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Length Bias Estimation Of Small Businesses Lifetime, Simeng Li
Length Bias Estimation Of Small Businesses Lifetime, Simeng Li
Honors Theses
Small businesses, particularly restaurants, play a crucial role in the economy by generating employment opportunities, boosting tourism, and contributing to the local economy. However, accurately estimating their lifetimes can be challenging due to the presence of length bias, which occurs when the likelihood of sampling any particular restaurant's closure is influenced by its duration in operation. To address the issue, this study conducts goodness-of-fit tests on exponential/gamma family distributions and employs the Kaplan-Meier method to more accurately estimate the average lifetime of restaurants in Carytown. By providing insights into the challenges of estimating the lifetimes of small businesses, this study …
Mean Value Theorems For Riemannian Manifolds Via The Obstacle Problem, Brian Benson, Ivan Blank, Jeremy Lecrone
Mean Value Theorems For Riemannian Manifolds Via The Obstacle Problem, Brian Benson, Ivan Blank, Jeremy Lecrone
Department of Math & Statistics Faculty Publications
We develop some of the basic theory for the obstacle problem on Riemannian manifolds, and we use it to establish a mean value theorem. Our mean value theorem works for a very wide class of Riemannian manifolds and has no weights at all within the integral.
Optimal Weak Parallelogram Constants For L-P Spaces, Raymond Cheng, Javad Mashreghi, William T. Ross
Optimal Weak Parallelogram Constants For L-P Spaces, Raymond Cheng, Javad Mashreghi, William T. Ross
Department of Math & Statistics Faculty Publications
Inspired by Clarkson's inequalities for L-p and continuing work from [5], this paper computes the optimal constant C in the weak parallelogram laws parallel to f + g parallel to(r )+ C parallel to f - g parallel to(r )= 2(r-1 )(parallel to f parallel to(r) + parallel to g parallel to(r)) for the L-p spaces, 1 < p < infinity.
A Survey On Reverse Carleson Measures, Emmanuel Fricain, Andreas Hartmann, William T. Ross
A Survey On Reverse Carleson Measures, Emmanuel Fricain, Andreas Hartmann, William T. Ross
Department of Math & Statistics Faculty Publications
This is a survey on reverse Carleson measures for various Hilbert spaces of analytic functions. These spaces include the Hardy, Bergman, certain harmonically weighted Dirichlet, Paley-Wiener, Fock, model (backward shift invariant), and de Branges-Rovnyak spaces. The reverse Carleson measure for backward shift invariant subspaces in the non-Hilbert situation is new.
Bad Boundary Behavior In Star Invariant Subspaces I, William T. Ross, Andreas Hartmann
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, Heather M. Russell, Moshe Cohen, Oliver Dasbach
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.
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
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.
Model Spaces: A Survey, William T. Ross, Stephan Ramon Garcia
Model Spaces: A Survey, William T. Ross, Stephan Ramon Garcia
Department of Math & Statistics Faculty Publications
This is a brief and gentle introduction, aimed at graduate students, to the subject of model subspaces of the Hardy space.
Oddification Of The Cohomology Of Type A Springer Varieties, Heather M. Russell, Aaron D. Lauda
Oddification Of The Cohomology Of Type A Springer Varieties, Heather M. Russell, Aaron D. Lauda
Department of Math & Statistics Faculty Publications
We identify the ring of odd symmetric functions introduced by Ellis and Khovanov as the space of skew polynomials fixed by a natural action of the Hecke algebra at q = −1. This allows us to define graded modules over the Hecke algebra at q = −1 that are ‘odd’ analogs of the cohomology of type A Springer varieties. The graded module associated to the full flag variety corresponds to the quotient of the skew polynomial ring by the left ideal of nonconstant odd symmetric functions. The top degree component of the odd cohomology of Springer varieties is identifiedwith the …
Model Spaces: A Survey, William T. Ross, Stephan Ramon Garcia
Model Spaces: A Survey, William T. Ross, Stephan Ramon Garcia
Department of Math & Statistics Faculty Publications
This is a brief and gentle introduction, aimed at graduate students, to the subject of model subspaces of the Hardy space.
Direct And Reverse Carleson Measure For Hb Spaces, William T. Ross, Alain Blandigneres, Emmanuel Fricain, Frederic Gaunard, Andreas Hartmann
Direct And Reverse Carleson Measure For Hb Spaces, William T. Ross, Alain Blandigneres, Emmanuel Fricain, Frederic Gaunard, Andreas Hartmann
Department of Math & Statistics Faculty Publications
In this paper we discuss direct and reverse Carleson measures for the de Branges-Rovnyak spaces H(b), mainly when b is a non-extreme point of the unit ball of H∞.
On A Theorem Of Livsic, William T. Ross, Alexandru Aleman, R. T. W. Martin
On A Theorem Of Livsic, William T. Ross, Alexandru Aleman, R. T. W. Martin
Department of Math & Statistics Faculty Publications
The theory of symmetric, non-selfadjoint operators has several deep applications to the complex function theory of certain reproducing kernel Hilbert spaces of analytic functions, as well as to the study of ordinary differential operators such as Schrodinger operators in mathematical physics. Examples of simple symmetric operators include multiplication operators on various spaces of analytic functions such as model subspaces of Hardy spaces, deBranges-Rovnyak spaces and Herglotz spaces, ordinary differential operators (including Schrodinger operators from quantum mechanics), Toeplitz operators, and infinite Jacobi matrices.
In this paper we develop a general representation theory of simple symmetric operators with equal deficiency indices, and …
Boundary Values In Range Spaces Of Co-Analytic Truncated Toeplitz Operator, William T. Ross, Andreas Hartmann
Boundary Values In Range Spaces Of Co-Analytic Truncated Toeplitz Operator, William T. Ross, Andreas Hartmann
Department of Math & Statistics Faculty Publications
Functions in backward shift invariant subspaces have nice analytic continuation properties outside the spectrum of the inner function defining the space. Inside the spectrum of the inner function, Ahern and Clark showed that under some distribution condition on the zeros and the singular measure of the inner function, it is possible to obtain non-tangential boundary values of every function in the backward shift invariant subspace as well as for their derivatives up to a certain order. Here we will investigate, at least when the inner function is a Blaschke product, the non-tangential boundary values of the functions of the backward …
Springer Representations On The Khovanov Springer Varieties, Heather M. Russell, Julianna Tymoczko
Springer Representations On The Khovanov Springer Varieties, Heather M. Russell, Julianna Tymoczko
Department of Math & Statistics Faculty Publications
Springer varieties are studied because their cohomology carries a natural action of the symmetric group Sn and their top-dimensional cohomology is irreducible. In his work on tangle invariants, Khovanov constructed a family of Springer varieties Xn as subvarieties of the product of spheres (S2)n. We show that if Xn is embedded antipodally in (S2)n then the natural Sn-action on (S2)n induces an Sn-representation on the image of H*(Xn). This representation is the Springer representation. Our construction admits an elementary (and geometrically …
Tree-Like Continua And 2-To-1 Maps, Jo Heath, Van C. Nall
Tree-Like Continua And 2-To-1 Maps, Jo Heath, Van C. Nall
Department of Math & Statistics Faculty Publications
It is not known if there is a 2-to-1 map from a continuum onto a tree-like continuum. In fact, it is not known if there is a 2-to-1 map onto a hereditarily decomposable tree-like continuum. We show that the domain of such a map would have to contain an indecomposable continuum.
[Introduction To] Mathematics Calculus Bc, John R. Hubbard, David R. Arterburn, Michael A. Perl
[Introduction To] Mathematics Calculus Bc, John R. Hubbard, David R. Arterburn, Michael A. Perl
Bookshelf
This book gives you the tools to prepare effectively for the Advanced Placement Examination in Mathematics: Calculus BC. These tools include a concise topical review and six full-length practice tests. Our review succinctly covers areas considered most relevant to this exam. Following each of our tests is an answer key complete with detailed explanations designed to clarify the material for you.
The Set Of Hemispheres Containing A Closed Curve On The Sphere, Mary Kate Boggiano, Mark Desantis
The Set Of Hemispheres Containing A Closed Curve On The Sphere, Mary Kate Boggiano, Mark Desantis
Department of Math & Statistics Technical Report Series
Suppose you get in your car and take a drive on the sphere of radius R, so that when you return to your starting point the odometer indicates you've traveled less than 2πR. Does your path, γ, have to lie in some hemisphere?
This question was presented to us by Dr. Robert Foote of Wabash College. Previous authors chose two points, A and B, on γ such that these points divided γ into two arcs of equal length. Then they took the midpoint of the great circle arc joining A and B to be the North Pole and showed that …
Using The Simplex Code To Construct Relative Difference Sets In 2-Groups, James A. Davis, Surinder K. Sehgal
Using The Simplex Code To Construct Relative Difference Sets In 2-Groups, James A. Davis, Surinder K. Sehgal
Department of Math & Statistics Faculty Publications
Relative Difference Sets with the parameters (2a, 2b, 2a, 2a-b) have been constructed many ways (see [2], [3], [5], [6], and [7] for examples). This paper modifies an example found in [1] to construct a family of relative difference sets in 2-groups that gives examples for b = 2 and b = 3 that have a lower rank than previous examples. The Simplex code is used in the construction.
Hyperinvariant Subspaces Of The Harmonic Dirichlet Space, William T. Ross, Stefan Richter, Carl Sundberg
Hyperinvariant Subspaces Of The Harmonic Dirichlet Space, William T. Ross, Stefan Richter, Carl Sundberg
Department of Math & Statistics Faculty Publications
No abstract provided.