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University of Richmond

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2013

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Articles 31 - 35 of 35

Full-Text Articles in Physical Sciences and Mathematics

Direct And Reverse Carleson Measure For Hb Spaces, William T. Ross, Alain Blandigneres, Emmanuel Fricain, Frederic Gaunard, Andreas Hartmann Jan 2013

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∞.

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An Extremal Problem For Characteristic Functions, William T. Ross, Isabelle Chalendar, Stephan Ramon Garcia, Dan Timotin Jan 2013

An Extremal Problem For Characteristic Functions, William T. Ross, Isabelle Chalendar, Stephan Ramon Garcia, Dan Timotin

Department of Math & Statistics Faculty Publications

Suppose E is a subset of the unit circle T and H∞C L∞ is the Hardy subalgebra. We examine the problem of Finding the distance from the characteristic function of E to zn H∞. This admits an alternate description as a dual extremal problem. Precise solutions are given in several important cases. The techniques used involve the theory of Toeplitz and Hankel operators as well as the construction of certain conformal mappings.

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An Explicit Bijection Between Semistandard Tableaux And Non-Elliptic Sl3 Webs, Heather M. Russell Jan 2013

An Explicit Bijection Between Semistandard Tableaux And Non-Elliptic Sl3 Webs, Heather M. Russell

Department of Math & Statistics Faculty Publications

The sl3 spider is a diagrammatic category used to study the representation theory of the quantum group Uq(sl3). The morphisms in this category are generated by a basis of non-elliptic webs. Khovanov- Kuperberg observed that non-elliptic webs are indexed by semistandard Young tableaux. They establish this bijection via a recursive growth algorithm. Recently, Tymoczko gave a simple version of this bijection in the case that the tableaux are standard and used it to study rotation and joins of webs. We build on Tymoczko’s bijection to give a simple and explicit algorithm for constructing all …

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Model Spaces: A Survey, William T. Ross, Stephan Ramon Garcia Jan 2013

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.

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A Single-Parameter Model Of The Immune Response To Bacterial Invasion, Lester Caudill Jan 2013

A Single-Parameter Model Of The Immune Response To Bacterial Invasion, Lester Caudill

Department of Math & Statistics Faculty Publications

The human immune response to bacterial pathogens is a remarkably complex process, involving many different cell types, chemical signals, and extensive lines of communication. Mathematical models of this system have become increasingly high-dimensional and complicated, as researchers seek to capture many of the major dynamics. In this paper, we argue that, in some important instances, preference should be given to low-dimensional models of immune response, as opposed to their high-dimensional counterparts. One such model is analyzed and shown to reflect many of the key phenomenological properties of the immune response in humans. Notably, this model includes a single parameter values, …

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