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Articles 1 - 7 of 7
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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.
C*-Algebras Generated By Truncated Toeplitz Operators, William T. Ross, Stephan Ramon Garcia, Warren R. Wogen
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.
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.
Promoting Reu Participation From Students In Underrepresented Groups, Heather M. Russell, Heather A. Dye
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, Jeremy Lecrone
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.
Statistical Analysis Of The Variability And Reliability Of Eye-Tracking Test In Measuring Mild Traumatic Brain Injury, Xi He
Honors Theses
Saccadic eye-tracking tests have been advocated as a useful tool to distinguish mTBI patients from healthy people. However, intra-individual variances sometimes interfere with the interpretation of eye-tracking results, especially in experiments when group size is restricted. This study analyzes eye-tracking results of 14 mTBI patients taking the test twice with no medical administration in between. Using more accurate models to fit each individual's result, variables such as asymptote (of the fit functions) and hypothetical values for peak velocity, peak acceleration, and duration are derived for variability analysis. We conclude that the asymptotes for peak velocity and peak acceleration are the …