Hankel Vector Moment Sequences And The Non-Tangential Regularity At Infinity Of Two Variable Pick Functions,
2014
University of California - San Diego
Hankel Vector Moment Sequences And The Non-Tangential Regularity At Infinity Of Two Variable Pick Functions, Jim Agler, John E. Mccarthy
Mathematics Faculty Research
A Pick function of variables is a holomorphic map from to , where is the upper halfplane. Some Pick functions of one variable have an asymptotic expansion at infinity, a power series with real numbers that gives an asymptotic expansion on non-tangential approach regions to infinity. In 1921 H. Hamburger characterized which sequences can occur. We give an extension of Hamburger's results to Pick functions of two variables.
Multi-Peak Solutions To Two Types Of Free Boundary Problems,
2014
Wright State University - Main Campus
Multi-Peak Solutions To Two Types Of Free Boundary Problems, Yi Li, Shuangjie Peng
Mathematics and Statistics Faculty Publications
We consider the existence of multi-peak solutions to two types of free boundary problems arising in confined plasma and steady vortex pair under conditions on the nonlinearity we believe to be almost optimal. Our results show that the “core” of the solution has multiple connected components, whose boundary called free boundary of the problems consists approximately of spheres which shrink to distinct single points as the parameter tends to zero.
A Reduced Set Of Moves On One-Vertex Ribbon Graphs Coming From Links,
2014
University of Richmond
A Reduced Set Of Moves On One-Vertex Ribbon Graphs Coming From Links, Heather M. Russell, Susan Abernathy, Cody Armond, Moshe Cohen, Oliver T. Dasbach, Hannah Manuel, Chris Penn, Neal W. Stoltzfus
Department of Math & Statistics Faculty Publications
Every link in R3 can be represented by a one-vertex ribbon graph. We prove a Markov type theorem on this subset of link diagrams.
Promoting Reu Participation From Students In Underrepresented Groups,
2014
University of Richmond
Promoting Reu Participation From Students In Underrepresented Groups, Heather M. Russell, Heather A. Dye
Department of Math & Statistics Faculty Publications
Research experiences for undergraduates (REUs) are an important component of undergraduate education. However, at the 2012 Trends in Undergraduate Research in the Mathematical Sciences conference, questions were raised about why many REU programs see few applications from students that are members of underrepresented groups. We examine the benefits of REUs and factors preventing or promoting participation in REUs.
Stability And Bifurcation Of Equilibria For The Axisymmetric Averaged Mean Curvature Flow,
2014
University of Richmond
Stability And Bifurcation Of Equilibria For The Axisymmetric Averaged Mean Curvature Flow, Jeremy Lecrone
Department of Math & Statistics Faculty Publications
We study the averaged mean curvature ow, also called the volume preserving mean curvature ow, in the particular setting of axisymmetric surfaces embedded in R3 satisfying periodic boundary conditions. We establish analytic well-posedness of the ow within the space of little-Holder continuous surfaces, given rough initial data. We also establish dynamic properties of equilibria, including stability, instability, and bifurcation behavior of cylinders, where the radius acts as a bifurcation parameter.
C*-Algebras Generated By Truncated Toeplitz Operators,
2014
University of Richmond
C*-Algebras Generated By Truncated Toeplitz Operators, William T. Ross, Stephan Ramon Garcia, Warren R. Wogen
Department of Math & Statistics Faculty Publications
We obtain an analogue of Coburn’s description of the Toeplitz algebra in the setting of truncated Toeplitz operators. As a byproduct, we provide several examples of complex symmetric operators which are not unitarily equivalent to truncated Toeplitz operators having continuous symbols.
Bad Boundary Behavior In Star Invariant Subspaces I,
2014
University of Richmond
Bad Boundary Behavior In Star Invariant Subspaces I, William T. Ross, Andreas Hartmann
Department of Math & Statistics Faculty Publications
We discuss the boundary behavior of functions in star invariant subspaces (BH2)1, where B is a Blaschke product. Extending some results of Ahern and Clark, we are particularly interested in the growth rates of functions at points of the spectrum of B where B does not admit a derivative in the sense of Carathéodory.
A Twisted Dimer Model For Knots,
2014
University of Richmond
A Twisted Dimer Model For Knots, Heather M. Russell, Moshe Cohen, Oliver Dasbach
Department of Math & Statistics Faculty Publications
We develop a dimer model for the Alexander polynomial of a knot. This recovers Kauffman's state sum model for the Alexander polynomial using the language of dimers. By providing some additional structure we are able to extend this model to give a state sum formula for the twisted Alexander polynomial of a knot depending on a representation of the knot group.
Global Existence And Finite Time Blow-Up In A Class Of Stochastic Nonlinear Wave Equations,
2014
Clarkson University
Global Existence And Finite Time Blow-Up In A Class Of Stochastic Nonlinear Wave Equations, Rana D. Parshad, Matthew Beauregard, Aslan Kasimov, Belkacem Said-Houari
Faculty Publications
We consider a stochastic extension of a class of wave equations with nonlinear viscoelastic damping and nonlinear forcing. We show the global existence of the solution of the stochastic equation and, additionally, when the source term dominates the damping term and when the initial data are large enough, we show that the expected value of the L p norm of the solution, blows up in finite time. In the presence of noise, we extend the previously known range of initial data corresponding to blow-up. Furthermore we use a spectral stochastic Galerkin method to perform numerical simulations that verify certain special …
Adaptive Wavelet Discretization Of Tensor Products In H-Tucker Format,
2014
Missouri University of Science and Technology
Adaptive Wavelet Discretization Of Tensor Products In H-Tucker Format, Mazen Ali
Masters Theses
"In previous work, the solution to a system of coupled parabolic PDEs, modeling the price of a CDO, was approximated numerically. Due to the nature of the problem, the system involved a large number of equations such that the parameters cannot be stored explicitly. The authors combined the data sparse H-Tucker storage format with the Galerkin method to approximate the solution, using wavelets for the space discretization together with time stepping (Method of Lines). The aforementioned approximation is of the linear kind, i.e., using a nonadaptive method. In this work, three methods for solving such systems adaptively are presented, together …
An Iterative Algorithm For Variational Data Assimilation Problems,
2014
Missouri University of Science and Technology
An Iterative Algorithm For Variational Data Assimilation Problems, Xin Shen
Masters Theses
"Data assimilation is a very powerful and efficient tool to use collected raw data for improving model prediction in numerical weather forecasting, hydrology, and many other areas of geosciences. In this thesis, an iterative algorithm [23] of variational data assimilation with finite element method is utilized to study different models. One motivation for this fundamental mathematical study is to provide a potential tool for simulation of CO2 sequestration by extending it to more realistic and sophisticated models in the future. The basic idea of variational data assimilation is to utilize the framework of optimal control problems. We apply the …
Rainbow Generalizations Of Ramsey Theory - A Dynamic Survey,
2014
Maebashi Institute of Technology, Maebashi, Japan
Rainbow Generalizations Of Ramsey Theory - A Dynamic Survey, Shinya Fujita, Colton Magnant, Yaping Mao, Kenta Ozeki
Theory & Applications of Graphs
In this work, we collect Ramsey-type results concerning rainbow edge colorings of graphs.
Differences In Beliefs Across A Series Of Four Mathematics Content Courses,
2014
Kennesaw State University
Differences In Beliefs Across A Series Of Four Mathematics Content Courses, Susanna Molitoris Miller, Caitlin Walkey
Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators
College students often ask questions such as, “Why do I have to take this class? Is there a point to it?” For Early Childhood Education (ECE) majors these questions may often take on a slightly different form, wondering, “How can I incorporate this information into my classroom?” or “Do I understand this well enough to teach this to my students?” It is especially important for pre- service teachers to feel confident working with the mathematical content that they are learning and for them to believe that they can successfully teach that same information to a group of students. Swackhamer, Koellner, …
Weak Isometries Of Hamming Spaces,
2014
Michigan Technological University
Weak Isometries Of Hamming Spaces, Ryan Walter Bruner
Dissertations, Master's Theses and Master's Reports - Open
In this thesis we study weak isometries of Hamming spaces. These are permutations of a Hamming space that preserve some but not necessarily all distances. We wish to find conditions under which a weak isometry is in fact an isometry. This type of problem was first posed by Beckman and Quarles for Rn. In chapter 2 we give definitions pertinent to our research. The 3rd chapter focuses on some known results in this area with special emphasis on papers by V. Krasin as well as S. De Winter and M. Korb who solved this problem for the Boolean …
Study Of A Direct Sampling Method For The Inverse Medium Scattering Problem,
2014
Michigan Technological University
Study Of A Direct Sampling Method For The Inverse Medium Scattering Problem, Natasha Weerasinghe
Dissertations, Master's Theses and Master's Reports - Open
Direct sampling methods are increasingly being used to solve the inverse medium scattering problem to estimate the shape of the scattering object. A simple direct method using one incident wave and multiple measurements was proposed by Ito, Jin and Zou. In this report, we performed some analytic and numerical studies of the direct sampling method. The method was found to be effective in general. However, there are a few exceptions exposed in the investigation. Analytic solutions in different situations were studied to verify the viability of the method while numerical tests were used to validate the effectiveness of the method.
Rank-Based Two Sample Tests Under A General Alternative,
2014
University of Mississippi
Rank-Based Two Sample Tests Under A General Alternative, Jamye Curry
Electronic Theses and Dissertations
The problem of testing whether two samples come from the same or different population is a classical one in statistics. In this dissertation, I first study rank based formulation of univariate two-sample distribution-free tests. One form of the test statistic is the average of between-group distances of ranks. The other form of the test statistic is the difference between the average of between-group distances of ranks and the average of within-group distances of ranks. Although they are different in formulation, they are closely related to the two-sample Cramer-von Mises criterion. The first one is a linear transformation of Cramer-von Mises …
New Techniques To Analyse The Prediction Of Fuzzy Models,
2014
University of New Mexico
New Techniques To Analyse The Prediction Of Fuzzy Models, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral
Branch Mathematics and Statistics Faculty and Staff Publications
For the first time authors have ventured to study, analyse and investigate the properties of the fuzzy models, the experts opinion and so on. Here the concept of merged Fuzzy Cognitive Maps and Neutrosophic Cognitive Maps are carried out, which are based on merged graphs and merged matrices. This concept is better than the usual combined Fuzzy Cognitive Maps. Further by this new technique we are able to give equal importance to all the experts who work with the problem. Here the new concept of New Average Fuzzy Cognitive Maps and Neutrosophic Cognitive Maps is defined and described. This new …
New Research On Neutrosophic Algebraic Structures,
2014
University of New Mexico
New Research On Neutrosophic Algebraic Structures, Florentin Smarandache, Mumtaz Ali, Muhammad Shabir
Branch Mathematics and Statistics Faculty and Staff Publications
In this book, we define several new neutrosophic algebraic structures and their related properties. The main focus of this book is to study the important class of neutrosophic rings such as neutrosophic LA-semigroup ring, neutrosophic loop ring, neutrosophic groupoid ring and so on. We also construct their generalization in each case to study these neutrosophic algebraic structures in a broader sense. The indeterminacy element “ I “ gives rise to a more bigger algebraic structure than the classical algebraic structures. It mainly classifies the algebraic structures in three categories: such as neutrosophic algebraic structures, strong neutrosophic algebraic structures, and classical …
Some Properties Of The Harmonic Quadrilateral,
2014
University of New Mexico
Some Properties Of The Harmonic Quadrilateral, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
In this article, we review some properties of the harmonic quadrilateral related to triangle simedians and to Apollonius circles.
On Crittenden And Vanden Eynden's Conjecture,
2014
University of New Mexico
On Crittenden And Vanden Eynden's Conjecture, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
It is possible to cover all (positive) integers with n geometrical progressions of integers? Find a necessary and sufficient condition for a general class of positive integer sequences such that, for a fixed n , there are n (distinct) sequences of this class which cover all integers.
