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Articles 1 - 9 of 9
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Finite Blaschke Products: A Survey, Stephan Ramon Garcia, Javad Mashreghi, William T. Ross
Finite Blaschke Products: A Survey, Stephan Ramon Garcia, Javad Mashreghi, William T. Ross
Department of Math & Statistics Faculty Publications
A finite Blaschke product is a product of finitely many automorphisms of the unit disk. This brief survey covers some of the main topics in the area, including characterizations of Blaschke products, approximation theorems, derivatives and residues of Blaschke products, geometric localization of zeros, and selected other topics.
Multipliers Between Model Spaces, Emmanuel Fricain, Andreas Hartmann, William T. Ross
Multipliers Between Model Spaces, Emmanuel Fricain, Andreas Hartmann, William T. Ross
Department of Math & Statistics Faculty Publications
In this paper we examine the multipliers from one model space to another.
The Range And Valence Of A Real Smirnov Function, Timothy Ferguson, William T. Ross
The Range And Valence Of A Real Smirnov Function, Timothy Ferguson, William T. Ross
Department of Math & Statistics Faculty Publications
We give a complete description of the possible ranges of real Smirnov functions (quotients of two bounded analytic functions on the open unit disk where the denominator is outer and such that the radial boundary values are real almost everywhere on the unit circle). Our techniques use the theory of unbounded symmetric Toeplitz operators, some general theory of unbounded symmetric operators, classical Hardy spaces, and an application of the uniformization theorem. In addition, we completely characterize the possible valences for these real Smirnov functions when the valence is finite. To do so we construct Riemann surfaces we call disk trees …
A Probability Model For Strategic Bidding On The Price Is Right, Paul H. Kvam
A Probability Model For Strategic Bidding On The Price Is Right, Paul H. Kvam
Department of Math & Statistics Faculty Publications
The TV game show “The Price is Right” features a bidding auction called “Contestants’ Row” that rewards the player (out of 4) who bids closest to an item’s value, without overbidding. This paper considers ways in which players can maximize a winning probability based on the player's bidding order. We consider marginal strategies in which players assume opponents are bidding individually perceived values of the merchandise. Based on preceding bids of others, players have information available to create strategies. We consider conditional strategies in which players adjust bids knowing other players are using strategies. The last bidder has a large …
Multipliers Between Model Spaces, Emmanuel Fricain, Andreas Hartmann, William T. Ross
Multipliers Between Model Spaces, Emmanuel Fricain, Andreas Hartmann, William T. Ross
Department of Math & Statistics Faculty Publications
In this paper we examine the multipliers from one model space to another.
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.
Range Spaces Of Co-Analytic Toeplitz Operators, Emmanuel Fricain, Andreas Hartmann, William T. Ross
Range Spaces Of Co-Analytic Toeplitz Operators, Emmanuel Fricain, Andreas Hartmann, William T. Ross
Department of Math & Statistics Faculty Publications
In this paper we discuss the range of a co-analytic Toeplitz operator. These range spaces are closely related to de Branges-Rovnyak spaces (in some cases they are equal as sets). In order to understand its structure, we explore when the range space decomposes into the range of an associated analytic Toeplitz operator and an identifiable orthogonal complement. For certain cases, we compute this orthogonal complement in terms of the kernel of a certain Toeplitz operator on the Hardy space, where we focus on when this kernel is a model space (backward shift invariant subspace). In the spirit of Ahern-Clark, we …
Equivalence Of Edge Bicolored Graphs On Surfaces, Oliver T. Dasbach, Heather M. Russell
Equivalence Of Edge Bicolored Graphs On Surfaces, Oliver T. Dasbach, Heather M. Russell
Department of Math & Statistics Faculty Publications
Consider the collection of edge bicolorings of a graph that are cellularly embedded on an orientable surface. In this work, we count the number of equivalence classes of such colorings under two relations: reversing colors around a face and reversing colors around a vertex. In the case of the plane, this is well studied, but for other surfaces, the computation is more subtle. While this question can be stated purely graph theoretically, it has interesting applications in knot theory.
Developing A Minimally Structured Mathematical Mode Of Cancer Treatment With Oncolytic Viruses And Dendritic Cell Injections, Jane L. Gevertz, Joanna R. Wares
Developing A Minimally Structured Mathematical Mode Of Cancer Treatment With Oncolytic Viruses And Dendritic Cell Injections, Jane L. Gevertz, Joanna R. Wares
Department of Math & Statistics Faculty Publications
Mathematical models of biological systems must strike a balance between being sufficiently complex to capture important biological features, while being simple enough that they remain tractable through analysis or simulation. In this work, we rigorously explore how to balance these competing interests when modeling murine melanoma treatment with oncolytic viruses and dendritic cell injections. Previously, we developed a system of six ordinary differential equations containing fourteen parameters that well describes experimental data on the efficacy of these treatments. Here, we explore whether this previously developed model is the minimal model needed to accurately describe the data. Using a variety of …