Algebras of truncated Toeplitz operators

We find necessary and sufficient conditions for the product of two truncated Toeplitz operators on a model space to itself be a truncated Toeplitz operator, and as a result find a characterization for the maximal algebras of bounded truncated Toeplitz operators.Comment: 20 pages, one minor correction made 11/18/10 to the proof of Prop. 6.1 (1

Properties of truncated Toeplitz operators

We discuss the multiplication of truncated Toeplitz operators: or TTOs) on backward shift invariant subspaces of the Hardy space of the unit disc. Specifically we discuss when the product of two TTOs is itself a TTO, finding an equivalent to a similar result of Brown and Halmos for ordinary Toeplitz operators. This leads us to investigate the commutants of certain rank-one perturbations of the compressed shift operator, deriving a symbol calculus for TTOs, as well as several other results

Building better working relationships between high school library media specialists and school technology coordinators

The impetus for this study came from numerous conversations regarding the frustrations colleagues had when communicating with their technology coordinators and/or technology services. In many ways, technology and technology-integration within school media centers are just as important these days as traditional curriculum and teachings. Embracing this fact is essential to a successful school library media program, especially those programs whose main goal is to produce the next generation of information-literate, lifelong learners. By analyzing the results and open-ended responses of a survey presented to New Jersey high school library media specialists, guidelines were proposed on how to establish and maintain a better working relationship between the school library media specialist and the technology coordinator

Constitutional Law - Fifth Amendment - Due Process - Equal Protection - Sex Discrimination

The United States Supreme Court has held that enactment of a male-only draft registration requirement does not violate the equal protection component of the fifth amendment due process clause. Rostker v. Goldberg, 453 U.S. 57 (1981)

Fundamental theory of modules over rings

Any subsequent statements pertaining to modules also apply to abelian groups and general rings when interpreted

Equality of bond percolation critical exponents for pairs of dual lattices

For a certain class of two-dimensional lattices, lattice-dual pairs are shown to have the same bond percolation critical exponents. A computational proof is given for the martini lattice and its dual to illustrate the method. The result is generalized to a class of lattices that allows the equality of bond percolation critical exponents for lattice-dual pairs to be concluded without performing the computations. The proof uses the substitution method, which involves stochastic ordering of probability measures on partially ordered sets. As a consequence, there is an infinite collection of infinite sets of two-dimensional lattices, such that all lattices in a set have the same critical exponents.Comment: 10 pages, 7 figure

Lifting the Heavy Vocal Load: SLPs and Their Vocal Habits

Novice speech-language pathologists (SLPs) are a vulnerable population that is at-risk for dysphonia. Previous literature has highlighted the high vocal-demand occupations of teaching and entertaining but there is minimal research to understand the prevalence of dysphonia in SLPs. The purpose of this investigation was to determine the prevalence of vocal fatigue and vocal loading in novice SLPs in western Kentucky to increase awareness of the vulnerability for dysphonia in this population. This investigation was descriptive in nature using a survey format and was sent to SLPs in the western Kentucky region. A total of 21 SLPs responded to the survey. Results indicated that while novice SLPs in western Kentucky are at risk for vocal fatigue, vocal loading, and dysphonia, these SLPs often do not prescribe to the same recommendations and strategies provided to clients with dysphonia. This investigation adds to the growing body of literature regarding the prevalence of dysphonia in SLPs

The critical manifolds of inhomogeneous bond percolation on bow-tie and checkerboard lattices

We give a conditional derivation of the inhomogeneous critical percolation manifold of the bow-tie lattice with five different probabilities, a problem that does not appear at first to fall into any known solvable class. Although our argument is mathematically rigorous only on a region of the manifold, we conjecture that the formula is correct over its entire domain, and we provide a non-rigorous argument for this that employs the negative probability regime of the triangular lattice critical surface. We discuss how the rigorous portion of our result substantially broadens the range of lattices in the solvable class to include certain inhomogeneous and asymmetric bow-tie lattices, and that, if it could be put on a firm foundation, the negative probability portion of our method would extend this class to many further systems, including F Y Wu’s checkerboard formula for the square lattice. We conclude by showing that this latter problem can in fact be proved using a recent result of Grimmett and Manolescu for isoradial graphs, lending strong evidence in favor of our other conjectured results. This article is part of ‘Lattice models and integrability’, a special issue of Journal of Physics A: Mathematical and Theoretical in honour of F Y Wu's 80th birthday.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/98528/1/1751-8121_45_49_494005.pd

Development and testing of the Stakeholder Quality Improvement Perspectives Survey (SQuIPS)

BACKGROUND: To create a theory-informed survey that quality improvement (QI) teams can use to understand stakeholder perceptions of an intervention. METHOD: We created the survey then performed a cross-sectional survey of QI stakeholders of three QI projects. The projects sought to: (1) reduce unplanned extubations in a neonatal intensive care unit; (2) maintain normothermia during colorectal surgery and (3) reduce specimen processing errors for ambulatory gastroenterology procedures. We report frequencies of responses to survey items, results of exploratory factor analysis, and how QI team leaders used the results. RESULTS: Overall we received surveys from 319 out of 386 eligible stakeholders (83% response rate, range for the three QI projects 57%-86%). The QI teams found that the survey results confirmed existing concerns (eg, the intervention would not make work easier) and revealed unforeseen concerns such as lack of consensus about the overall purpose of the intervention and its importance. The results of our factor analysis indicate that one 7-item scale (Cronbach\u27s alpha 0.9) can efficiently measure important aspects of stakeholder perceptions, and that two additional Likert-type items could add valuable information for leaders. Two QI team leaders made changes to their project based on survey responses that indicated the intervention made stakeholders\u27 jobs harder, and that there was no consensus about the purpose of the intervention. CONCLUSIONS: The Stakeholder Quality Improvement Perspectives Survey was feasible for QI teams to use, and identified stakeholder perspectives about QI interventions that leaders used to alter their QI interventions to potentially increase the likelihood of stakeholder acceptance of the intervention

Single-locus species delimitation: a test of the mixed Yule–coalescent model, withan empirical application to Philippine round-leaf bats

Prospects for a comprehensive inventory of global biodiversity would be greatly improved by automating methods of species delimitation. The general mixed Yule–coalescent (GMYC) was recently proposed as a potential means of increasing the rate of biodiversity exploration. We tested this method with simulated data and applied it to a group of poorly known bats (Hipposideros) from the Philippines. We then used echolocation call characteristics to evaluate the plausibility of species boundaries suggested by GMYC. In our simulations, GMYC performed relatively well (errors in estimated species diversity less than 25%) when the product of the haploid effective population size (Ne) and speciation rate (SR; per lineage per million years) was less than or equal to 105 , while interspecific variation in Ne was twofold or less. However, at higher but also biologically relevant values of Ne SR and when Ne varied tenfold among species, performance was very poor. GMYC analyses of mitochondrial DNA sequences from Philippine Hipposideros suggest actual diversity may be approximately twice the current estimate, and available echolocation call data are mostly consistent with GMYC delimitations. In conclusion, we consider the GMYC model useful under some conditions, but additional information on Ne, SR and/or corroboration from independent character data are needed to allow meaningful interpretation of results