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Articles 1 - 9 of 9
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Truncated Toeplitz Operators On Finite Dimensional Spaces, William T. Ross, Joseph A. Cima, Warren R. Wogen
Truncated Toeplitz Operators On Finite Dimensional Spaces, William T. Ross, Joseph A. Cima, Warren R. Wogen
Department of Math & Statistics Faculty Publications
In this paper, we study the matrix representations of compressions of Toeplitz operators to the finite dimensional model spaces H2ƟBH2, where B is a finite Blaschke product. In particular, we determine necessary and sufficient conditions - in terms of the matrix representation - of when a linear transformation on H2ƟBH2 is the compression of a Toeplitz operator. This result complements a related result of Sarason [6].
Indestructible Blaschke Products, William T. Ross
Indestructible Blaschke Products, William T. Ross
Department of Math & Statistics Faculty Publications
No abstract provided.
Algorithm-Independent Optimal Input Fluxes For Boundary Identification In Thermal Imaging, Kurt Bryan, Lester Caudill
Algorithm-Independent Optimal Input Fluxes For Boundary Identification In Thermal Imaging, Kurt Bryan, Lester Caudill
Department of Math & Statistics Faculty Publications
An inverse boundary determination problem for a parabolic model, arising in thermal imaging, is considered. The focus is on intelligently choosing an effective input heat flux, so as to maximize the practical effectiveness of an inversion algorithm. Three different methods, based on different interpretations of the term “effective", are presented and analyzed, then demonstrated through numerical examples. It is noteworthy that each of these flux-selection methods is independent of the particular inversion algorithm to be used.
The Bar-Natan Skein Module Of The Solid Torus And The Homology Of (N,N) Springer Varieties, Heather M. Russell
The Bar-Natan Skein Module Of The Solid Torus And The Homology Of (N,N) Springer Varieties, Heather M. Russell
Department of Math & Statistics Faculty Publications
This paper establishes an isomorphism between the Bar-Natan skein module of the solid torus with a particular boundary curve system and the homology of the (n, n) Springer variety. The results build on Khovanov's work with crossingless matchings and the cohomology of the (n, n) Springer variety. We also give a formula for comultiplication in the Bar-Natan skein module for this specific three-manifold and boundary curve system.
G-Perfect Nonlinear Functions, James A. Davis, Laurent Poinsot
G-Perfect Nonlinear Functions, James A. Davis, Laurent Poinsot
Department of Math & Statistics Faculty Publications
Perfect nonlinear functions are used to construct DES-like cryptosystems that are resistant to differential attacks. We present generalized DES-like cryptosystems where the XOR operation is replaced by a general group action. The new cryptosystems, when combined with G-perfect nonlinear functions (similar to classical perfect nonlinear functions with one XOR replaced by a general group action), allow us to construct systems resistant to modified differential attacks. The more general setting enables robust cryptosystems with parameters that would not be possible in the classical setting. We construct several examples of G-perfect nonlinear functions, both Z2 -valued and Za …
Length Bias In The Measurements Of Carbon Nanotubes, Paul H. Kvam
Length Bias In The Measurements Of Carbon Nanotubes, Paul H. Kvam
Department of Math & Statistics Faculty Publications
To measure carbon nanotube lengths, atomic force microscopy and special software are used to identify and measure nanotubes on a square grid. Current practice does not include nanotubes that cross the grid, and, as a result, the sample is length-biased. The selection bias model can be demonstrated through Buffon’s needle problem, extended to general curves that more realistically represent the shape of nanotubes observed on a grid. In this article, the nonparametric maximum likelihood estimator is constructed for the length distribution of the nanotubes, and the consequences of the length bias are examined. Probability plots reveal that the corrected length …
Load Sharing Models, Paul H. Kvam, Jye-Chyi Lu
Load Sharing Models, Paul H. Kvam, Jye-Chyi Lu
Department of Math & Statistics Faculty Publications
Consider a system of components whose lifetimes are governed by a probability distribution. Load sharing refers to a model of stochastic interdependency between components that operate within a system. If components are set up in a parallel system (see Parallel, Series, and Series–Parallel Systems) for example, the system survives as long as at least one component is operating. In a typical load-sharing system, once a component fails, the remaining components suffer an increase in failure rate due to the extra “load” they must encumber due to the failed component.
Degradation Models, Suk Joo Bae, Paul H. Kvam
Degradation Models, Suk Joo Bae, Paul H. Kvam
Department of Math & Statistics Faculty Publications
Reliability testing typically generates product lifetime data, but for some tests, covariate information about the wear and tear on the product during the life test can provide additional insight into the product’s lifetime distribution. This usage, or degradation, can be the physical parameters of the product (e.g., corrosion thickness on a metal plate) or merely indicated through product performance (e.g., the luminosity of a light emitting diode). The measurements made across the product’s lifetime are degradation data, and degradation analysis is the statistical tool for providing inference about the lifetime distribution from the degradation data.
Sir Francis Galton, Sandra J. Peart, David M. Levy
Sir Francis Galton, Sandra J. Peart, David M. Levy
Jepson School of Leadership Studies articles, book chapters and other publications
Cousin to Charles Darwin and a talented statistician, Sir Francis Galton had an influence on social science that was profound. His major contributions to mathematical statistics included the initial development of quantiles and linear regression techniques. Along with F. Y. Edgeworth and Karl Pearson, he developed general techniques of multiple regression and correlation analysis, statistical devices that serve as substitutes for experiments in social science. Galton had a major impact on economics, and with W. R. Greg, was instrumental in creating the “science” of eugenics.