Patterns, Symmetries, And Mathematical Structures In The Arts, 2020 Georgia Southern University

#### Patterns, Symmetries, And Mathematical Structures In The Arts, Sarah C. Deloach

*University Honors Program Theses*

Mathematics is a discipline of academia that can be found everywhere in the world around us. Mathematicians and scientists are not the only people who need to be proficient in numbers. Those involved in social sciences and even the arts can benefit from a background in math. In fact, connections between mathematics and various forms of art have been discovered since as early as the fourth century BC. In this thesis we will study such connections and related concepts in mathematics, dances, and music.

Individual Based Modeling And Analysis Of Pathogen Levels In Poultry Chilling Process, 2019 Cleveland State University

#### Individual Based Modeling And Analysis Of Pathogen Levels In Poultry Chilling Process, Zachary Mccarthy, Ben Smith, Aamir Fazil, Jianhong Wu, Shawn D. Ryan, Daniel Munther

*Mathematics Faculty Publications*

Pathogen control during poultry processing critically depends on more enhanced insight into contamination dynamics. In this study we build an individual based model (IBM) of the chilling process. Quantifying the relationships between typical Canadian processing specifications, water chemistry dynamics and pathogen levels both in the chiller water and on individual carcasses, the IBM is shown to provide a useful tool for risk management as it can inform risk assessment models. We apply the IBM to Campylobacter spp. contamination on broiler carcasses, illustrating how free chlorine (FC) sanitization, organic load in the water, and pre-chill carcass pathogen levels affect pathogen levels ...

Oscillation In Mathematical Epidemiology, 2019 Bates College

#### Oscillation In Mathematical Epidemiology, Meredith Greer

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.

An Optimal Edg Method For Distributed Control Of Convection Diffusion Pdes, 2019 Missouri University of Science and Technology

#### An Optimal Edg Method For Distributed Control Of Convection Diffusion Pdes, X. Zhang, Y. Zhang, John R. Singler

*Mathematics and Statistics Faculty Research & Creative Works*

We propose an embedded discontinuous Galerkin (EDG) method to approximate the solution of a distributed control problem governed by convection diffusion PDEs, and obtain optimal a priori error estimates for the state, dual state, their uxes, and the control. Moreover, we prove the optimize-then-discretize (OD) and discrtize-then-optimize (DO) approaches coincide. Numerical results confirm our theoretical results.

Algebraic Methods For Proving Geometric Theorems, 2019 California State University, San Bernardino

#### Algebraic Methods For Proving Geometric Theorems, Lynn Redman

*Electronic Theses, Projects, and Dissertations*

Algebraic geometry is the study of systems of polynomial equations in one or more variables. Thinking of polynomials as functions reveals a close connection between affine varieties, which are geometric structures, and ideals, which are algebraic objects. An affine variety is a collection of tuples that represents the solutions to a system of equations. An ideal is a special subset of a ring and is what provides the tools to prove geometric theorems algebraically. In this thesis, we establish that a variety depends on the ideal generated by its defining equations. The ability to change the basis of an ideal ...

Introduction To Classical Field Theory, 2019 Department of Physics, Utah State University

#### Introduction To Classical Field Theory, Charles G. Torre

*Charles G. Torre*

Ideas & Graphs, 2019 Portland State University

#### Ideas & Graphs, Martin Zwick

*Martin Zwick*

A graph can specify the skeletal structure of an idea, onto which meaning can be added by interpreting the structure.

This paper considers graphs (but not hypergraphs) consisting of four nodes, and suggests meanings that can be associated with several different directed and undirected graphs.

Drawing on Bennett's "systematics," specifically on the Tetrad that systematics offers as a model of 'activity,' the analysis here shows that the Tetrad is versatile model of problem-solving, regulation and control, and other processes.

Comparing Design Ground Snow Load Prediction In Utah And Idaho, 2019 Utah State University

#### Comparing Design Ground Snow Load Prediction In Utah And Idaho, Brennan L. Bean, Marc Maguire, Yan Sun

*Marc Maguire*

Snow loads in the western United States are largely undefined due to complex geography and climates, leaving the individual states to publish detailed studies for their region, usually through the local Structural Engineers Association (SEAs). These associations are typically made up of engineers not formally trained to develop or evaluate spatial statistical methods for their regions and there is little guidance from ASCE 7. Furthermore, little has been written to compare the independently developed design ground snow load prediction methods used by various western states. This paper addresses this topic by comparing the accuracy of a variety of spatial methods ...

Generalization Of Real Interval Matrices To Other Fields, 2019 University of Florence

#### Generalization Of Real Interval Matrices To Other Fields, Elena Rubei

*Electronic Journal of Linear Algebra*

An interval matrix is a matrix whose entries are intervals in $\R$. This concept, which has been broadly studied, is generalized to other fields. Precisely, a rational interval matrix is defined to be a matrix whose entries are intervals in $\Q$. It is proved that a (real) interval $p \times q$ matrix with the endpoints of all its entries in $\Q$ contains a rank-one matrix if and only if it contains a rational rank-one matrix, and contains a matrix with rank smaller than $\min\{p,q\}$ if and only if it contains a rational matrix with rank smaller than $\min ...

Analysis Of Feast Spectral Approximations Using The Dpg Discretization, 2019 Portland State University

#### Analysis Of Feast Spectral Approximations Using The Dpg Discretization, Jay Gopalakrishnan, Luka Grubišić, Jeffrey S. Ovall, Benjamin Q. Parker

*Jeffrey S. Ovall*

A filtered subspace iteration for computing a cluster of eigenvalues and its accompanying eigenspace, known as “FEAST”, has gained considerable attention in recent years. This work studies issues that arise when FEAST is applied to compute part of the spectrum of an unbounded partial differential operator. Specifically, when the resolvent of the partial differential operator is approximated by the discontinuous Petrov Galerkin (DPG) method, it is shown that there is no spectral pollution. The theory also provides bounds on the discretization errors in the spectral approximations. Numerical experiments for simple operators illustrate the theory and also indicate the value of ...

Torsors Over Simplicial Schemes, 2019 The University of Western Ontario

#### Torsors Over Simplicial Schemes, Alexander S. Rolle

*Electronic Thesis and Dissertation Repository*

Let X be a simplicial object in a small Grothendieck site C, and let G be a sheaf of groups on C. We define a notion of G-torsor over X, generalizing a definition of Gillet, and prove that there is a bijection between the set of isomorphism classes of G-torsors over X, and the set of maps in the homotopy category of simplicial presheaves on C, with respect to the local weak equivalences, from X to BG. We prove basic results about the resulting non-abelian cohomology invariant, including an exact sequence associated to a central extension of sheaves of groups ...

Polynomial And Rational Convexity Of Submanifolds Of Euclidean Complex Space, 2019 The University of Western Ontario

#### Polynomial And Rational Convexity Of Submanifolds Of Euclidean Complex Space, Octavian Mitrea

*Electronic Thesis and Dissertation Repository*

The goal of this dissertation is to prove two results which are essentially independent, but which do connect to each other via their direct applications to approximation theory, symplectic geometry, topology and Banach algebras. First we show that every smooth totally real compact surface in complex Euclidean space of dimension 2 with finitely many isolated singular points of the open Whitney umbrella type is locally polynomially convex. The second result is a characterization of the rational convexity of a general class of totally real compact immersions in complex Euclidean space of dimension n..

Analysis Of Feast Spectral Approximations Using The Dpg Discretization, 2019 Portland State University

#### Analysis Of Feast Spectral Approximations Using The Dpg Discretization, Jay Gopalakrishnan, Luka Grubišić, Jeffrey S. Ovall, Benjamin Q. Parker

*Jay Gopalakrishnan*

A filtered subspace iteration for computing a cluster of eigenvalues and its accompanying eigenspace, known as “FEAST”, has gained considerable attention in recent years. This work studies issues that arise when FEAST is applied to compute part of the spectrum of an unbounded partial differential operator. Specifically, when the resolvent of the partial differential operator is approximated by the discontinuous Petrov Galerkin (DPG) method, it is shown that there is no spectral pollution. The theory also provides bounds on the discretization errors in the spectral approximations. Numerical experiments for simple operators illustrate the theory and also indicate the value of ...

The Dpg-Star Method, 2019 University of Texas at Austin

#### The Dpg-Star Method, Leszek Demkowicz, Jay Gopalakrishnan, Brendan Keith

*Jay Gopalakrishnan*

This article introduces the DPG-star (from now on, denoted DPG*) finite element method. It is a method that is in some sense dual to the discontinuous Petrov– Galerkin (DPG) method. The DPG methodology can be viewed as a means to solve an overdetermined discretization of a boundary value problem. In the same vein, the DPG* methodology is a means to solve an underdetermined discretization. These two viewpoints are developed by embedding the same operator equation into two different saddle-point problems. The analyses of the two problems have many common elements. Comparison to othermethods in the literature round out the newly ...

Classification Of Minimal Separating Sets In Low Genus Surfaces, 2019 Portland State University

#### Classification Of Minimal Separating Sets In Low Genus Surfaces, J. J. P. Veerman, William Maxwell, Victor Rielly, Austin K. Williams

*J. J. P. Veerman*

Consider a surface *S* and let *M* ⊂ *S*. If *S* \ *M* is not connected, then we say *M* separates *S*, and we refer to *M* as a separating set of *S*. If *M* separates *S*, and no proper subset of *M* separates *S*, then we say *M* is a minimal separating set of *S*. In this paper we use computational methods of combinatorial topology to classify the minimal separating sets of the orientable surfaces of genus *g* = 2 and *g* = 3. The classification for genus 0 and 1 was done in earlier work, using methods of algebraic topology.

Essential Dimension Of Parabolic Bundles, 2019 The University of Western Ontario

#### Essential Dimension Of Parabolic Bundles, Dinesh Valluri

*Electronic Thesis and Dissertation Repository*

Essential dimension of a geometric object is roughly the number of algebraically independent parameters needed to define the object. In this thesis we give upper bounds for the essential dimension of parabolic bundles over a non-singular curve X of genus g greater than or equal to 2 using Borne's correspondence between parabolic bundles on a curve and vector bundles on a root stack. This is a generalization of the work of Biswas, Dhillon and Hoffmann on the essential dimension of vector bundles, by following their method for curves and adapting it to root stacks. In this process, we invoke ...

Ricci Curvature Of Noncommutative Three Tori, Entropy, And Second Quantization, 2019 The University of Western Ontario

#### Ricci Curvature Of Noncommutative Three Tori, Entropy, And Second Quantization, Rui Dong

*Electronic Thesis and Dissertation Repository*

In noncommutative geometry, the metric information of a noncommutative space is encoded in the data of a spectral triple $(\mathcal{A}, \mathcal{H},D)$, where $D$ plays the role of the Dirac operator acting on the Hilbert space of spinors. Ideas of spectral geometry can then be used to define suitable notions such as volume, scalar curvature, and Ricci curvature. In particular, one can construct the Ricci curvature from the asymptotic expansion of the heat trace $\textrm{Tr}(e^{-tD^2})$. In Chapter 2, we will compute the Ricci curvature of a curved noncommutative three torus. The computation is done ...

General Nonlinear-Material Elasticity In Classical One-Dimensional Solid Mechanics, 2019 University of New Orleans

#### General Nonlinear-Material Elasticity In Classical One-Dimensional Solid Mechanics, Ronald Joseph Giardina Jr

*University of New Orleans Theses and Dissertations*

We will create a class of generalized ellipses and explore their ability to define a distance on a space and generate continuous, periodic functions. Connections between these continuous, periodic functions and the generalizations of trigonometric functions known in the literature shall be established along with connections between these generalized ellipses and some spectrahedral projections onto the plane, more specifically the well-known multifocal ellipses. The superellipse, or Lam\'{e} curve, will be a special case of the generalized ellipse. Applications of these generalized ellipses shall be explored with regards to some one-dimensional systems of classical mechanics. We will adopt the Ramberg-Osgood ...

Mathamigos: A Community Mathematics Initiative, 2019 Math Circles Collaborative of New Mexico

#### Mathamigos: A Community Mathematics Initiative, James C. Taylor, Delara Sharma, Shannon Rogers

*Journal of Math Circles (JMC)*

We present a broad, and we think novel, community mathematics initiative in its early stages in Santa Fe, New Mexico. At every level, the program embraces community-wide collaboration—from the leadership team, to the elements of the mathematics being implemented (primarily math circles and the Global Math Project’s Exploding Dots), to the funding model. Our MathAmigos program falls within two categories of math circle-related programs: outreach and professional development (PD). In *outreach*, we work with the Santa Fe Public School district (administration, teachers, students, and parents) and the City of Santa Fe government (our funders via a two-year contract ...

Connecting Mathematics And Community: Challenges, Successes, And Different Perspectives, 2019 Brown University

#### Connecting Mathematics And Community: Challenges, Successes, And Different Perspectives, Ariel Azbel, Margarita Azbel, Isabella F. Delbakhsh, Tami E. Heletz, Zeynep Teymuroglu

*Journal of Math Circles (JMC)*

In this article, we summarize our personal journey to establish a successful math circle in a community that is not very familiar with such mathematics enrichment programs. We share the story of how our math circle began three years ago, as well as the lessons we learned and our organizational challenges and successes. Additionally, we outline three primary perspectives: the founder perspective, the student volunteer perspective, and the faculty volunteer perspective.