Mathematics Commons^™

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 …