Mathematics Commons^™

Using Deep Neural Networks To Classify Astronomical Images, Andrew D. Macpherson

Honors Projects

As the quantity of astronomical data available continues to exceed the resources available for analysis, recent advances in artificial intelligence encourage the development of automated classification tools. This paper lays out a framework for constructing a deep neural network capable of classifying individual astronomical images by describing techniques to extract and label these objects from large images.

Evaluation Of Black Holes In An Evolving Universe, John P. Naan

Theses and Dissertations

There are various solutions to the Einstein field equations that represent different physical assumptions, but how to represent multiple black holes within an expanding universe remains an area of open interest. The first step to resolving this question involves evaluating spacetime models that contain a single black hole in an expanding universe. Here, we are primarily interested in understanding the energy distribution of black hole models by solving Einstein's equations using the associated spacetime metric and comparing the propagation of waves within the model against other known spacetime models. Specifically, we will evaluate the combined Schwarschild-de Sitter solution under a …

Dynamical Aspects In (4+1)-Body Problems, Ryan Gauthier

Theses and Dissertations (Comprehensive)

The n-body problem models a system of n-point masses that attract each other via some binary interaction. The (n + 1)-body problem assumes that one of the masses is located at the origin of the coordinate system. For example, an (n+1)-body problem is an ideal model for Saturn, seen as the central mass, and one of its outer rings. A relative equilibrium (RE) is a special solution of the (n+1)-body problem where the non-central bodies rotate rigidly about the centre of mass. In rotating coordinates, these solutions become equilibria.

In this thesis we study dynamical aspects of planar (4 + …

Hidden Symmetries Of The Kepler Problem, Julia Kathryn Sheffler

Senior Projects Spring 2022

The orbits of planets can be described by solving Kepler’s problem which considers the motion due to by gravity (or any inverse square force law). The solutions to Kepler’s problem, for energies less then 0, are ellipses, with a few conserved quantities: energy, angular momentum and the Laplace-Runge-Lenz (LRL) vector. Each conserved quantity corresponds to symmetries of the system via N ̈other’s theorem. Energy conservation relates to time translations and angular momentum to three dimensional rotations. The symmetry related to the LRL vector is more difficult to visualize since it lives in phase space rather than configuration space. To understand …

New Techniques In Celestial Mechanics, Ali Abdulrasool Abdulhussein

Graduate Theses, Dissertations, and Problem Reports

It is shown that for the classical system of the N body problem ( Newtonian Motion), if the motion of the N particles starts from a planar initial motion at t=t_{0}, then the motion of the N particles continues to be planar for every t\in[t_{0},t_{1}], assuming that no collisions occur between the N particles. Same argument is shown about the linear motion, namely, for the classical system of the N body problem, if the motion of the N particles starts from a linear initial motion at t=t_{0}, then the motion of the N particles continues to be linear for every …

The Kepler Problem On Complex And Pseudo-Riemannian Manifolds, Michael R. Astwood

Theses and Dissertations (Comprehensive)

The motion of objects in the sky has captured the attention of scientists and mathematicians since classical times. The problem of determining their motion has been dubbed the Kepler problem, and has since been generalized into an abstract problem of dynamical systems. In particular, the question of whether a classical system produces closed and bounded orbits is of importance even to modern mathematical physics, since these systems can often be analysed by hand. The aforementioned question was originally studied by Bertrand in the context of celestial mechanics, and is therefore referred to as the Bertrand problem. We investigate the qualitative …

Topics In Gravitational Wave Physics, Aaron David Johnson

Graduate Theses and Dissertations

We begin with a brief introduction to gravitational waves. Next we look into the origin of the Chandrasekhar transformations between the different equations found by perturbing a Schwarzschild black hole. Some of the relationships turn out to be Darboux transformations. Then we turn to GW150914, the first detected black hole binary system, to see if the nonlinear memory might be detectable by current and future detectors. Finally, we develop an updated code for computing equatorial extreme mass ratio inspirals which will be open sourced as soon as it has been generalized for arbitrary inclinations.

Alpha Capture Reaction Rates For Nucleosynthesis Within An Ab Initio Framework, Alison Constance Dreyfuss

LSU Doctoral Dissertations

Clustering in nuclear systems has broad impacts on all phases of stellar burning, and plays a significant role in our understanding of nucleosynthesis, or how and where nuclei are produced in the universe. The role of alpha particles in particular is extremely important for nuclear astrophysics: ⁴He was one of the earliest elements produced in the Big Bang, it is one of the most abundant elements in the universe, and helium burning -- in particular, the triple-alpha process -- is one of the most important ``engines'' in stars. To better understand nucleosynthesis and stellar burning, then, it is important …

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.

General Relativity And Differential Geometry, Harry Hausner

Honors Theses

N/A

On The Existence And Uniqueness Of Static, Spherically Symmetric Stellar Models In General Relativity, Josh Michael Lipsmeyer

Masters Theses

The "Fluid Ball Conjecture" states that a static stellar model is spherically symmetric. This conjecture has been the motivation of much work since first mentioned by Kunzle and Savage in 1980. There have been many partial results( ul-Alam, Lindblom, Beig and Simon,etc) which rely heavily on arguments using the positive mass theorem and the equivalence of conformal flatness and spherical symmetry. The purpose of this paper is to outline the general problem, analyze and compare the key differences in several of the partial results, and give existence and uniqueness proofs for a particular class of equations of state which represents …

Rationality Of The Spectral Action For Robertson-Walker Metrics And The Geometry Of The Determinant Line Bundle For The Noncommutative Two Torus, Asghar Ghorbanpour

Electronic Thesis and Dissertation Repository

In noncommutative geometry, the geometry of a space is given via a spectral triple $(\mathcal{A,H},D)$. Geometric information, in this approach, is encoded in the spectrum of $D$ and to extract them, one should study spectral functions such as the heat trace $\Tr (e^{-tD^2})$, the spectral zeta function $\Tr(|D|^{-s})$ and the spectral action functional, $\Tr f(D/\Lambda)$.

The main focus of this thesis is on the methods and tools that can be used to extract the spectral information. Applying the pseudodifferential calculus and the heat trace techniques, in addition to computing the newer terms, we prove the rationality of the spectral action …

On The Spherical Symmetry Of Perfect-Fluid Stellar Models In General Relativity, Joshua M Brewer

Masters Theses

It is well known in Newtonian theory that static self-gravitating perfect fluids in a vacuum are necessarily spherically symmetric. The necessity of spherical symmetry of perfect-fluid static spacetimes with constant density in general relativity is shown.

The History And Mathematics Behind The Construction Of The Islamic Astrolabe, Lyda P. Urresta

Honors Theses

In this paper, we examine the mathematical methods employed in the construction of the astrolabe, an ancient measuring device used to solve problems in the field of astronomy. Essentially, the astrolabe is a two dimensional representation of the heavens obtained by projecting the celestial sphere onto the plane. Though several different types of astrolabes exist, our primary focus is on the most popular deisgn, which is created by the stereographic projection of the celestial sphere onto the plane defined by the equator with the south pole as the projection point.

A Three Dimensional Green's Function Solution Technique For The Transport Of Heavy Ions In Laboratory And Space, Candice Rockell Gerstner

Mathematics & Statistics Theses & Dissertations

In the future, astronauts will be sent into space for longer durations of time compared to previous missions. The increased risk of exposure to ionizing radiation, such as Galactic Cosmic Rays and Solar Particle Events, is of great concern. Consequently, steps must be taken to ensure astronaut safety by providing adequate shielding. The shielding and exposure of space travelers is controlled by the transport properties of the radiation through the spacecraft, its onboard systems and the bodies of the individuals themselves. Meeting the challenge of future space programs will therefore require accurate and efficient methods for performing radiation transport calculations …

Three Channel Polarimetric Based Data Deconvolution, Kurtis G. Engelson

Theses and Dissertations

A three channel polarimetric deconvolution algorithm was developed to mitigate the degrading effects of atmospheric turbulence in astronomical imagery. Tests were executed using both simulation and laboratory data. The resulting efficacy of the three channel algorithm was compared to a recently developed two channel approach under identical conditions ensuring a fair comparison amongst both algorithms. Two types of simulations were performed. The first was a binary star simulation to compare resulting resolutions between the three and two channel algorithms. The second simulation measured how effective both algorithms could deconvolve a blurred satellite image. The simulation environment assumed the key parameters …

A Mathematical Exploration Of Low-Dimensional Black Holes, Abigail Lauren Stevens

Senior Projects Spring 2011

In this paper we will be mathematically exploring low-dimensional gravitational physics and, more specifically, what it tells us about low-dimensional black holes and if there exists a Schwarzschild solution to Einstein's field equation in 2+1 dimensions. We will be starting with an existing solution in 3+1 dimensions, and then reconstructing the classical and relativistic arguments for 2+1 dimensions. Our conclusion is that in 2+1 dimensions, the Schwarzschild solution to Einstein's field equation is non-singular, and therefore it does not yield a black hole. While we still arrive at conic orbits, the relationship between Minkowski-like and Newtonian forces, energies, and geodesics …

Problems In Classical Potential Theory With Applications To Mathematical Physics, Erik Lundberg

USF Tampa Graduate Theses and Dissertations

In this thesis we are interested in some problems regarding harmonic functions. The topics are divided into three chapters.

Chapter 2 concerns singularities developed by solutions of the Cauchy problem for a holomorphic elliptic equation, especially Laplace's equation. The principal motivation is to locate the singularities of the Schwarz potential. The results have direct applications to Laplacian growth (or the Hele-Shaw problem).

Chapter 3 concerns the Dirichlet problem when the boundary is an algebraic set and the data is a polynomial or a real-analytic function. We pursue some questions related to the Khavinson-Shapiro conjecture. A main topic of interest is …

Foundations And Interpretations Of Quantum Mechanics, Cory Johnson

Honors Theses

The first famous thought experiment of Einstein gives rise to his theories of relativity, the bedrock of modern astrophysics and cosmology. His second famous thought experiment begins the investigation into the foundations of quantum mechanics. It leads to a paradox, inspiring various 'no-go' theorems proven by Bell, Kochen, and Specker. Physicists and philosophers worldwide become increasingly dissatisfied with the probabilistic complementarity interpretation (Born-Bohr) and eventually offer their own accounts of the theory. By the end of the 20th century two alternative approaches stand out as the best candidates: Both the hidden variables interpretation (de Broglie-Bohm) and the many worlds interpretation …

Effects Of Context Of Natural And Artifactual Objects On Categorization, Linsey Walker

Honors Theses

Categorization of animals and vehicles in different contexts was investigated in three experiments using event related potentials (ERPs). The presence of a background and congruency of the background in relation to the object were both manipulated in order to determine the effects of context on visual processing. In Experiment 1, adults were presented with images of animals and vehicles in two conditions: situated in a congruent context (e.g. an animal in a field) and in the absence of a context (an animal in a white homogeneous background). In experiment 2, adults were presented with images of animals and vehicles in …

World Bank -Cpa Conflict: The Struggle To Define Human Rights And Development In The Philippines, Adam B. Robbins

Honors Theses

This thesis analyzes the interactions between the World Bank (hereafter, the Bank) and the Cordillera Peoples Alliance (CPA), an indigenous and environmental advocacy group based in the Cordillera region of Luzon, in the Philippines. Using data gathered through both text-based and participatory research methods, I analyze the discursive relationship and violent confrontations between the two organizations. Conflicting development and human rights values cause the majority of these conflicts. I focus on how each organization enacts development and human rights, and how this leads to conflict. Ultimately, I intend for this thesis to offer practical guidance for the reader involved in …

Sedimentological And Plant Taphonomic Evaluation Of The Early Middle Devonian Trout Valley Formation, Jonathan Allen

Honors Theses

The Trout Valley Formation of Emsian-Eifelian age, outcropped in Baxter State Park, Maine, consists offluvial and coastal deposits preserving early land plants. Massive, crudely bedded conglomerate represents deposits of proximal braided channels on an alluvial fan complex. Lithic sandstone bodies in channel-form geometries represent deposits of river channels draining the Acadian highlands whereas associated siltstones represent overbank deposits, intertidal flats, and tidal channels. Localized lenticular quartz arenites represent nearshore shelf bar deposits that were storm influenced. The majority of plant assemblages preserved mainly in siltstone lithologies are allochthonous and parautochthonous, with only one autochthonous assemblage identified in the sequence. Plant …

Communicator-In-Chief: Presidential Use Of Television Past, Present, And Future, Jenna Wasson

Honors Theses

This thesis seeks to determine how television has changed as a communication medium for presidents over the past half century. An evaluation of the evolving ways presidents use television to communicate with and to build support from the American people has been conducted. Presidential communication strategies have been identified by drawing primarily from primary sources written by presidents and White House staff. Television technology and the television audience have changed over the years. Presidents have taken a more pro-active, aggressive role in their efforts to harness television for their own purposes. Why have these changes occurred? What impact have these …

Mathematical Models Of Quiescent Solar Prominences, Iain Mckaig

Mathematics & Statistics Theses & Dissertations

Magnetic fields in the solar atmosphere suspend and insulate dense regions of cool plasma known as prominences. The convection zone may be the mechanism that both generates and expels this magnetic flux through the photosphere in order to make these formations possible. The connection is examined here by modeling the convection zone as both one-dimensional, then more realistically, two-dimensional.

First a Dirichlet problem on a semi-infinite strip is solved using conformal mapping and the method of images. The base of the strip represents the photosphere where a current distribution can be given as a boundary condition, and the strip extends …

Celluloid Blackness : Race, Modernity, And The Conflicted Roots Of American Cinema (1915-1939), Lincoln Farr

Honors Theses

Introduction: "The Problem of the Twentieth Century" In a full page interview in the New York Times on May 29, 1912, the Swiss psychiatrist Dr. Carl G. Jung told the American people, "It seems to me that you are about to discover yourselves. You have discovered everything else-all the land of this continent; all the resources, all the hidden things of nature."Jung used the interview to address the American people, at a moment which he somehow recognized as crucial in the development of human civilization. America, the "tragic" country which he struggled to comprehend, would soon become the harbinger of …

Transitions In Masculinity And Hemingway's Developed "Code", Daniel Polk

Honors Theses

The "Hemingway Code" is much more than two words that fit nicely together for a scholar's usage; the words signify a much deeper championing of masculinity, almost a haunting presence. For Ernest Hemingway living life every day, every moment with its fullest masculine fervor, became an obsession, a never-ending quest to be at one with the attitude of never complaining, never crying out, panicking, thinking too much, or regretting. To live a manly life in a series of tactical victories, performed with steadfast ritualistic mannerisms, is to embody masculinity, and therefore the "Hemingway Code."

Rise To Power Of Senator Joseph R. Mccarthy: Reflections Of The Cold War Mccarthy Era In American Film, Scott Lainer

Honors Theses

The common bond between much of the film industry and Joseph McCarthy was insecurity and the drive for national approval. If one grasps the specific characteristics of McCarthy the man, and the methods of these politically "inspired" movies, we can to better place the period into context and acknowledge the fact that, if the citizenry is not aware, and is again caught by an ever-building wave of trickle down sentiment, the 1950s might not prove to be an isolated period in American history. Insecurity was not a fifties novelty. It still exists, and could potentially escalate anti-Communist policy and sentiment …