Open Access. Powered by Scholars. Published by Universities.®
![Digital Commons Network](http://assets.bepress.com/20200205/img/dcn/DCsunburst.png)
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Keyword
-
- Active Feedback (1)
- Coarse geometry (1)
- Control Theory (1)
- Dedekind (1)
- Existence (1)
-
- General Relativity (1)
- Injective envelopes (1)
- Kuramoto Model (1)
- LOCSET (1)
- Laser Array (1)
- Lip(1/2) norm (1)
- Loewner equation (1)
- Mathematics (1)
- Noetherian (1)
- Ring (1)
- Scales (1)
- Semi-simple (1)
- Semigroup (1)
- Space-filling curves (1)
- Spherically symmetric (1)
- Static (1)
- Stellar model (1)
- System Dynamics (1)
- Uniform topology (1)
- Uniqueness (1)
- Zero-divisor (1)
- Zero-divisor graph (1)
Articles 1 - 6 of 6
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 …
Geometry Of Scales, Kyle Stephen Austin
Geometry Of Scales, Kyle Stephen Austin
Doctoral Dissertations
The geometry of coverings has widely been used throughout mathematics and it has recently been a promising tool for resolving longstanding problems in topological rigidity such as the Novikov conjecture and Gromov's positive scalar curvature conjecture. We discuss rigidity conjectures and how large scale geometry is being applied in order to resolve them for important cases.
Not only is small scale and large scale geometry very applicable to understanding global geometry of objects, but it is an interesting topic in its own right. The first chapter of this paper is devoted to building a framework for small scale geometry alongside …
The Congruence-Based Zero-Divisor Graph, Elizabeth Fowler Lewis
The Congruence-Based Zero-Divisor Graph, Elizabeth Fowler Lewis
Doctoral Dissertations
Let R be a commutative ring with nonzero identity and ~ a multiplicative congruence relation on R. Then, R/~ is a semigroup with multiplication [x][y] = [xy], where [x] is the congruence class of an element x of R. We define the congruence-based zero-divisor graph of R ito be the simple graph with vertices the nonzero zero-divisors of R/~ and with an edge between distinct vertices [x] and [y] if and only if [x][y] = [0]. Examples include the usual …
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 …
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 …
Loewner Space-Filling Curves, Hannah Marie Clark
Loewner Space-Filling Curves, Hannah Marie Clark
Chancellor’s Honors Program Projects
No abstract provided.