Orthogonal polynomials on the unit circle and chain sequences

Szego{double acute} has shown that real orthogonal polynomials on the unit circle can be mapped to orthogonal polynomials on the interval [-1,1] by the transformation 2x=z+z-1. In the 80's and 90's Delsarte and Genin showed that real orthogonal polynomials on the unit circle can be mapped to symmetric orthogonal polynomials on the interval [-1,1] using the transformation 2x=z1/2+z-1/2. We extend the results of Delsarte and Genin to all orthogonal polynomials on the unit circle. The transformation maps to functions on [-1,1] that can be seen as extensions of symmetric orthogonal polynomials on [-1,1] satisfying a three-term recurrence formula with real coefficients {cn} and {dn}, where {dn} is also a positive chain sequence. Via the results established, we obtain a characterization for a point w(|w|=1) to be a pure point of the measure involved. We also give a characterization for orthogonal polynomials on the unit circle in terms of the two sequences {cn} and {dn}. © 2013 Elsevier Inc.

Development and validation of the ankle fracture outcome of rehabilitation measure (A-FORM)

Study Design Delphi panel and cohort study. Objective To develop and refine a condition-specific, patient-reported outcome measure, the Ankle Fracture Outcome of Rehabilitation Measure (A-FORM), and to examine its psychometric properties, including factor structure, reliability, and validity, by assessing item fit with the Rasch model. Background To our knowledge, there is no patient-reported outcome measure specific to ankle fracture with a robust content foundation. Methods A 2-stage research design was implemented. First, a Delphi panel that included patients and health professionals developed the items and refined the item wording. Second, a cohort study (n = 45) with 2 assessment points was conducted to permit preliminary maximum-likelihood exploratory factor analysis and Rasch analysis. Results The Delphi panel reached consensus on 53 potential items that were carried forward to the cohort phase. From the 2 time points, 81 questionnaires were completed and analyzed; 38 potential items were eliminated on account of greater than 10% missing data, factor loadings, and uniqueness. The 15 unidimensional items retained in the scale demonstrated appropriate person and item reliability after (and before) removal of 1 item (anxious about footwear) that had a higher-than-ideal outfit statistic (1.75). The “anxious about footwear” item was retained in the instrument, but only the 14 items with acceptable infit and outfit statistics (range, 0.5–1.5) were included in the summary score. Conclusion This investigation developed and refined the A-FORM (Version 1.0). The A-FORM items demonstrated favorable psychometric properties and are suitable for conversion to a single summary score. Further studies utilizing the A-FORM instrument are warranted. J Orthop Sports Phys Ther 2014;44(7):488–499. Epub 22 May 2014. doi:10.2519/jospt.2014.4980

Challenges of managing medications for older people at transition points of care

In clinical practice, pharmacists play a very important role in identifying and correcting medication discrepancies as older patients move across transition points of care. With increasing complexity of health care needs of older people, these discrepancies are likely to increase. The major concern with identifying and correcting medication discrepancies is that medication reconciliation is considered a retrospective problem – that is, dealing with medication discrepancies after they have occurred. It is argued here that a more proactive stance should be taken where doctors, nurses and pharmacists collectively work together to prevent medication discrepancies from happening in the first place. Improved involvement of patients and family members will help to facilitate better management of medications across transition points of care. Efficient use of information technology aids, such as electronic medication reconciliation tools, should also assist with organizational systems problems associated with the working culture, heavy workloads, and staff and skill mix of health professionals.

POINTS OF VIEW: Multi-Roling Performance in Ireland in the 1990s, Part 1 (Layering)

This series of posts will consider the acting techniques required for this style of performance with reference to four productions from the 1990s in which two actors took on multiple roles: Frank Pig Says Hello (1992), Co-Motion’s stage adaptation of Pat McCabe’s novel; The Butcher Boy, Corca Dorca’s production of Disco Pigs (1996) by Enda Walsh; DubbleJoint’s production of Stones in his Pockets by Marie Jones (1996) and its subsequent award-winning revival which I produced at Belfast’s Lyric Theatre in 1999; and Kabosh’s production of Mojo Mickybo by Owen McCafferty (1998). The discussion will focus primarily on my own empirical exploration of the demands multi-roling places on an actor through the direction of recent revivals of Mojo Mickybo for Belfast’s Chatterbox Theatre Company (2013) and Bedlam Productions (2015).

POINTS OF VIEW: Multi-Roling Performance in Ireland in the 1990s, Part 2 (Characterisation)

The 1990s in Ireland saw a series of highly successful theatre productions in which actors played a multiplicity of roles. This has often been attributed to the economic exigencies of the times, but it also depended on the availability of flexible actors with the physical and psychological capacity to embody a wide range of identifiable characters within the one production.

This second of two posts considers the acting techniques required for this style of performance in relation to the differentiation of one character from another. The discussion will focus primarily on my own empirical exploration of the demands multi-roling places on an actor through the direction of recent revivals of Mojo Mickybo for Belfast’s Chatterbox Theatre Company (2013) and Bedlam Productions (2015).

Calculating Flash Point Numbers from Molecular Structure: An Improved Method for Predicting the Flash Points of Acyclic Alkanes

We report a novel method for calculating flash points of acyclic alkanes from flash point numbers, N(FP), which can be calculated from experimental or calculated boiling point numbers (Y(BP)) with the equation N(FP) = 1.020Y(BP) - 1.083 Flash points (FP) are then determined from the relationship FP(K) = 23.369N(FP)(2/3) + 20.010N(FP)(1/3) + 31.901 For it data set of 102 linear and branched alkanes, the correlation of literature and predicted flash points has R(2) = 0.985 and an average absolute deviation of 3.38 K. N(FP) values can also be estimated directly from molecular structure to produce an even closer correspondence of literature and predicted FP values. Furthermore, N(FP) values provide a new method to evaluate the reliability of literature flash point data.

Simple Method to Evaluate and to Predict Flash Points of Organic Compounds

Flash points (T(FP)) of organic compounds are calculated from their flash point numbers, N(FP), with the relationship T(FP) = 23.369N(FP)(2/3) + 20.010N(FP)(1/3) + 31.901. In turn, the N(FP) values can be predicted from boiling point numbers (Y(BP)) and functional group counts with the equation N(FP) = 0.974Y(BP) + Sigma(i)n(i)G(i) + 0.095 where G(i) is a functional group-specific contribution to the value of N(FP) and n(i) is the number of such functional groups in the structure. For a data set consisting of 1000 diverse organic compounds, the average absolute deviation between reported and predicted flash points was less than 2.5 K.

A Simple Method to Evaluate, Correlate and Predict Boiling and Flash Points of Alkynes

Boiling points (T-B) of acyclic alkynes are predicted from their boiling point numbers (Y-BP) with the relationship T-B(K) = -16.802Y(BP)(2/3) + 337.377Y(BP)(1/3) - 437.883. In turn, Y-BP values are calculated from structure using the equation Y-BP = 1.726 + A(i) + 2.779C + 1.716M(3) + 1.564M + 4.204E(3) + 3.905E + 5.007P - 0.329D + 0.241G + 0.479V + 0.967T + 0.574S. Here A(i) depends on the substitution pattern of the alkyne and the remainder of the equation is the same as that reported earlier for alkanes. For a data set consisting of 76 acyclic alkynes, the correlation of predicted and literature T-B values had an average absolute deviation of 1.46 K, and the R-2 of the correlation was 0.999. In addition, the calculated Y-BP values can be used to predict the flash points of alkynes.

Validation of the MEASURE automobile emissions model : a statistical analysis

The Mobile Emissions Assessment System for Urban and Regional Evaluation (MEASURE) model provides an external validation capability for hot stabilized option; the model is one of several new modal emissions models designed to predict hot stabilized emission rates for various motor vehicle groups as a function of the conditions under which the vehicles are operating. The validation of aggregate measurements, such as speed and acceleration profile, is performed on an independent data set using three statistical criteria. The MEASURE algorithms have proved to provide significant improvements in both average emission estimates and explanatory power over some earlier models for pollutants across almost every operating cycle tested.

An extended measure of work-life balance culture : development and confirmation of the measure

This paper extends the work of Thompson, Beauvais and Lyness (1999) to develop a more comprehensive measure of work-life balance culture. Thompson et al. developed a survey based on three sub-dimensions which examine work-family culture. We have extended this to incorporate extra dimensions, and to broaden the measure to encompass life aspects beyond the family. Two studies were conducted in order to test and refine the measure. Over 700 participants in the first study completed the survey, and the Confirmatory Factor Analysis results show that the extended measure is robust. Further, a second study with a sample of 629 participants confirmed the general measure, with slight adaptations. The results are discussed in relation to the use of the measure for work-life balance research.

Points of convergence and divergence : normative, institutional and operational relationships between R2P and POC

As an international norm, the Responsibility to Protect (R2P) has gained substantial influence and institutional presence—and created no small controversy—in the ten years since its first conceptualisation. Conversely, the Protection of Civilians in Armed Conflict (PoC) has a longer pedigree and enjoys a less contested reputation. Yet UN Security Council action in Libya in 2011 has thrown into sharp relief the relationship between the two. UN Security Council Resolutions 1970 and 1973 follow exactly the process envisaged by R2P in response to imminent atrocity crimes, yet the operative paragraphs of the resolutions themselves invoke only PoC. This article argues that, while the agendas of PoC and R2P converge with respect to Security Council action in cases like Libya, outside this narrow context it is important to keep the two norms distinct. Peacekeepers, humanitarian actors, international lawyers, individual states and regional organisations are required to act differently with respect to the separate agendas and contexts covered by R2P and PoC. While overlap between the two does occur in highly visible cases like Libya, neither R2P nor PoC collapses normatively, institutionally or operationally into the other.