southern California) is a regional conference in its ninth incarnation. The conference is the result of the efforts of Professor Cymra Haskell (USC) to create a supportive local community for women mathematicians. At our first meeting in 2007, a confluence of Ami’s EDGE regional cluster and Cymra’s WISE group at USC, we socialized, got to know each other and brainstormed about what we, as a group, would like to see happen. It was clear that our younger colleagues wanted to meet as mathematicians, sharing intellectual ideas as well as anecdotes from the trenches.

Does Academic Performance Predict Workplace Productivity?, Jodie-Gaye Hunter

Honors Projects in Economics

This research examines if college GPA affects productivity and compensation in the workplace. It uses data collected from a survey of approximately 23,000 Bryant University graduates in different stages of their career. About 10 percent of the alumni surveyed completed the survey. The econometric model used in this study allows estimating the effect of GPA on income after controlling for various demographic and socioeconomic variables, including education, major, occupation, gender, among others. The empirical work provides evidence that GPA has a positive and statistically significant impact on workplace productivity for females, but GPA seems to be a weaker predictor of …

Two Generalizations Of The Filippov Operation, Menevse Eryuzlu

Masters Theses & Specialist Projects

The purpose of this thesis is to generalize Filippov's operation, and to get more useful results. It includes two main parts: The C-Filippov operation for the finite and countable cases and the Filippov operation with different measures. In the first chapter, we give brief information about the importance of Filippov's operation, our goal and the ideas behind our generalizations. In the second chapter, we give some sufficient background notes. In the third chapter, we introduce the Filippov operation, explain how to calculate the Filippov of a function and give some sufficient properties of it. In the fourth chapter, we introduce …

Fuzzy Techniques Provide A Theoretical Explanation For The Heuristic L^P-Regularization Of Signals And Images, Fernando Cervantes, Bryan E. Usevitch, Leobardo Valera, Vladik Kreinovich, Olga Kosheleva

Departmental Technical Reports (CS)

One of the main techniques used to de-noise and de-blur signals and images is regularization, which is based on the fact that signals and images are usually smoother than noise. Traditional Tikhonov regularization assumes that signals and images are differentiable, but, as Mandelbrot has shown in his fractal theory, many signals and images are not differentiable. To de-noise and de-blur such images, researchers have designed a heuristic method of l^p-regularization.

l^p-regularization leads to good results, but it is not used as widely as should be, because it lacks a convincing theoretical explanation -- and thus, practitioners are often reluctant to …

Membership Functions Representing A Number Vs. Representing A Set: Proof Of Unique Reconstruction, Hung T. Nguyen, Vladik Kreinovich, Olga Kosheleva

Departmental Technical Reports (CS)

In some cases, a membership function m(x) represents an unknown number, but in many other cases, it represents an unknown crisp set. In this case, for each crisp set S, we can estimate the degree m(S) to which this set S is the desired one. A natural question is: once we know the values m(S) corresponding to all possible crisp sets S, can we reconstruct the original membership function? In this paper, we show that the original membership function m(x) can indeed be uniquely reconstructed from the values m(S).