The Implicit Function Theorem And Free Algebraic Sets, 2016 Washington University in St Louis
The Implicit Function Theorem And Free Algebraic Sets, Jim Agler, John E. Mccarthy
Mathematics Faculty Publications
We prove an implicit function theorem for non-commutative functions. We use this to show that if p ( X;Y ) is a generic non-commuting polynomial in two variables, and X is a generic matrix, then all solutions Y of p ( X;Y ) = 0 will commute with X
Duality Of Scales, 2016 University of Tennessee - Knoxville
Duality Of Scales, Michael Christopher Holloway
Doctoral Dissertations
We establish an interaction between the large scale and small scale using two types of maps from large scale spaces to small scale spaces. First we use slowly oscillating maps, which can be described as those having arbitrarily small variation at infinity. These lead to a Galois connection between certain collections of large scale structures and small scale structures on a given set. Slowly oscillating functions can also be used to define to the notion of a dual pair of scale structures on a space. A dual pair consists of a large and a small scale structure on a space …
Non-Compact Solutions To Inverse Mean Curvature Flow In Hyperbolic Space, 2016 University of Tennessee - Knoxville
Non-Compact Solutions To Inverse Mean Curvature Flow In Hyperbolic Space, Brian Daniel Allen
Doctoral Dissertations
We investigate Inverse Mean Curvature Flow (IMCF) of non-compact hypersurfaces in hyperbolic space. Specifically, we look at bounded graphs over horospheres in Hyperbolic space and show long time existence of the flow as well as asymptotic convergence to horospheres. Along the way many important local estimates as well as global estimates are obtained. In addition, we develop a useful family of cutoff functions for IMCF as well as a non-compact ODE maximum principle at infinity which are integral tools used throughout the document.
The Conway Polynomial And Amphicheiral Knots, 2016 University of Tennessee - Knoxville
The Conway Polynomial And Amphicheiral Knots, Vajira Asanka Manathunga
Doctoral Dissertations
The Conant's conjecture [7] which has foundation on the Conway polynomial and Vassiliev invariants is the main theme of this research. The Conant's conjecture claim that the Conway polynomial of amphicheiral knots split over integer modulo 4 space. We prove Conant's conjecture for amphicheiral knots coming from braid closure in certain way. We give several counter examples to a conjecture of A. Stoimenow [32] regarding the leading coefficient of the Conway polynomial. We also construct integer bases for chord diagrams up to order 7 and up to order 6 for Vassiliev invariants. Finally we develop a method to extract integer …
Hankel Operators On The Drury-Arveson Space, 2016 University of Tennessee - Knoxville
Hankel Operators On The Drury-Arveson Space, James Allen Sunkes Iii
Doctoral Dissertations
The Drury-Arveson space, initially introduced in the proof of a generalization of von Neumann's inequality, has seen a lot of research due to its intrigue as a Hilbert space of analytic functions. This space has been studied in the context of Besov-Sobolev spaces, Hilbert spaces with complete Nevanlinna Pick kernels, and Hilbert modules. More recently, McCarthy and Shalit have studied the connections between the Drury-Arveson space and Hilbert spaces of Dirichlet series, and Davidson and Cloutare have established analogues of classic results of the ball algebra to the multiplier algebra for the Drury-Arveson Space.
The goal of this dissertation is …
Completing Partial Latin Squares With One Nonempty Row, Column, And Symbol, 2016 Marshall University
Completing Partial Latin Squares With One Nonempty Row, Column, And Symbol, Jaromy Kuhl, Michael W. Schroeder
Mathematics Faculty Research
Let r,c,s ∈{1,2,…,n} and let PP be a partial latin square of order n in which each nonempty cell lies in row r, column c, or contains symbol s. We show that if n ∉ {3, 4, 5} and row r, column c, and symbol s can be completed in P, then a completion of P exists. As a consequence, this proves a conjecture made by Casselgren and Häggkvist. Furthermore, we show exactly when row r, column c, and symbol s can be completed.
The Entangling Properties Of Knots And Links, 2016 Illinois Mathematics and Science Academy
The Entangling Properties Of Knots And Links, Eshan Mehrotra '17
IMSAloquium Student Investigation Showcase
It has been conjectured that quantum entanglement operators can be lifted to braiding operators by the way of the topological quantum field theory axioms set forth by Witten and Atiyah. Moreover, it can be readily shown that quantum link invariants need entanglement to construct topological invariants. Given these results and the already dense mathematical framework underlying topology and quantum field theory, we propose that, through the usage of quantum algebra and bracket models, we can identify a significant area of overlap where entangling R-matrix solutions to the Yang-Baxter equation can be used to construct invariants of knots and links. Such …
Infinite Color Urn Models., 2016 Indian Statistical Institute
Infinite Color Urn Models., Debleena Thacker Dr.
Doctoral Theses
In recent years, there has been a wide variety of work on random reinforcement models of various kinds. Urn models form an important class of random reinforcement models, with numerous applications in engineering and informatics and bioscience. In recent years there have been several works on different kinds of urn models and their generalizations. For occupancy urn models, where one considers recursive addition of balls into finite or infinite number of boxes, there are some works which introduce models with infinitely many colors, typically represented by the boxes.As observed in [51], the earliest mentions of urn models are in the …
Essays On Strategy-Proofness And Implementation., 2016 Indian Statistical Institute
Essays On Strategy-Proofness And Implementation., Sonal Yadav Dr.
Doctoral Theses
This thesis comprises of three chapters relating to strategy-proofness and implementation. We provide a brief description of each chapter below.1.1 A Hurwicz Type Result in a Model with Public Good Production We consider a two-good model with an arbitrary number of agents. One of the goods is a public good and the other is a private good. Each agent has an endowment of the private good and the private good can be converted into the public good using a well-behaved production function. A Social Choice Function (SCF) associates an allocation with each admissible preference profile. We impose the following requirements …
The Ko-Lee Key Exchange Protocol With Generalized Dihedral Groups, 2016 University of Mary Washington
The Ko-Lee Key Exchange Protocol With Generalized Dihedral Groups, Christopher Lloyd
Student Research Submissions
Given an arbitrary abelian group A, one may form the generalized dihedral group D(A). As D(A) is usually non-abelian, this makes it a possible candidate for use with certain non-commutative key exchange protocols. Specifically, we examine the security of using D(A) with the Ko-Lee key exchange protocol. An appropriate presentation for D(A) is developed alongside methods for computing within the group in the context of the Ko-Lee protocol. Lastly we show that for such groups Ko-Lee is susceptible to a polynomial time attack.
A Comparison Of Methods To Fit A Model To Simultaneous Time Series, 2016 University of Mary Washington
A Comparison Of Methods To Fit A Model To Simultaneous Time Series, Victoria Marie Moore
Student Research Submissions
This research project determines which methods are the most effective for finding a best fit model for simultaneous time series. The type of model used was an Autoregressive Integrated Moving Average (ARIMA) model. Two distinct methods were used when determining what order to assign to the ARIMA model: 1.) using the floor of the average number of autoregressive and moving average terms, and 2.) using the ceiling of the average number of autoregressive and moving average terms. After fitting the model, the Akaike Information Criterion (AIC) value for each method measured the goodness of fit to compare to fitting separate …
Blossom: A Language Built To Grow, 2016 Macalester College
Blossom: A Language Built To Grow, Jeffrey Lyman
Mathematics, Statistics, and Computer Science Honors Projects
No abstract provided.
Dagum-Poisson Distribution: Model, Properties And Application, 2016 Georgia Southern University
Dagum-Poisson Distribution: Model, Properties And Application, Broderick O. Oluyede, Galelhakanelwe Motsewabagale, Shujiao Huang, Gayan Warahena-Liyanage, Marvis Pararai
Department of Mathematical Sciences Faculty Publications
A new four parameter distribution called the Dagum-Poisson (DP) distribution is introduced and studied. This distribution is obtained by compounding Dagum and Poisson distributions. The structural properties of the new distribution are discussed, including explicit algebraic formulas for its survival and hazard functions, quantile function, moments, moment generating function, conditional moments, mean and median deviations, Bonferroni and Lorenz curves, distribution of order statistics and R\'enyi entropy. Method of maximum likelihood is used for estimating the model parameters. A Monte Carlo simulation study is conducted to examine the bias, mean square error of the maximum likelihood estimators and width of the …
Measuring Dependence In Uncertainty Should Start In The Introduction To Probability And Statistics, 2016 Kettering University
Measuring Dependence In Uncertainty Should Start In The Introduction To Probability And Statistics, Boyan N. Dimitrov
Mathematics Presentations And Conference Materials
No abstract provided.
The Chromatic Number Of The Square Of Subcubic Planar Graphs, 2016 University of Colorado, Denver
The Chromatic Number Of The Square Of Subcubic Planar Graphs, Stephen Hartke, Sogol Jahanbekam, Brent Thomas
Faculty Publications
Wegner conjectured in 1977 that the square of every planar graph with maximum degree at most 3 is 7-colorable. We prove this conjecture using the discharging method and computational techniques to verify reducible configurations.
On A Multiple-Choice Guessing Game, 2016 Bethel College - Mishawaka
On A Multiple-Choice Guessing Game, Ryan Cushman, Adam J. Hammett
The Research and Scholarship Symposium (2013-2019)
We consider the following game (a generalization of a binary version explored by Hammett and Oman): the first player (“Ann”) chooses a (uniformly) random integer from the first n positive integers, which is not revealed to the second player (“Gus”). Then, Gus presents Ann with a k-option multiple choice question concerning the number she chose, to which Ann truthfully replies. After a predetermined number m of these questions have been asked, Gus attempts to guess the number chosen by Ann. Gus wins if he guesses Ann’s number. Our goal is to determine every m-question algorithm which maximizes the probability of …
Introductory And Intermediate Algebra Mth 100x, 2016 University of Rhode Island
Introductory And Intermediate Algebra Mth 100x, Joanna Burkhardt
Library Impact Statements
No abstract provided.
Applied Calculus Mth 103x, 2016 University of Rhode Island
Applied Calculus Mth 103x, Joanna Burkhardt
Library Impact Statements
No abstract provided.
Finite Math Mth 107, 2016 University of Rhode Island
Pooling Strength Amongst Limited Datasets Using Hierarchical Bayesian Analysis, With Application To Pyroclastic Density Current Mobility Metrics, 2016 State University of New York at Buffalo
Pooling Strength Amongst Limited Datasets Using Hierarchical Bayesian Analysis, With Application To Pyroclastic Density Current Mobility Metrics, Sarah E. Ogburn, James Berger, Eliza S. Calder, Danilo Lopes, Abani K. Patra, E. Bruce Pitman, Regis Rutarindwa, Elaine Spiller, Robert L. Wolpert
Mathematics, Statistics and Computer Science Faculty Research and Publications
In volcanology, the sparsity of datasets for individual volcanoes is an important problem, which, in many cases, compromises our ability to make robust judgments about future volcanic hazards. In this contribution we develop a method for using hierarchical Bayesian analysis of global datasets to combine information across different volcanoes and to thereby improve our knowledge at individual volcanoes. The method is applied to the assessment of mobility metrics for pyroclastic density currents in order to better constrain input parameters and their related uncertainties for forward modeling. Mitigation of risk associated with such flows depends upon accurate forecasting of possible inundation …