Perturbed Three Vortex Dynamics

It is well known that the dynamics of three point vortices moving in an ideal fluid in the plane can be expressed in Hamiltonian form, where the resulting equations of motion are completely integrable in the sense of Liouville and Arnold. The focus of this investigation is on the persistence of regular behavior (especially periodic motion) associated to completely integrable systems for certain (admissible) kinds of Hamiltonian perturbations of the three vortex system in a plane. After a brief survey of the dynamics of the integrable planar three vortex system, it is shown that the admissible class of perturbed systems is broad enough to include three vortices in a half-plane, three coaxial slender vortex rings in three-space, and `restricted' four vortex dynamics in a plane. Included are two basic categories of results for admissible perturbations: (i) general theorems for the persistence of invariant tori and periodic orbits using Kolmogorov-Arnold-Moser and Poincare-Birkhoff type arguments; and (ii) more specific and quantitative conclusions of a classical perturbation theory nature guaranteeing the existence of periodic orbits of the perturbed system close to cycles of the unperturbed system, which occur in abundance near centers. In addition, several numerical simulations are provided to illustrate the validity of the theorems as well as indicating their limitations as manifested by transitions to chaotic dynamics.Comment: 26 pages, 9 figures, submitted to the Journal of Mathematical Physic

Gender and educational leadership in England: a comparison of secondary headteachers' views over time

In the context of gender being a barrier to accessing leadership, this paper presents a comparison of the views of men and women head teacher (principals) of secondary schools in England in the 1990s and in 2004. The same survey instrument was used on both occasions. The perceptions of the head teachers show change in some areas and no change in others. Overall, women are more likely to become head teachers and are now less likely to be categorised into pastoral roles, but in some cases women still meet prejudice from governors and others in the wider community. Women head teachers are more likely to have partners and children than in the 1990s, sharing equally or carrying most of the domestic responsibilities, whereas male colleagues are most likely to have partners who take the majority of responsibility in the home. Essentialist stereotypes about women and men as leaders still prevail, although both the women and men head teachers see themselves as adopting a traditionally ‘feminine’ style of leadership. Women head teachers are likely to see some benefits in being a woman in a role stereotypically associated with men. However, there has been an increase in the proportion of women who feel that they have to prove their worth as a leader, and this may be linked with increased levels of accountability in schools

The differential-algebraic and bi-Hamiltonian integrability analysis of the Riemann type hierarchy revisited

A differential-algebraic approach to studying the Lax type integrability of the generalized Riemann type hydrodynamic hierarchy is revisited, its new Lax type representation and Poisson structures constructed in exact form. The related bi-Hamiltonian integrability and compatible Poissonian structures of the generalized Riemann type hierarchy are also discussed.Comment: 18 page

List Decoding of Matrix-Product Codes from nested codes: an application to Quasi-Cyclic codes

A list decoding algorithm for matrix-product codes is provided when $C_1,..., C_s$ are nested linear codes and $A$ is a non-singular by columns matrix. We estimate the probability of getting more than one codeword as output when the constituent codes are Reed-Solomon codes. We extend this list decoding algorithm for matrix-product codes with polynomial units, which are quasi-cyclic codes. Furthermore, it allows us to consider unique decoding for matrix-product codes with polynomial units

A Memetic Analysis of a Phrase by Beethoven: Calvinian Perspectives on Similarity and Lexicon-Abstraction

This article discusses some general issues arising from the study of similarity in music, both human-conducted and computer-aided, and then progresses to a consideration of similarity relationships between patterns in a phrase by Beethoven, from the first movement of the Piano Sonata in A flat major op. 110 (1821), and various potential memetic precursors. This analysis is followed by a consideration of how the kinds of similarity identified in the Beethoven phrase might be understood in psychological/conceptual and then neurobiological terms, the latter by means of William Calvin’s Hexagonal Cloning Theory. This theory offers a mechanism for the operation of David Cope’s concept of the lexicon, conceived here as a museme allele-class. I conclude by attempting to correlate and map the various spaces within which memetic replication occurs

Early respiratory viral infections in infants with cystic fibrosis

This article is made available for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.Background Viral infections contribute to morbidity in cystic fibrosis (CF), but the impact of respiratory viruses on the development of airway disease is poorly understood. Methods Infants with CF identified by newborn screening were enrolled prior to 4 months of age to participate in a prospective observational study at 4 centers. Clinical data were collected at clinic visits and weekly phone calls. Multiplex PCR assays were performed on nasopharyngeal swabs to detect respiratory viruses during routine visits and when symptomatic. Participants underwent bronchoscopy with bronchoalveolar lavage (BAL) and a subset underwent pulmonary function testing. We present findings through 8.5 months of life. Results Seventy infants were enrolled, mean age 3.1 ± 0.8 months. Rhinovirus was the most prevalent virus (66%), followed by parainfluenza (19%), and coronavirus (16%). Participants had a median of 1.5 viral positive swabs (range 0–10). Past viral infection was associated with elevated neutrophil concentrations and bacterial isolates in BAL fluid, including recovery of classic CF bacterial pathogens. When antibiotics were prescribed for respiratory-related indications, viruses were identified in 52% of those instances. Conclusions Early viral infections were associated with greater neutrophilic inflammation and bacterial pathogens. Early viral infections appear to contribute to initiation of lower airway inflammation in infants with CF. Antibiotics were commonly prescribed in the setting of a viral infection. Future investigations examining longitudinal relationships between viral infections, airway microbiome, and antibiotic use will allow us to elucidate the interplay between these factors in young children with CF

The nonabelian Liouville-Arnold integrability by quadratures problem: a symplectic approach

A symplectic theory approach is devised for solving the problem of algebraic-analytical construction of integral submanifold imbeddings for integrable (via the nonabelian Liouville-Arnold theorem) Hamiltonian systems on canonically symplectic phase spaces

Improved Measurement of the K+ to pi+ nu nubar Branching Ratio

An additional event near the upper kinematic limit for K+ to pi+ nu nubar has been observed by Experiment E949 at Brookhaven National Laboratory. Combining previously reported and new data, the branching ratio is B(K+ to pi+ nu nubar)= 1.47 (+1.30, - 0.89) x 10-10 based on three events observed in the pion momentum region 211<P<229 MeV/c. At the measured central value of the branching ratio, the additional event had a signal-to-background ratio of 0.9

Further Evidence for the Decay K+ to pi+ neutrino-antineutrino

Additional evidence for the rare kaon decay K+ to pi+ neutrino-antineutrino has been found in a new data set with comparable sensitivity to the previously reported result. One new event was observed in the pion momentum region examined, 211<P<229 MeV/c, bringing the total for the combined data set to two. Including all data taken, the backgrounds were estimated to contribute 0.15 pm 0.05 events. The branching ratio is B=1.57^{+1.75}_{-0.82} 10^{-10}.Comment: 10 pages, 2 figure

Looking for the women in Baron and Taylor's (1969) Educational administration and the social sciences

A search for women in Baron and Taylor's (1969) Educational administration and the social sciences [London: The Athlone Press] using feminist poststructural discourse analysis (FPDA) has revealed a changing discourse about gendered educational administration over the course of 50 years. Whilst few women are featured in the text itself, citations of women's writing surface the historical contributions of women as headmistresses and public servants. Women who have cited the text since its publication have challenged gendered theory and academic writing conventions. FPDA is used to explore the gendered educational administration discourse through the intertextuality of academic writing. Fluctuations between powerfulness and powerlessness are revealed depending on the socio-political context and women's circumstances