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Articles 1 - 8 of 8
Full-Text Articles in Physical Sciences and Mathematics
On The Existence And Uniqueness Of Static, Spherically Symmetric Stellar Models In General Relativity, Josh Michael Lipsmeyer
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 …
Injective Modules And Divisible Groups, Ryan Neil Campbell
Injective Modules And Divisible Groups, Ryan Neil Campbell
Masters Theses
An R-module M is injective provided that for every R-monomorphism g from R-modules A to B, any R-homomorphism f from A to M can be extended to an R-homomorphism h from B to M such that hg = [equals] f. That is one of several equivalent statements of injective modules that we will be discussing, including concepts dealing with ideals of rings, homomorphism modules, short exact sequences, and splitting sequences. A divisible group G is defined when for every element x of G and every nonzero integer n, there exists y in …
Phase Dynamics Of Locset Control Methodology, Brendan Neschke
Phase Dynamics Of Locset Control Methodology, Brendan Neschke
Masters Theses
Single-mode fiber amplifiers produce diffraction-limited beams very efficiently. Maximum beam intensity requires that an array of these amplifiers have their beams coherently combined at the target. Optical path differences and noise adversely affect beam quality. An existing closed loop phase control methodology, called the locking of optical coherence by single-detector electronic-frequency tagging (LOCSET), corrects phase errors in real time by electronically detecting path length differences and sending signals to lithium niobate phase adjusters. Broadening the line-width using “jitter” of the input signal can increase the output power of an individual amplifier by suppressing nonlinearity. The system dynamics of LOCSET are …
Day Of The Week Effect In Returns And Volatility Of The S&P 500 Sector Indices, Juan Liu
Day Of The Week Effect In Returns And Volatility Of The S&P 500 Sector Indices, Juan Liu
Masters Theses
"Previous studies have shown that returns associated with the stock market or foreign exchange's futures show variations across the day of the week. On such study, that employs a modified GARCH model for estimation, shows that returns associated with the S&P 500 stock index is highest on Wednesday and lowest returns on Monday. The same study shows that volatility is highest on Fridays and lowest on Wednesdays. In this study we investigate if this day-of-the-week effect on returns and volatility is present in the different sectors that constitute the S&P 500 index. The data set used provides daily returns from …
A Glance At Tropical Operations And Tropical Linear Algebra, Semere Tsehaye Tesfay
A Glance At Tropical Operations And Tropical Linear Algebra, Semere Tsehaye Tesfay
Masters Theses
The tropical semiring is ℝ ∪ {∞} with the operations x ⊕ y = min{x, y}, x ⊕ ∞ = ∞ ⊕ x = x, x ⊙ y = x + y, x ⊙ ∞ = ∞ ⊙ y = ∞. This paper explores how ideas from classical algebra and linear algebra over the real numbers such as polynomials, roots of polynomials, lines, matrices and matrix operations, determinants, eigen values and eigen vectors would appear in tropical mathematics. It uses numerous computed examples to illustrate these concepts and explores the relationship between certain tropical matrices and graph …
Generation And Validation Of Optimal Topologies For Solid Freeform Fabrication, Purnajyoti Bhaumik
Generation And Validation Of Optimal Topologies For Solid Freeform Fabrication, Purnajyoti Bhaumik
Masters Theses
"The study of fabricating topologically optimized parts is presented hereafter. The mapping of topology optimization results for Standard Tessellation Language (STL) writing would enable the solid freeform fabrication of lightweight mechanisms. Aerospace leaders such as NASA, Boeing, Airbus, European Aeronautic Defense And Space Company (EADS), and GE Aero invest in topology optimization research for the production of lightweight materials. Certain concepts such as microstructural homogenization, discretization, and mapping are reviewed and presented in the context of topology optimization. Future biomedical applications of solid freeform fabrication such as organ printing stand to save millions of lives through the robust development of …
Some Combinatorial Applications Of Sage, An Open Source Program, Jessica Ruth Chowning
Some Combinatorial Applications Of Sage, An Open Source Program, Jessica Ruth Chowning
Masters Theses
"In this thesis, we consider the usefulness of Sage, an online and open-source program, in analyzing permutation puzzles such as the Rubik's cube and a specific combinatorial structure called the projective plane. Many programs exist to expedite calculations in research and provide previously-unavailable solutions; some require purchase, while others, such as Sage, are available for free online. Sage is asked to handle a small permutation puzzle called Swap, and then we explore how it calculates solutions for a Rubik's cube. We then discuss projective planes, Sage's library of functions for dealing with projective planes, and how they relate to the …
Hyperbolic Geometry With And Without Models, Chad Kelterborn
Hyperbolic Geometry With And Without Models, Chad Kelterborn
Masters Theses
We explore the development of hyperbolic geometry in the 18th and early 19th following the works of Legendre, Lambert, Saccheri, Bolyai, Lobachevsky, and Gauss. In their attempts to prove Euclid's parallel postulate, they developed hyperbolic geometry without a model. It was not until later in the 19th century, when Felix Klein provided a method (which was influenced by projective geometry) for viewing the hyperbolic plane as a disk in the Euclidean plane, appropriately named the "Klein disk model". Later other models for viewing the hyperbolic plane as a subset of the Euclidean plane were created, namely the Poincaré disk model, …