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Articles 1 - 7 of 7
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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.
Prolongations And Cyclic Vectors, William T. Ross, Harold S. Shapiro
Prolongations And Cyclic Vectors, William T. Ross, Harold S. Shapiro
Department of Math & Statistics Faculty Publications
For functions belonging to invariant subspaces of the backward shift operator Bf = (f − f(0))/z on spaces of analytic functions on the unit disk D, we explore, in a systematic way, the continuation properties of these functions.
Zeros Of Functions With Finite Dirichlet Integral, William T. Ross, Stefan Richter, Carl Sundberg
Zeros Of Functions With Finite Dirichlet Integral, William T. Ross, Stefan Richter, Carl Sundberg
Department of Math & Statistics Faculty Publications
In this paper, we refine a result of Nagel, Rudin, and Shapiro (1982) concerning the zeros of holomorphic functions on the unit disk with finite Dirichlet integral.
Common Cyclic Vectors For Normal Operators, William T. Ross, Warren R. Wogen
Common Cyclic Vectors For Normal Operators, William T. Ross, Warren R. Wogen
Department of Math & Statistics Faculty Publications
If μis a finite compactly supported measure on C, then the set Sμ of multiplication operators Mᵩ : L2 (μ) --> L2 (μ), Mᵩ f = ᵩ f, where ᵩ ϵ L ∞ (μ) is injective on a set of full μ measure, is the complete set of cyclic multiplication operators on L2 (μ) In this paper, we explore the question as to whether or not Sμ has a common cyclic vector
The Backward Shift On The Space Of Chauchy Transforms, William T. Ross, Joseph A. Cima, Alec L. Matheson
The Backward Shift On The Space Of Chauchy Transforms, William T. Ross, Joseph A. Cima, Alec L. Matheson
Department of Math & Statistics Faculty Publications
This note examines the subspaces of the space of Cauchy transforms of measures on the unit circle that are invariant under the backward shift operator f --> z-1 (f—f (0)). We examine this question when the space of Cauchy transforms is endowed with both the norm and weak* topologies.
Reliability Estimation Based On System Data With An Unknown Load Share Rule, Hyoungtae Kim, Paul H. Kvam
Reliability Estimation Based On System Data With An Unknown Load Share Rule, Hyoungtae Kim, Paul H. Kvam
Department of Math & Statistics Faculty Publications
We consider a multicomponent load-sharing system in which the failure rate of a given component depends on the set of working components at any given time. Such systems can arise in software reliability models and in multivariate failure-time models in biostatistics, for example. A load-share rule dictates how stress or load is redistributed to the surviving components after a component fails within the system. In this paper, we assume the load share rule is unknown and derive methods for statistical inference on load-share parameters based on maximum likelihood. Components with (individual) constant failure rates are observed in two environments: (1) …
A Nonlinear Random Coefficients Model For Degradation Testing, Suk Joo Bae, Paul H. Kvam
A Nonlinear Random Coefficients Model For Degradation Testing, Suk Joo Bae, Paul H. Kvam
Department of Math & Statistics Faculty Publications
As an alternative to traditional life testing, degradation tests can be effective in assessing product reliability when measurements of degradation leading to failure can be observed. This article presents a degradation model for highly reliable light displays, such as plasma display panels and vacuum fluorescent displays (VFDs). Standard degradation models fail to capture the burn-in characteristics of VFDs, when emitted light actually increases up to a certain point in time before it decreases (or degrades) continuously. Random coefficients are used to model this phenomenon in a nonlinear way, which allows for a nonmonotonic degradation path. In many situations, the relative …