Mathematics Commons^™

Decompositions Of Ideals Of Minors Meeting A Submatrix, Kent M. Neuerburg, Zach Teitler

Mathematics Faculty Publications and Presentations

We compute the primary decomposition of certain ideals generated by subsets of minors in a generic matrix or in a generic symmetric matrix, or subsets of Pfaffians in a generic skew-symmetric matrix. Specifically, the ideals we consider are generated by minors that have at least some given number of rows and columns in certain submatrices.

Quandle Coloring And Cocycle Invariants Of Composite Knots And Abelian Extensions, W Edwin Clark, Masahico Saito, Leandro Vendramin

Mathematics and Statistics Faculty Publications

Quandle colorings and cocycle invariants are studied for composite knots, and applied to chirality and abelian extensions. The square and granny knots, for example, can be distinguished by quandle colorings, so that a trefoil and its mirror can be distinguished by quandle coloring of composite knots. We investigate this and related phenomena. Quandle cocycle invariants are studied in relation to quandle coloring of the connected sum, and formulas are given for computing the cocycle invariant from the number of colorings of composite knots. Relations to corresponding abelian extensions of quandles are studied, and extensions are examined for the table of …

Section Abstracts: Astronomy, Mathematics And Physics

Virginia Journal of Science

Abstracts of the Astronomy, Mathematics, and Physics Section for the 94th Annual Virginia Academy of Science Meeting, May 18-20, 2016, at University of Mary Washington, Fredericksburg, VA.

Volume 08, Meghan Enzinna, Casey Dawn Gailey, Raven Collins, Chiara Enriquez, Amelia Mcconnell, Alexander Morton, Emma Beckett, Leah G. Parr, Briana Adhikusuma, Taylor Embrey, Rowan Davis, Danielle Sisson, Bianca Cherry, Melissa Cacho, Chloe Woodward, Catherine Rollins, Carson Reeher, Landon Cooper, Haley Vasquez, Marlisha Stewart, Eric Whitehead, Sabrina Walker, James Bates

Incite: The Journal of Undergraduate Scholarship

Introduction from Interim Dean Dr. Jennifer Apperson

Indigenous Peoples and the Modern Era by Meghan Enzinna

"Who Says": How Selena Gomez and the Scene Attempt to Subvert the Popular Standards of Beauty by Casey Dawn Gailey

Art by Raven Collins

Meltdown on Social Media: Amy's Baking Company Meets Kitchen Nightmares by Nathena Haddrill

Art by Chiara Enriquez

Design by Amelia Mcconnell

Worth More Than a Thousand Words: A Visual Rhetorical Discussion of Virtual Reality by Examining "Clouds Over Sidra" by Alexander Morton

Design by Emma Beckett

The Sonata: An Analysis of Piano Sonata No. 14 in C Minor, K. …

Superstable Semigroups, Stephanie Olsen

Honors Capstones

No abstract provided.

Perfect Matchings And Their Applications, Amanda Mayhall

Honors Capstones

No abstract provided.

Regularity Of Solutions And The Free Boundary For A Class Of Bernoulli-Type Parabolic Free Boundary Problems With Variable Coefficients, Thomas H. Backing

Open Access Dissertations

In this work the regularity of solutions and of the free boundary for a type of parabolic free boundary problem with variable coefficients is proved. After introducing the problem and its history in the introduction, we proceed in Chapter 2 to prove the optimal Lipschitz regularity of viscosity solutions under the main assumption that the free boundary is Lipschitz. In Chapter 3, we prove that Lipschitz free boundaries possess a classical normal in both space and time at each point and that this normal varies with a Hölder modulus of continuity. As a consequence, the viscosity solution is in fact …

Rank Constrained Homotopies Of Matrices And The Blackadar-Handelman Conjectures On C*-Algebras, Kaushika De Silva

Open Access Dissertations

Rank constrained homotopies of matrices:

For any n ≥ k ≥ l ∈ N, let S( n,k,l) be the set of all non-negative definite matrices a ∈ Mn(C) with l ≤ rank a ≤ k. We investigate homotopy equivalence of continuous maps from a compact Hausdorff space X into sets of the form S(n,k,l). From [37] it is known that for any n, if 4dim X ≤ k-l where dim X denote the covering dimension of X, then there is exactly one homotopy class of maps from X into S …

Kernels Of Adjoints Of Composition Operators On Hilbert Spaces Of Analytic Functions, Brittney Rachele Miller

Open Access Dissertations

This thesis contains a collection of results in the study of the adjoint of a composition operator and its kernel in weighted Hardy spaces, in particular, the classical Hardy, Bergman, and Dirichlet spaces. In 2006, Cowen and Gallardo-Gutiérrez laid the groundwork for an explicit formula for the adjoint of a composition operator with rational symbol acting on the Hardy space, and in 2008, Hammond, Moorhouse, and Robbins established such a formula. In 2014, Goshabulaghi and Vaezi obtained analogous formulas for the adjoint of a composition operator in the Bergman and Dirichlet spaces. While it is known that the kernel of …

Monotonicity Formulas For Diffusion Operators On Manifolds And Carnot Groups, Heat Kernel Asymptotics And Wiener's Criterion On Heisenberg-Type Groups, Kevin L. Rotz

Open Access Dissertations

The contents of this thesis are an assortment of results in analysis and subRiemannian geometry, with a special focus on the Heisenberg group Hn, Heisenbergtype (H-type) groups, and Carnot groups.

As we wish for this thesis to be relatively self-contained, the main definitions and background are covered in Chapter 1. This includes basic information about Carnot groups, Hn, H-type groups, diffusion operators, and the curvature dimension inequality.

Chapter 2 incorporates excerpts from a paper by N. Garofalo and the author, [42]. In it, we propose a generalization of Almgren’s frequency function N : (0, 1) → R for solutions to …

Finite Dimensional Approximations And Deformations Of Group C*-Algebras, Andrew James Schneider

Open Access Dissertations

Quasidiagonality is a finite-dimensional approximation property of a C*-algebra which indicates that it has matricial approximations that capture the structure of the C*-algebra. We investigate when C*-algebras associated to discrete groups have such a property with particular emphasis on finding obstructions. In particular, we point out that groups with Kazhdan's Property (T) and only finitely many unitary equivalence classes of finite dimensional representations do not produce quasidiagonal C*-algebras. We then observe and note interactions with Property (T) and other approximation properties.

Property (QH) is a related but stronger approximation property with deep connections to E-Theory and …

College Algebra (College Of Coastal Georgia), German Vargas, Jose Lugo, Laura Lynch, Jamil Mortada, Treg Thompson, Victor Vega

Mathematics Grants Collections

This Grants Collection for College Algebra was created under a Round Two ALG Textbook Transformation Grant.

Affordable Learning Georgia Grants Collections are intended to provide faculty with the frameworks to quickly implement or revise the same materials as a Textbook Transformation Grants team, along with the aims and lessons learned from project teams during the implementation process.

Documents are in .pdf format, with a separate .docx (Word) version available for download. Each collection contains the following materials:

• Linked Syllabus
• Initial Proposal
• Final Report

Precalculus (Albany State University), Wanjun Hu, Li Feng

Mathematics Grants Collections

This Grants Collection for Precalculus was created under a Round Two ALG Textbook Transformation Grant.

Affordable Learning Georgia Grants Collections are intended to provide faculty with the frameworks to quickly implement or revise the same materials as a Textbook Transformation Grants team, along with the aims and lessons learned from project teams during the implementation process.

Documents are in .pdf format, with a separate .docx (Word) version available for download. Each collection contains the following materials:

• Linked Syllabus
• Initial Proposal
• Final Report

Separation Of Parallel Encoded Complex-Valued Slices (Specs) From A Single Complex-Valued Aliased Coil Image, Daniel B. Rowe, Iain P. Bruce, Andrew S. Nencka, James S. Hyde, Mary C. Kociuba

Mathematics, Statistics and Computer Science Faculty Research and Publications

Purpose

Achieving a reduction in scan time with minimal inter-slice signal leakage is one of the significant obstacles in parallel MR imaging. In fMRI, multiband-imaging techniques accelerate data acquisition by simultaneously magnetizing the spatial frequency spectrum of multiple slices. The SPECS model eliminates the consequential inter-slice signal leakage from the slice unaliasing, while maintaining an optimal reduction in scan time and activation statistics in fMRI studies.

Materials and Methods

When the combined k-space array is inverse Fourier reconstructed, the resulting aliased image is separated into the un-aliased slices through a least squares estimator. Without the additional spatial information from …

Roles Of A Teacher And Researcher During In Situ Professional Development Around The Implementation Of Mathematical Modeling Tasks, Hyunyi Jung, Corey Brady

Mathematics, Statistics and Computer Science Faculty Research and Publications

Partnership with teachers for professional development has been considered beneficial because of the potential of collaborative work in the teacher’s own classroom to be relevant to practice. From this perspective, both teachers and researchers can draw on their own expertise and work as authentic partners. In this study, we address the need for such collaboration and focus on how a teacher and a researcher performed their roles when collaboratively implementing mathematical modeling tasks within a context of in situ professional development. Using multi-tier design-based research, as a framework, a researcher worked in a teacher’s classroom to implement a series of …

General Multi-Sum Transformations And Some Implications, James Mclaughlin

Mathematics Faculty Publications

We give two general transformations that allows certain quite general basic hypergeometric multi-sums of arbitrary depth (sums that involve an arbitrary sequence {g(k)}), to be reduced to an infinite q-product times a single basic hypergeometric sum. Various applications are given, including summation formulae for some q orthogonal polynomials, and various multisums that are expressible as infinite products.

College Algebra (Fort Valley State University), Josephine Davis, Samuel Cartwright, Shadreck Chitsonga, Bhavana Burell, Ian Toppin

Mathematics Grants Collections

This Grants Collection for College Algebra was created under a Round Two ALG Textbook Transformation Grant.

Affordable Learning Georgia Grants Collections are intended to provide faculty with the frameworks to quickly implement or revise the same materials as a Textbook Transformation Grants team, along with the aims and lessons learned from project teams during the implementation process.

Documents are in .pdf format, with a separate .docx (Word) version available for download. Each collection contains the following materials:

• Linked Syllabus
• Initial Proposal
• Final Report

Trigonometry, German Vargas, Jose Lugo, Laura Lynch, Jamil Mortada, Victor Vega, Treg Thompson

Mathematics Grants Collections

This Grants Collection for Trigonometry was created under a Round Two ALG Textbook Transformation Grant.

Affordable Learning Georgia Grants Collections are intended to provide faculty with the frameworks to quickly implement or revise the same materials as a Textbook Transformation Grants team, along with the aims and lessons learned from project teams during the implementation process.

Documents are in .pdf format, with a separate .docx (Word) version available for download. Each collection contains the following materials:

• Linked Syllabus
• Initial Proposal
• Final Report

Precalculus (University Of North Georgia), Michael Goodroe, Berhanu Kidane, Julian Allagan, John Williams

Mathematics Grants Collections

This Grants Collection for Precalculus was created under a Round Two ALG Textbook Transformation Grant.

Affordable Learning Georgia Grants Collections are intended to provide faculty with the frameworks to quickly implement or revise the same materials as a Textbook Transformation Grants team, along with the aims and lessons learned from project teams during the implementation process.

Documents are in .pdf format, with a separate .docx (Word) version available for download. Each collection contains the following materials:

• Linked Syllabus
• Initial Proposal
• Final Report

Precalculus (College Of Coastal Georgia), German Vargas, Jose Lugo, Laura Lynch, Jamil Mortada, Treg Thompson, Victor Vega

Mathematics Grants Collections

This Grants Collection for Precalculus was created under a Round Two ALG Textbook Transformation Grant.

Affordable Learning Georgia Grants Collections are intended to provide faculty with the frameworks to quickly implement or revise the same materials as a Textbook Transformation Grants team, along with the aims and lessons learned from project teams during the implementation process.

Documents are in .pdf format, with a separate .docx (Word) version available for download. Each collection contains the following materials:

• Linked Syllabus
• Initial Proposal
• Final Report

College Algebra (University Of North Georgia), Minsu Kim, Hashim Saber, Bikash Das, Thomas Hartfield

Mathematics Grants Collections

This Grants Collection for College Algebra was created under a Round Four ALG Textbook Transformation Grant.

Affordable Learning Georgia Grants Collections are intended to provide faculty with the frameworks to quickly implement or revise the same materials as a Textbook Transformation Grants team, along with the aims and lessons learned from project teams during the implementation process.

Documents are in .pdf format, with a separate .docx (Word) version available for download. Each collection contains the following materials:

• Linked Syllabus
• Initial Proposal
• Final Report

Coding Strategies, The Choquet Game And Domain Representability, Lynne Yengulalp

Mathematics Faculty Publications

We prove that if the NONEMPTY player has a winning strategy in the strong Choquet game on a regular space X then NONEMPTY has a winning coding strategy in that game (a strategy that only depends on the previous 2 moves). We also prove that any regular domain representable space is generalized subcompact.

2016 (Spring), University Of Dayton. Department Of Mathematics

Colloquia

Abstracts of the talks given at the 2016 Spring Colloquium.

Exploring The Relationship Between High School Diploma Requirements In Mathematics And College Remediation Rates, Derek J. Brown

Doctor of Education (EdD)

This study examined the relationship between the essential skill of math and college remediation rates using a dataset of 1,858 recent high school graduates attending public, 4-year Oregon universities. Using a logistic regression methodology, this study explored (a) the extent to which the essential skill of math improved college remediation rates, (b) the association between allowable essential skill of math sources of evidence and college remediation rates, and (c) the impact of the essential skill of math on students from various demographic backgrounds. Results from this study suggest the essential skill of math graduation requirement significantly predicts the likelihood of …

Domain Representability And Topological Completeness, Matthew D. Devilbiss

Honors Theses

Topological completeness properties seek to generalize the definition of complete metric space to the context of topologies. Chapter 1 gives an overview of some of these properties. Chapter 2 introduces domain theory, a field originally intended for use in theoretical computer science. Finally, Chapter 3 examines how this computer-scientific notion can be employed in the study of topological completeness in the form of domain representability. The connections between domain representability and other topological completeness properties are subsequently examined.

Choosing The Right Tool, Stacy K. Boote

UNF Faculty Research and Scholarship

No abstract provided.

The Gold Standard And Education Intervention Research: A Consideration Of Middle School Mathematics Interventions As A Particular Case, Sarah Nielsen , '16

Senior Theses, Projects, and Awards

This thesis explores the benefits and drawbacks of various experimental designs, outcome measures, and specific methodological techniques in education intervention research. Through an analysis of nine top-tier journals in education, I describe which experimental designs and outcome measures are most commonly used in current middle school mathematics intervention research. Then, four case intervention studies with different experimental designs are closely examined. This discussion is juxtaposed with consideration of evaluation standards published by government agencies. Each study represents different discourses about the effectiveness of the intervention reported. Although the standards for intervention research no longer only promote randomized quantitative research, I …

Out-Tournament Adjacency Matrices With Equal Ranks, Zachary Buelow

Dissertations (1934 -)

Much work has been done in analyzing various classes of tournaments, giving a partial characterization of tournaments with adjacency matrices having equal and full real, nonnegative integer, Boolean, and term ranks. Relatively little is known about the corresponding adjacency matrix ranks of local out-tournaments, a larger family of digraphs containing the class of tournaments. Based on each of several structural theorems from Bang-Jensen, Huang, and Prisner, we will identify several classes of out-tournaments which have the desired adjacency matrix rank properties. First we will consider matrix ranks of out-tournament matrices from the perspective of the structural composition of the strong …

Relaxations And Discretizations For The Pooling Problem, Akshay Gupte, Shabbir Ahmed, Santanu S. Dey, Myun Seok Cheon

Publications

The pooling problem is a folklore NP-hard global optimization problem that finds applications in industries such as petrochemical refining, wastewater treatment and mining. This paper assimilates the vast literature on this problem that is dispersed over different areas and gives new insights on prevalent techniques. We also present new ideas for computing dual bounds on the global optimum by solving high-dimensional linear programs. Finally, we propose discretization methods for inner approximating the feasible region and obtaining good primal bounds. Valid inequalities are derived for the discretized models, which are formulated as mixed integer linear programs. The strength of our relaxations …

Area And Volume Where Do The Formulas Come From?, Roger Yarnell

Masters Essays

No abstract provided.