Physical Sciences and Mathematics Commons^™

Extension Properties Of Asymptotic Property C And Finite Decomposition Complexity, Susan Beckhardt

Legacy Theses & Dissertations (2009 - 2024)

We prove extension theorems for several geometric properties such as asymptotic property C (APC), finite decomposition complexity (FDC), straight finite decomposition complexity (sFDC) which are weakenings of Gromov’s finite asymptotic dimension (FAD).

Assessment Of Rockfall Rollout Risk Along Varying Slope Geometries Using The Rocfall And Crsp Software, Mariam S. Al E'Bayat

Masters Theses

"Most routes in mountainous areas suffer from rock falling, rolling and bouncing risk. There are many computer programs concerned with simulating the rockfall problem, and whereas they have the same purpose, they however differ in the input data that's needed to simulate the problem, and they also differ in the way of processing and kind of output.

This study used Rocfall® and the Colorado Rockfall Simulation Program (CRSP®) to simulate sixty-three models of varying slope geometry, where only the slope geometry is changed with the same material properties for both the slope and the rocks.

Both programs were fast and …

Normal Surfaces And 3-Manifold Algorithms, Josh D. Hews

Honors Theses

This survey will develop the theory of normal surfaces as they apply to the S3 recognition algorithm. Sections 2 and 3 provide necessary background on manifold theory. Section 4 presents the theory of normal surfaces in triangulations of 3-manifolds. Section 6 discusses issues related to implementing algorithms based on normal surfaces, as well as an overview of the Regina, a program that implements many 3-manifold algorithms. Finally section 7 presents the proof of the 3-sphere recognition algorithm and discusses how Regina implements the algorithm.

Series Solutions Of Polarized Gowdy Universes, Doniray Brusaferro

Theses and Dissertations

Einstein's field equations are a system of ten partial differential equations. For a special class of spacetimes known as Gowdy spacetimes, the number of equations is reduced due to additional structure of two dimensional isometry groups with mutually orthogonal Killing vectors. In this thesis, we focus on a particular model of Gowdy spacetimes known as the polarized T³ model, and provide an explicit solution to Einstein's equations.

Classification Of Spacetimes With Symmetry, Jesse W. Hicks

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Spacetimes with symmetry play a critical role in Einstein's Theory of General Relativity. Missing from the literature is a correct, usable, and computer accessible classification of such spacetimes. This dissertation fills this gap; specifically, we

i) give a new and different approach to the classification of spacetimes with symmetry using modern methods and tools such as the Schmidt method and computer algebra systems, resulting in ninety-two spacetimes;

ii) create digital databases of the classification for easy access and use for researchers;

iii) create software to classify any spacetime metric with symmetry against the new database;

iv) compare results of our …

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

Masters Essays

No abstract provided.

Algorithmic Foundations Of Heuristic Search Using Higher-Order Polygon Inequalities, Newton Henry Campbell Jr.

CCE Theses and Dissertations

The shortest path problem in graphs is both a classic combinatorial optimization problem and a practical problem that admits many applications. Techniques for preprocessing a graph are useful for reducing shortest path query times. This dissertation studies the foundations of a class of algorithms that use preprocessed landmark information and the triangle inequality to guide A* search in graphs. A new heuristic is presented for solving shortest path queries that enables the use of higher order polygon inequalities. We demonstrate this capability by leveraging distance information from two landmarks when visiting a vertex as opposed to the common single landmark …

Quantization Of Two Types Of Multisymplectic Manifolds, Baran Serajelahi

Electronic Thesis and Dissertation Repository

This thesis is concerned with quantization of two types of multisymplectic manifolds that have multisymplectic forms coming from a Kahler form. In chapter 2 we show that in both cases they can be quantized using Berezin-Toeplitz quantization and that the quantizations have reasonable semiclassical properties.

In the last chapter of this work, we obtain two additional results. The first concerns the deformation quantization of the (2n-1)-plectic structure that we examine in chapter 2, we make the first step toward the definition of a star product on the Nambu-Poisson algebra (C^{\infty}(M),{.,...,.}). The second result concerns the algebraic properties of the generalized …

Differential Geometry: Curvature And Holonomy, Austin Christian

Math Theses

We develop the basic language of differential geometry, including smooth manifolds, bundles, and differential forms. Once this background is established, we explore parallelism in smooth manifolds -- in particular, in Riemannian manifolds -- and conclude by presenting a proof of the Ambrose-Singer theorem, which relates parallelism (holonomy) to curvature in principal bundles.

A Critique Of A Student-Centered Learning Approach Used In A Geometry Classroom, Alana Blackwell Day

LSU Master's Theses

This thesis offers a framework for identifying effective classroom materials to support student-centered learning. Based on a review of published studies on effective classroom activities, as well as theses by Louisiana Math and Science Teachers Institute (LaMSTI) graduates, we identify promising characteristics. We employed these in five lessons, refined them into questions, and offer in final form for use.

Writing In The Geometry Classroom, Amy Lynn Rome

LSU Master's Theses

This study sought a time-efficient way to implement writing in ninth-grade Geometry. Students wrote responses to five expository writing prompts spread out over the spring semester of the 2014-2015 school year. Students’ first attempts were graded and returned to them along with feedback in the form of a teacher-written exemplar. Students rewrote assignments to improve their grades. All first and second attempts were collected and evaluated. We found that students were more successful after seeing the exemplar. Moreover, on assignments occurring later in the semester, more students were able to score in the top categories of the writing assignments on …

A Kleinian Approach To Fundamental Regions, Joshua L. Hidalgo

Electronic Theses, Projects, and Dissertations

This thesis takes a Kleinian approach to hyperbolic geometry in order to illustrate the importance of discrete subgroups and their fundamental domains (fundamental regions). A brief history of Euclids Parallel Postulate and its relation to the discovery of hyperbolic geometry be given first. We will explore two models of hyperbolic $n$-space: $U^n$ and $B^n$. Points, lines, distances, and spheres of these two models will be defined and examples in $U^2$, $U^3$, and $B^2$ will be given. We will then discuss the isometries of $U^n$ and $B^n$. These isometries, known as M\"obius transformations, have special properties and turn out to be …

A Volume Bound For Montesinos Links, Kathleen Arvella Finlinson

Theses and Dissertations

The hyperbolic volume of a knot complement is a topological knot invariant. Futer, Kalfagianni, and Purcell have estimated the volumes of Montesinos link complements for Montesinos links with at least three positive tangles. Here we extend their results to all hyperbolic Montesinos links.

Teaching Strategies For Proof Based Geometry, Kristina Marie Chaves

LSU Master's Theses

This study aims is to discover the best methods for geometry students to master proof writing. Students who are taught how to write proofs in a traditional setting find proofs to be very difficult - struggling throughout the school year writing proofs on their own. Studies have been conducted regarding the use of dynamic geometry software in proof writing. To further study the effects of proof writing using dynamic geometry software, forty-eight freshmen students enrolled in an honors geometry course at a high performing suburban high school in Louisiana were given several proofs to complete, along with self-reflection surveys. During …

Developing Auxiliary Resource Materials To Support The Engageny Geometry Curriculum, Joanne Griffin

LSU Master's Theses

With the advent of current education reform, and the introduction of the Common Core State Standards for Mathematics, the present offerings of the geometry curriculum have become dated. One contribution to remedy this situation is a project by the state of New York called EngageNY. EngageNY is a common core aligned mathematics curriculum across all grades. The EngageNY Geometry Curriculum Module 1 is the basis from which this thesis was developed. It is the purpose of this thesis to present a supplement to the EngageNY Geometry Module 1 Curriculum and to describe why it is advantageous to have such a …

Professional Development For Geometry Teachers Under Common Core State Standards In Mathematics, Ellen Fort

LSU Master's Theses

This thesis offers a model professional development workshop to high school geometry teachers, with a focus on the Common Core State Standards in geometry, including a description of the workshop, materials to assist in the presentation, and follow-up materials. This workshop, which is based upon curriculum written for EngageNY under the direction of Common Core, Inc., has been presented by the author on four separate occasions to a total of approximately two hundred teachers and other school and district personnel over the past few months. Feedback obtained from attendees has been uniformly positive, indicating that the information and understanding obtained …

Open Books On Contact Three Orbifolds, Daniel Herr

Open Access Dissertations

In 2002, Giroux showed that every contact structure had a corresponding open book decomposition. This was the converse to a previous construction of Thurston and Winkelnkemper, and made open books a vital tool in the study of contact three-manifolds. We extend these results to contact orbifolds, i.e. spaces that are locally diffeomorphic to the quotient of a contact manifold and a compatible finite group action. This involves adapting some of the main concepts and constructions of three dimensional contact geometry to the orbifold setting.

Hyperbolicity Equations For Knot Complements, Christopher Martin Jacinto

Theses Digitization Project

This study analyzes Carlo Petronio's paper, An Algorithm Producing Hyperbolicity Equations for a Link Complement in S³. Using the figure eight knot as an example, we will explain how Petronio's algorithm was able to decompose the knot complement of an alternating knot into tetrahedra. Then, using the vertex invariants of these tetrahedra, we will explain how Petronio was able to create hyperbolicity equations.

A Potential Framework For Emergent Space-Time And Geometry From Order, Newshaw Bahreyni

Legacy Theses & Dissertations (2009 - 2024)

This research is about seeking laws of physics and geometry from order. Anything that is measured is the result of something influencing something else. An act of influencing and the response to such influence form a pair of events. A collection of such events along with their binary ordering relation of influence which forms a

Using Formative Assessment To Enhance Student Performance On Geometric Proof Writing, Benjamin Hargrave

LSU Master's Theses

The purpose of this research is to uncover best practices to create competent proof writers. Studies have shown the best setting to do this is in the high school geometry classroom. Throughout a yearlong study of geometry, students were exposed to theorems and their demonstrations. Despite constant exposure, students were still unable to produce their own proof of propositions. The questions then became how can an educator provide critical feedback that encourages student reasoning and develops logical argumentation skills? With the goal in mind, twenty-five students enrolled in a geometry course at Baton Rouge High School in Baton Rouge, Louisiana …

Using Writing Assignments In High School Geometry To Improve Students' Proof Writing Ability, Amanda Choppin Mcallister

LSU Master's Theses

The Common Core State Standards encourage the use of writing in mathematics classrooms. This study was designed to create a template for high school teachers to use in a geometry class to improve students’ proof writing ability. The students enrolled in the class were asked to complete journal and expository writing assignments throughout the course. The assignments were scored with a rubric. To assess if growth was made in proof writing, the students were all given a test four times throughout the school year. All four tests were assessed using the same rubric. We provide evidence that the template was …

Swelling And Folding As Mechanisms Of 3d Shape Formation In Thin Elastic Sheets, Marcelo A. Dias

Open Access Dissertations

We work with two different mechanisms to generate geometric frustration on thin elastic sheets; isotropic differential growth and folding. We describe how controlled growth and prescribing folding patterns are useful tools for designing three-dimensional objects from information printed in two dimensions. The first mechanism is inspired by the possibility to control shapes by swelling polymer films, where we propose a solution for the problem of shape formation by asking the question, ``what 2D metric should be prescribed to achieve a given 3D shape?'', namely the reverse problem. We choose two different types of initial configurations of sheets, disk-like with one …

Degree Constrained Triangulation, Roshan Gyawali

UNLV Theses, Dissertations, Professional Papers, and Capstones

Triangulation of simple polygons or sets of points in two dimensions is a widely investigated problem in computational geometry. Some researchers have considered variations of triangulation problems that include minimum weight triangulation, de-launay triangulation and triangulation refinement. In this thesis we consider a constrained version of the triangulation problem that asks for triangulating a given domain (polygon or point sites) so that the resulting triangulation has an increased number of even degree vertices. This problem is called Degree Constrained Triangulation (DCT). We propose four algorithms to solve DCT problems. We also present experimental results based on the implementation of the …

Geometries In Soft Matter, Zhenwei Yao

Physics - Dissertations

No abstract provided.

Generalized Branching In Circle Packing, James Russell Ashe

Doctoral Dissertations

Circle packings are configurations of circle with prescribed patterns of tangency. They relate to a surprisingly diverse array of topics. Connections to Riemann surfaces, Apollonian packings, random walks, Brownian motion, and many other topics have been discovered. Of these none has garnered more interest than circle packings' relationship to analytical functions. With a high degree of faithfulness, maps between circle packings exhibit essentially the same geometric properties as seen in classical analytical functions. With this as motivation, an entire theory of discrete analytic function theory has been developed. However limitations in this theory due to the discreteness of circle packings …

Some Aspects Of Toric Topology., Soumen Sarkar Dr.

Doctoral Theses

The main goal of this thesis is to study the topology of torus actions on manifolds and orbifolds. In algebraic geometry actions of the torus (C * ) n on algebraic varieties with nice properties produce bridges between geometry and combinatorics see [Dan78], [Oda88] and [Ful93]. We see a similar bridge called moment map for Hamiltonian action of compact torus on symplectic manifolds see [Aud91] and [Gui94]. In particular whenever the manifold is compact the image of moment map is a simple polytope, the orbit space of the action. A topological counterpart called quasitoric manifolds, a class of topological manifolds …

The Hyperboloid Model Of Hyperbolic Geometry, Zachery S. Lane Solheim

EWU Masters Thesis Collection

"The main goal of this thesis is to introduce and develop the hyperboloid model of Hyperbolic Geometry. In order to do that, some time is spent on Neutral Geometry as well as Euclidean Geometry; these are used to build several models of Hyperbolic Geometry. At this point the hyperboloid model is introduced, related to the other models visited, and developed using some concepts from physics as aids. After the development of the hyperboloid model, Fuchsian groups are briefly discussed and the more familiar models of Hyperbolic Geometry are further investigated"--Document.

The Hyperboloid Model Of Hyperbolic Geometry, Zachery S. Lane Solheim

EWU Masters Thesis Collection

"The main goal of this thesis is to introduce and develop the hyperboloid model of Hyperbolic Geometry. In order to do that, some time is spent on Neutral Geometry as well as Euclidean Geometry; these are used to build several models of Hyperbolic Geometry. At this point the hyperboloid model is introduced, related to the other models visited, and developed using some concepts from physics as aids. After the development of the hyperboloid model, Fuchsian groups are briefly discussed and the more familiar models of Hyperbolic Geometry are further investigated"--Document.

Writing In Geometry With The Common Core State Standards: Developing Mathematical Thinkers, Yvonne Mariki Chimwaza

LSU Master's Theses

The newly released Common Core State Standards (CCSS) were adopted with the goal in mind that in the future our students will leave high school ready and better prepared for college and careers. In particular, the CCSS insists that a faithful implementation of the eight Standard of Mathematical Practices will lead to a generation of mathematical thinkers who have learned how to read, write, model, reason, and solve problems in mathematical terms. Unfortunately, at present, my students and others do not know how to write and reason mathematically. By way of this thesis, I searched for ways to help forty-five …

Quantum Stochastic Flows: Trotter Product Formula, Dilations And Quantum Brownian Motion., Biswarup Das Dr.

Doctoral Theses

Motivated by the major role played by probabilistic models in many areas of science, several quantum (i.e. non-commutative) generalizations of classical probability have been attempted by a number of mathematicians. The pioneering works of K.R. Parthasarathy, L. Accardi, R.L. Hudson, P.A. Meyer and others led to the development of one such non-commutative model called ‘quantum probability’ which has a very rich theory of quantum stochastic calculus a la Hudson and Parthasarathy. Within the framework of quantum stochastic calculus, the ‘grand design’ that engages us is the canonical construction and study of ∗-homomorphic flows (jt)t≥0 on a given C ∗ or …