A lifting of graphs to 3-uniform hypergraphs, its generalization, and further investigation of hypergraph Ramsey numbers

Ramsey theory has posed many interesting questions for graph theorists that have yet to besolved. Many different methods have been used to find Ramsey numbers, though very feware actually known. Because of this, more mathematical tools are needed to prove exactvalues of Ramsey numbers and their generalizations. Budden, Hiller, Lambert, and Sanfordhave created a lifting from graphs to 3-uniform hypergraphs that has shown promise. Theybelieve that many results may come of this lifting, and have discovered some themselves.This thesis will build upon their work by considering other important properties of theirlifting and analogous liftings for higher-uniform hypergraphs. We also consider ways inwhich one may extend many known results in Ramsey Theory for graphs to the r-uniformhypergraph setting

Symmetric dual-wind discontinuous Galerkin methods for elliptic variational inequalities

The main goal of this dissertation is to formulate and analyze a dual wind discontinuous Galerkin method for approximating solutions to elliptic variational inequalities. A discontinuous Galerkin (DG) finite-element interior calculus is used as a common framework to describe various DG approximation methods for second-order elliptic problems. The dual-wind discontinuous Galerkin method is formulated for the obstacle problem with Dirichlet boundary conditions, ??_u _ f on with u = g on @, u _ on , and (_u ?? f)(u ?? ) = 0 on . A complete convergence analysis is developed and numerical experiments are recorded that verify these results. A secondary goal of this dissertation is to explore the effect of the penalty parameter on the error of the dual-wind discontinuous Galerkin method’s approximation to an elliptic partial differential equation. The dual-wind discontinuous Galerkin method is applied to the Poisson problem in two dimensions. The dual-wind discontinuous Galerkin approximation to the Poisson problem is constructed using various penalty parameters and the error is recorded for each approximation across various initial meshes and their refinements. [This abstract has been edited to remove characters that will not display in this system. Please see the PDF for the full abstract.]]]> 2020 Galerkin methods Discontinuous functions Variational inequalities (Mathematics) English http://libres.uncg.edu/ir/uncg/f/Rapp_uncg_0154D_13093.pdf oai:libres.uncg.edu/33277 2020-09-24T15:20:27Z UNCG Collectives and countercollectives: how the rhetoric of mass media persuades citizens in wartime NC DOCKS at The University of North Carolina at Greensboro Reed, Stacy <![CDATA[The purpose of the following analysis is to highlight rhetorical patterns common during wartime across multiple decades and forms of mass media communication, and to demonstrate how the technologies of media intersect with rhetorical patterns in the creation of collectives and countercollectives. By drawing on and extending the theories of Kenneth Burke and Marshall McLuhan, I pinpoint the similarities and differences in persuasive strategies across shifting electronic mass media, noting how rhetorical appeals remain consistent though the forms they take and the modes in which they are delivered by rhetors changes with historical context and technological affordances. Historical accounts and primary sources provide the basis for such rhetorical analysis. While the technology may change and become increasingly sophisticated in its affordances and accessibility, the rhetorical patterns of collectives and countercollectives remain similar, as strategic appeals to logos, pathos, and ethos are relied upon similarly by both pro- and antiwar collectives. The rhetorical analyses of the collectives and countercollectives across the four wars under investigation suggests useful strategies for rhetors of both present-day and future mass media communications

The James Webb Space Telescope Mission

Twenty-six years ago a small committee report, building on earlier studies, expounded a compelling and poetic vision for the future of astronomy, calling for an infrared-optimized space telescope with an aperture of at least $4m$. With the support of their governments in the US, Europe, and Canada, 20,000 people realized that vision as the $6.5m$ James Webb Space Telescope. A generation of astronomers will celebrate their accomplishments for the life of the mission, potentially as long as 20 years, and beyond. This report and the scientific discoveries that follow are extended thank-you notes to the 20,000 team members. The telescope is working perfectly, with much better image quality than expected. In this and accompanying papers, we give a brief history, describe the observatory, outline its objectives and current observing program, and discuss the inventions and people who made it possible. We cite detailed reports on the design and the measured performance on orbit.Comment: Accepted by PASP for the special issue on The James Webb Space Telescope Overview, 29 pages, 4 figure

Symmetric Dual-Wind Discontinuous Galerkin Methods for Elliptic Variational Inequalities

The main goal of this dissertation is to formulate and analyze a dual wind discontinuous Galerkin method for approximating solutions to elliptic variational inequalities. A discontinuous Galerkin (DG) finite-element interior calculus is used as a common framework to describe various DG approximation methods for second-order elliptic problems. The dual-wind discontinuous Galerkin method is formulated for the obstacle problem with Dirichlet boundary conditions, −∆u ≥ ƒ on Ω with u = g on ∂Ω, u ≥ ψ on Ω, and (-∆u − ƒ)(u − ψ) = 0 on Ω. A complete convergence analysis is developed and numerical experiments are recorded that verify these results. A secondary goal of this dissertation is to explore the effect of the penalty parameter on the error of the dual-wind discontinuous Galerkin method’s approximation to an elliptic partial differential equation. The dual-wind discontinuous Galerkin method is applied to the Poisson problem in two dimensions. The dual-wind discontinuous Galerkin approximation to the Poisson problem is constructed using various penalty parameters and the error is recorded for each approximation across various initial meshes and their refinements

The James Webb Space Telescope Mission

Twenty-six years ago a small committee report, building on earlier studies, expounded a compelling and poetic vision for the future of astronomy, calling for an infrared-optimized space telescope with an aperture of at least 4 m. With the support of their governments in the US, Europe, and Canada, 20,000 people realized that vision as the 6.5 m James Webb Space Telescope. A generation of astronomers will celebrate their accomplishments for the life of the mission, potentially as long as 20 yr, and beyond. This report and the scientific discoveries that follow are extended thank-you notes to the 20,000 team members. The telescope is working perfectly, with much better image quality than expected. In this and accompanying papers, we give a brief history, describe the observatory, outline its objectives and current observing program, and discuss the inventions and people who made it possible. We cite detailed reports on the design and the measured performance on orbit