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

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

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)

Developing the Improving Post-event Analysis and Communication Together (IMPACT) Tool to Involve Patients and Families in Post-Event Analysis

The analysis of harmful errors is typically led by a team within the hospital and includes clinicians and staff who were involved at the time of the event. However, the patient and family are often left out of this process and are not asked to participate in the investigation. Because little guidance is available for facilitating patient input, an interprofessional team convened to develop a semi-structured tool to be used in eliciting patient feedback. Some 72 persons who had experienced adverse events were interviewed. Using a thematic analysis approach, the team learned that 51% of the interviewees preferred to participate in event analysis directly through an interview and 47% recommended that patients and families should be offered the opportunity to provide their views immediately (within 24-48 hours of the event). The resulting tool, IMPACT, incorporates a conversational flow of questions that allows patients to tell their story, focus their attention on specific causative factors, and give recommendations to improve healthcare in their institutions or to prevent further harm

Increased Usage of Antiseptics Is Associated with Reduced Susceptibility in Clinical Isolates of Staphylococcus aureus

Hospital-acquired infection is a major cause of morbidity and mortality, and regimes to prevent infection are crucial in infection control. These include the decolonization of vulnerable patients with methicillin-resistant Staphylococcus aureus (MRSA) carriage using antiseptics, including chlorhexidine and octenidine. Concern has been raised, however, regarding the possible development of biocide resistance. In this study, we assembled a panel of S. aureus isolates, including isolates collected before the development of chlorhexidine and octenidine and isolates, from a major hospital trust in the United Kingdom during a period when the decolonization regimes were altered. We observed significant increases in the MIC and minimum bactericidal concentration (MBC) of chlorhexidine in isolates from periods of high usage of chlorhexidine. Isolates with increased MICs and MBCs of octenidine rapidly emerged after octenidine was introduced in the trust. There was no apparent cross-resistance between the two biocidal agents. A combination of variable-number tandem repeat (VNTR) analysis, PCR for qac genes, and whole-genome sequencing was used to type isolates and examine possible mechanisms of resistance. There was no expansion of a single strain associated with decreased biocide tolerance, and biocide susceptibility did not correlate with carriage of qac efflux pump genes. Mutations within the NorA or NorB efflux pumps, previously associated with chlorhexidine export, were identified, however, suggesting that this may be an important mechanism of biocide tolerance. We present evidence that isolates are evolving in the face of biocide challenge in patients and that changes in decolonization regimes are reflected in changes in susceptibility of isolates

Fundamental theory of modules over rings

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

Record of forearc devolatilization in low-T, high-P/T metasedimentary suites: Significance for models of convergent margin chemical cycling

[1] The Franciscan Complex (Coast Ranges and Diablo Range, California) and the Western Baja Terrane (WBT; Baja California, Mexico) were metamorphosed along high-P/T paths like those experienced in many active subduction zones, recording peak conditions up to ∼1 GPa and 300°C. Franciscan and WBT metasedimentary rocks are similar in lithology and geochemistry to clastic sediments outboard of many subduction zones. These metamorphic suites provide evidence regarding devolatilization history experienced by subducting sediments, information that is needed to mass-balance the inputs of materials into subduction zones with their respective outputs. Analyzed samples have lower total volatile contents than their likely protoliths. Little variation in LOI among similar lithologies at differing metamorphic grades, suggests that loss of structurally bound water occurred during early clay-mineral transformations. Finely disseminated carbonate is present in the lowest-grade rocks, but absent in all higher-grade rocks. δ13CVPDB of reduced-C is uniform in the lower-grade Franciscan samples (mean = −25.1‰, 1σ = 0.4‰), but varies in higher-grade rocks (−28.8 to −21.9‰). This likely reflects a combination of devolatilization and C-isotope exchange, between organic and carbonate reservoirs. Nitrogen concentration ranges from 102 to 891 ppm, with δ15Nair of +0.1 to +3.0‰ (n = 35); this organic-like δ15N probably represents an efficient transfer of N from decaying organic matter to reacting clay minerals. The lowest-grade rocks in the Coastal Belt have elevated carbonate contents and correlated N-δ15N variations, and exhibit the most uniform δ13C and C/N, all consistent with these rocks having experienced less devolatilization. Most fluid-mobile trace elements are present at concentrations indistinguishable from protoliths. Suggesting that, despite apparent loss of much clay-bound H2O and CO2 from diagenetic cements (combined, <5–10 wt. %), most fluid-mobile trace elements are retained to depths of up to ∼40 km. Organic-like δ15N, lower than that of many seafloor sediments, is consistent with some loss of adsorbed N (perhaps as NO3−) during early stages of diagenesis. The efficient entrainment of fluid-mobile elements to depths of at least 40 km in these relatively cool subduction zone settings lends credence to models invoking transfer of these elements to the subarc mantle

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