Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Keyword
-
- Weakly holomorphic modular forms (2)
- (trans- finitely valued) Euclidean domain (1)
- Admissible primes (1)
- Algebraic topology (1)
- Automorphism (1)
-
- Bass-Serre (1)
- Boussinesq equations (1)
- Bruinier-Funke pairing (1)
- Clean index (1)
- Clean rings (1)
- Combinatorial Game Theory (1)
- Computational fluid dynamics (1)
- Congruences (1)
- Conjugacy (1)
- Control Theory (1)
- Convection (1)
- Covering space (1)
- Data assimilation (1)
- Dedalus (1)
- Equitable Partition (1)
- Foliations (1)
- Fourier coefficients (1)
- Fundamental group (1)
- Group Rings (1)
- Harmonic Maass forms (1)
- Homotopy (1)
- Indecomposable ordinal (1)
- Invariant manifolds (1)
- Inverse limit (1)
- Isospectral Network Reduction (1)
Articles 1 - 12 of 12
Full-Text Articles in Physical Sciences and Mathematics
Clean Indices Of Common Rings, Benjamin L. Schoonmaker
Clean Indices Of Common Rings, Benjamin L. Schoonmaker
Theses and Dissertations
Lee and Zhou introduced the clean index of rings in 2004. Motivated by this work, Basnet and Bhattacharyya introduced both the weak clean index of rings and the nil clean index of rings and Cimpean and Danchev introduced the weakly nil clean index of rings. In this work, we calculate each of these indices for the rings ℤ/nℤ and matrix rings with entries in ℤ/nℤ. A generalized index is also introduced.
Model Predictive Linear Control With Successive Linearization, Jesse Robert Friedbaum
Model Predictive Linear Control With Successive Linearization, Jesse Robert Friedbaum
Theses and Dissertations
Robots have been a revolutionizing force in manufacturing in the 20th and 21st century but have proven too dangerous around humans to be used in many other fields including medicine. We describe a new control algorithm for robots developed by the Brigham Young University Robotics and Dynamics and Robotics Laboratory that has shown potential to make robots less dangerous to humans and suitable to work in more applications. We analyze the computational complexity of this algorithm and find that it could be a feasible control for even the most complicated robots. We also show conditions for a system which guarantee …
Adding Limit Points To Bass-Serre Graphs Of Groups, Alexander Jin Shumway
Adding Limit Points To Bass-Serre Graphs Of Groups, Alexander Jin Shumway
Theses and Dissertations
We give a brief overview of Bass-Serre theory and introduce a method of adding a limit point to graphs of groups. We explore a basic example of this method, and find that while the fundamental theorem of Bass-Serre theory no longer applies in this case we still recover a group action on a covering space of sorts with a subgroup isomorphic to the fundamental group of our new base space with added limit point. We also quantify how much larger the fundamental group of a graph of groups becomes after this construction, and discuss the effects of adding and identifying …
Euclidean Domains, Vandy Jade Tombs
Euclidean Domains, Vandy Jade Tombs
Theses and Dissertations
In the usual definition of a Euclidean domain, a ring has a norm function whose codomain is the positive integers. It was noticed by Motzkin in 1949 that the codomain could be replaced by any well-ordered set. This motivated the study of transfinite Euclidean domains in which the codomain of the norm function is replaced by the class of ordinals. We prove that there exists a (transfinitely valued) Euclidean Domain with Euclidean order type for every indecomposable ordinal. Modifying the construction, we prove that there exists a Euclidean Domain with no multiplicative norm. Following a definition of Clark and Murty, …
Finding Torsion-Free Groups Which Do Not Have The Unique Product Property, Lindsay Jennae Soelberg
Finding Torsion-Free Groups Which Do Not Have The Unique Product Property, Lindsay Jennae Soelberg
Theses and Dissertations
This thesis discusses the Kaplansky zero divisor conjecture. The conjecture states that a group ring of a torsion-free group over a field has no nonzero zero divisors. There are situations for which this conjecture is known to hold, such as linearly orderable groups, unique product groups, solvable groups, and elementary amenable groups. This paper considers the possibility that the conjecture is false and there is some counterexample in existence. The approach to searching for such a counterexample discussed here is to first find a torsion-free group that has subsets A and B such that AB has no unique product. We …
Data Assimilation In The Boussinesq Approximation For Mantle Convection, Shane Alexander Mcquarrie
Data Assimilation In The Boussinesq Approximation For Mantle Convection, Shane Alexander Mcquarrie
Theses and Dissertations
Many highly developed physical models poorly approximate actual physical systems due to natural random noise. For example, convection in the earth's mantle—a fundamental process for understanding the geochemical makeup of the earth's crust and the geologic history of the earth—exhibits chaotic behavior, so it is difficult to model accurately. In addition, it is impossible to directly measure temperature and fluid viscosity in the mantle, and any indirect measurements are not guaranteed to be highly accurate. Over the last 50 years, mathematicians have developed a rigorous framework for reconciling noisy observations with reasonable physical models, a technique called data assimilation. …
Congruences For Fourier Coefficients Of Modular Functions Of Levels 2 And 4, Eric Brandon Moss
Congruences For Fourier Coefficients Of Modular Functions Of Levels 2 And 4, Eric Brandon Moss
Theses and Dissertations
We give congruences modulo powers of 2 for the Fourier coefficients of certain level 2 modular functions with poles only at 0, answering a question posed by Andersen and Jenkins. The congruences involve a modulus that depends on the binary expansion of the modular form's order of vanishing at infinity. We also demonstrate congruences for Fourier coefficients of some level 4 modular functions.
The Arithmetic Of Modular Grids, Grant Steven Molnar
The Arithmetic Of Modular Grids, Grant Steven Molnar
Theses and Dissertations
Let Mk(∞) (Gamma, nu) denote the space of weight k weakly holomorphic weight modular forms with poles only at the cusp (∞), and let widehat Mk(∞) (Gamma, nu) subseteq Mk(∞) (Gamma, nu) denote the space of weight k weakly holomorphic modular forms in Mk(∞) (Gamma, nu) which vanish at every cusp other than (∞). We construct canonical bases for these spaces in terms of Maass--Poincaré series, and show that the coefficients of these bases satisfy Zagier duality.
Network Specializations, Symmetries, And Spectral Properties, Dallas C. Smith
Network Specializations, Symmetries, And Spectral Properties, Dallas C. Smith
Theses and Dissertations
In this dissertation, we introduce three techniques for network sciences. The first of these techniques is a series of new models for describing network growth. These models, called network specialization models, are built with the idea that networks grow by specializing the function of subnetworks. Using these models we create theoretical networks which exhibit well-known properties of real networks. We also demonstrate how the spectral properties are preserved as the models grow. The second technique we describe is a method for decomposing networks that contain automorphisms in a way that preserves the spectrum of the original graph. This method …
Dynamics For A Random Differential Equation: Invariant Manifolds, Foliations, And Smooth Conjugacy Between Center Manifolds, Junyilang Zhao
Dynamics For A Random Differential Equation: Invariant Manifolds, Foliations, And Smooth Conjugacy Between Center Manifolds, Junyilang Zhao
Theses and Dissertations
In this dissertation, we first prove that for a random differential equation with the multiplicative driving noise constructed from a Q-Wiener process and the Wiener shift, which is an approximation to a stochastic evolution equation, there exists a unique solution that generates a local dynamical system. There also exist a local center, unstable, stable, centerunstable, center-stable manifold, and a local stable foliation, an unstable foliation on the center-unstable manifold, and a stable foliation on the center-stable manifold, the smoothness of which depend on the vector fields of the equation. In the second half of the dissertation, we show that any …
Subtraction Games: Range And Strict Periodicity, Bryce Emerson Blackham
Subtraction Games: Range And Strict Periodicity, Bryce Emerson Blackham
Theses and Dissertations
In this paper I introduce some background for subtraction games and explore the Sprague-Grundy functions defined on them. I exhibit some subtraction games where the functions are guaranteed to be strictly periodic. I also exhibit a class of subtraction games which have bounded range, and show there are uncountably many of these.
A New Family Of Topological Invariants, Nicholas Guy Larsen
A New Family Of Topological Invariants, Nicholas Guy Larsen
Theses and Dissertations
We define an extension of the nth homotopy group which can distinguish a larger class of spaces. (E.g., a converging sequence of disjoint circles and the disjoint union of countably many circles, which have isomorphic fundamental groups, regardless of choice of basepoint.) We do this by introducing a generalization of homotopies, called component-homotopies, and defining the nth extended homotopy group to be the set of component-homotopy classes of maps from compact subsets of (0,1)n into a space, with a concatenation operation. We also introduce a method of tree-adjoinment for "connecting" disconnected metric spaces and show how this method can …